Dissertations / Theses: 'Quantum trajectorie'

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ALBARELLI, FRANCESCO. "CONTINUOUS MEASUREMENTS AND NONCLASSICALITY AS RESOURCES FOR QUANTUM TECHNOLOGIES." Doctoral thesis, Università degli Studi di Milano, 2018. http://hdl.handle.net/2434/602166.

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This PhD thesis contains results about two different main topics. The first part deals with the application of continuously monitored quantum systems to high precision quantum metrology. A continuous in time measurement on a quantum system is a kind indirect measurement, which only weakly perturbs the system and leaves room for it to evolve under its dynamics. This time-continuous measurement allows one to collect information about some interesting parameter characterizing the dynamics. In this thesis we show how to apply the theory of quantum parameter estimation to continuously monitored quantum systems. In particular, we study the estimation of a magnetic field applied to an ensemble of two level atoms; we show that by continuously monitoring the system we can obtain a quadratic scaling of the precision with the number of atoms, in two different physical settings (dynamically generated entanglement or initial entanglement). In the second part we study different aspects of nonclassicality of continuous variable quantum systems (bosonic degree of freedoms). They can be described by distributions (in particular, the Wigner function) on a classical phase space, which however can take negative values, the hallmark of nonclassicality. In this context, states with a Gaussian distribution are very useful and very well studied; however, on a fundamental level they must be considered classical. We present several studies connected to the vast topic of non-Gaussian states, starting from an application to parameter estimation, as a link to the first part. We study the relationships between anharmonic Hamiltonians and the nonclassicality of their ground states; we also explore the connection between a quantum effect called `backflow of probability' and the negativity of the Wigner function. We end by showing that quantum operations made out of Gaussian building blocks give rise to a well-defined resource theory of Wigner negativity and non-Gaussianity.

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Campagne-Ibarcq, Philippe. "Quantum backaction and feedback in superconducting circuits." Thesis, Paris, Ecole normale supérieure, 2015. http://www.theses.fr/2015ENSU0011/document.

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Cette thèse décrit une série d’expériences mettant en lumière l’action en retour de la mesure et la décohérence pour un système quantique ouvert élémentaire, le qubit supraconducteur. Ces observations sont rendues possibles grâce au développement récent d’amplificateurs Josephson proches de la limite quantique. L’information extraite du système peut être utilisée dans des boucles de rétroaction quantique. Pour stabiliser un état arbitraire prédéterminé du qubit, une mesure projective est réalisée périodiquement et une boucle de rétroaction permet de corriger les erreurs détectées. En se substituant à l'environnement et en réalisant une mesure hétérodyne continue de la fluorescence du qubit, nous reconstituons des trajectoires quantiques individuelles lors de sa relaxation. En conditionnant cette détection au résultat d'une mesure projective postérieure, nous déterminons les weak values du signal de fluorescence. En formant une boucle de rétroaction continue à partir de ce signal, nous stabilisons également un état arbitraire du qubit. Enfin, nous observons dans une dernière expérience la dynamique quantique Zénon d'un mode micro-onde, induite par son couplage au qubit
This thesis presents a series of experiments highlighting measurement back action and decoherence in a basic open quantum system, the superconducting qubit. These observations are enabled by recent advances in amplification close to the quantum limit using Josephson circuits. The information extracted from the system can then be used as input in quantum feedback. A stroboscopic projective readout is performed and a feedback loop is used to correct for detected errors, thus stabilizing an arbitrary predetermined state of the qubit. When monitoring continuously the environment of the qubit by heterodyne detection of its fluorescence, we reconstruct individual quantum trajectories during relaxation. Conditioning this detection to the outcome of a following projective measurement, we access the weak values of the fluorescence signal. Included in a continuous feedback loop, this detection is also used to stabilize an arbitrary state of the qubit. Finally, a last experiment witnesses quantum Zeno dynamics of a resonant microwave mode, entailed by its coupling to the qubit

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Benoist, Tristan. "Open quantum systems and quantum stochastic processes." Thesis, Paris, Ecole normale supérieure, 2014. http://www.theses.fr/2014ENSU0006/document.

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De nombreux phénomènes de physique quantique ne peuvent être compris que par l'analyse des systèmes ouverts. Un appareil de mesure, par exemple, est un système macroscopique en contact avec un système quantique. Ainsi, tout modèle d'expérience doit prendre en compte les dynamiques propres aux systèmes ouverts. Ces dynamiques peuvent être complexes : l'interaction du système avec son environnement peut modifier ses propriétés, l'interaction peu créer des effets de mémoire dans l'évolution du système, . . . Ces dynamiques sont particulièrement importantes dans l'étude des expériences d'optique quantique. Nous sommes aujourd'hui capables de manipuler individuellement des particules. Pour cela la compréhension et le contrôle de l'influence de l'environnement est crucial. Dans cette thèse nous étudions d'un point de vue théorique quelques procédures communément utilisées en optique quantique. Avant la présentation de nos résultats, nous introduisons et motivons l'utilisation de la description markovienne des systèmes quantiques ouverts. Nous présentons a la fois les équations maîtresses et le calcul stochastique quantique. Nous introduisons ensuite la notion de trajectoire quantique pour la description des mesures indirectes continues. C'est dans ce contexte que l'on présente les résultats obtenus au cours de cette thèse. Dans un premier temps, nous étudions la convergence des mesures non destructives. Nous montrons qu'elles reproduisent la réduction du paquet d'onde du système mesuré. Nous montrons que cette convergence est exponentielle avec un taux fixe. Nous bornons le temps moyen de convergence. Dans ce cadre, en utilisant les techniques de changement de mesure par martingale, nous obtenons la limite continue des trajectoires quantiques discrètes. Dans un second temps, nous étudions l'influence de l'enregistrement des résultats de mesure sur la préparation d'état par ingénierie de réservoir. Nous montrons que l'enregistrement des résultats de mesure n'a pas d'influence sur la convergence proprement dite. Cependant, nous trouvons que l'enregistrement des résultats de mesure modifie le comportement du système avant la convergence. Nous retrouvons une convergence exponentielle avec un taux équivalent au taux sans enregistrement. Mais nous trouvons aussi un nouveau taux de convergence correspondant a une stabilité asymptotique. Ce dernier taux est interprété comme une mesure non destructive ajoutée. Ainsi l'état du système ne converge qu'après un temps aléatoire. A partir de ce temps la convergence peut être bien plus rapide. Nous obtenons aussi une borne sur le temps moyen de convergence
Many quantum physics phenomena can only be understood in the context of open system analysis. For example a measurement apparatus is a macroscopic system in contact with a quantum system. Therefore any experiment model needs to take into account open system behaviors. These behaviors can be complex: the interaction of the system with its environment might modify its properties, the interaction may induce memory effects in the system evolution, ... These dynamics are particularly important when studying quantum optic experiments. We are now able to manipulate individual particles. Understanding and controlling the environment influence is therefore crucial. In this thesis we investigate at a theoretical level some commonly used quantum optic procedures. Before the presentation of our results, we introduce and motivate the Markovian approach to open quantum systems. We present both the usual master equation and quantum stochastic calculus. We then introduce the notion of quantum trajectory for the description of continuous indirect measurements. It is in this context that we present the results obtained during this thesis. First, we study the convergence of non demolition measurements. We show that they reproduce the system wave function collapse. We show that this convergence is exponential with a fixed rate. We bound the mean convergence time. In this context, we obtain the continuous time limit of discrete quantum trajectories using martingale change of measure techniques. Second, we investigate the influence of measurement outcome recording on state preparation using reservoir engineering techniques. We show that measurement outcome recording does not influence the convergence itself. Nevertheless, we find that measurement outcome recording modifies the system behavior before the convergence. We recover an exponential convergence with a rate equivalent to the rate without measurement outcome recording. But we also find a new convergence rate corresponding to an asymptotic stability. This last rate is interpreted as an added non demolition measurement. Hence, the system state converges only after a random time. At this time the convergence can be much faster. We also find a bound on the mean convergence time

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Weber, Steven Joseph. "Quantum Trajectories of a Superconducting Qubit." Thesis, University of California, Berkeley, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3686046.

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In quantum mechanics, the process of measurement is intrinsically probabilistic. As a result, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. An accurate measurement record documents this stochastic evolution and can be used to reconstruct the quantum trajectory of the system state in a single experimental iteration. We use weak measurements to track the individual quantum trajectories of a superconducting qubit that evolves under the competing influences of continuous weak measurement and Rabi drive. We analyze large ensembles of such trajectories to examine their characteristics and determine their statistical properties. For example, by considering only the subset of trajectories that evolve between any chosen initial and final states, we can deduce the most probable path through quantum state space. Our investigation reveals the rich interplay between measurement dynamics, typically associated with wavefunction collapse, and unitary evolution. Our results provide insight into the dynamics of open quantum systems and may enable new methods of quantum state tomography, quantum state steering through measurement, and active quantum control.

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Warszawski, Prahlad. "Quantum Trajectories For, and As, Understanding." Thesis, University of Sydney, 2020. https://hdl.handle.net/2123/24237.

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Quantum trajectories provide a fundamental description of the measurement of individual quantum systems. As such, they have wide impact, and application, in the emerging field of quantum technology. Importantly, they also give a mechanism for developing our understanding of the nature of quantum mechanics. In Part I of this thesis, we develop and apply quantum trajectory methods, with a focus upon experimentally relevant optomechanical systems. By solving the stochastic master equation for sufficiently simple bosonic systems, and subsequently finding the positive operator-valued measure (POVM), we are able to conduct a detailed study of the use of parametric amplification for quantum state tomography of nonclassical optomechanical states of motion. Homodyne tomography is a cornerstone experimental tool, and an analysis of its convergence is carried out in the presence of realistic imperfections. We complete Part I by conducting a detailed preparatory analysis of superfluid optomechanical systems possessing vorticity. Part II of this thesis investigates the correspondence between open classical and open quantum systems. We prove a result shows that open quantum systems are, in general, harder to track than open classical systems. We couch this result in terms of physically realisable ensembles (PREs), which can describe the dynamics of a monitored, $D$-dimensional, quantum system obeying a master equation that has reached equilibrium. Associated with the PRE is a measurement scheme that leads to quantum trajectories in which the system evolution consists purely of jumps between the states that are members of the PRE. The occupation of the $K$, generally non-orthogonal, states in the ensemble can be used to track the system. The number of states in the ensemble, $K$, represents the amount of memory that is required to do so. In comparison, a classical $D$-dimensional system requires occupation of the $D$ states to be tracked. After first developing analysis tools that make feasible the discovery of PREs in $D>2$, we prove our main result that there are quantum systems that have a minimal sized PRE with $K>D$.

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Avanzini, Francesco. "Quantum molecular trajectory and stochastic theories of quantum fluctuations." Doctoral thesis, Università degli studi di Padova, 2017. http://hdl.handle.net/11577/3424724.

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Bohm theory is a formulation of Quantum Mechanics that characterises the state of a quantum system according to both the wave function, as in the conventional formulation, and the coordinates (positions) of all the particles that evolve in time drawing quantum continuous trajectories. Furthermore, a statistical ensemble of all the possible trajectories, raising from the impossibility to know the initial position of all the particles, establishes the exact correspondence with the traditional Quantum Mechanics. From a computational point of view, Bohm theory has found many applications in Chemical Physics especially to develop new methodologies for solving the Schrödinger equation and to address semi-classical approximations of Quantum Mechanics. From a theoretical point of view, the most appealing feature of Bohm theory is its capability to supply a conceptual map between the quantum formalism and our representation of what a chemical system is. Chemical systems are composed of molecules, but the same idea of molecule requires a specific arrangement in the space of particles, i.e., the nuclei of the atoms. The statistical description of conventional Quantum Mechanics on the basis of wave function alone is insufficient to establish a clear correspondence with such a picture of molecules. Indeed, chemists employ usually Classical Mechanics in order to overcome this drawback of the standard quantum theory. On the other hand, if the particles position is included in the quantum formalism, as Bohm theory does, the map can be defined in a self-consistent way. In other words, Bohm theory appears to be the suitable quantum framework to represent molecules and their motion. The chemical representation of molecular systems finds a natural correspondence with a single Bohm trajectory, since it is always implicitly assumed that molecular components have specific spatial position independently of our knowledge about it. Consequently, we develop a quantum method whose fundamental assumption is that a single Bohm trajectory, i.e., a quantum molecular trajectory, describes the molecular systems and the molecular motion correctly. First of all, we examine the correspondence between a single Bohm trajectory and the conventional Quantum Mechanics, without using the ensemble of trajectories. We verify that such a correspondence exists through numerical simulations and we prove formally that the statistical properties of a single Bohm trajectory explain the probabilistic description of Quantum Mechanics. Once the consistency of this original approach has been established, we investigate the predicted properties. For instance, we take into account the constants of motion (such as the energy) corresponding to the time evolution of the coordinates and the behaviour of simple chemical systems, e.g., the vibrational motion of single molecules interacting with a resonant field. In this way, unexpected features of the molecular motion are found. Secondly, we tackle the challenge of describing many components systems (like the chemical systems in ordinary conditions). As a matter of fact, the computation of the Bohm trajectory and of the wave function is extremely demanding. However, the statistical properties of the Bohm trajectory allow the derivation of stochastic theories for examining the dynamics of open quantum systems, i.e., few molecules (or few degrees of freedom) interacting with their environment (the other molecules). One of the developed stochastic methods correlates the dynamics of the reduced density matrix, for the degrees of freedom of interest, to the evolution of the corresponding Bohm coordinates. In other words, the Bohm equation, determining the set of all the particles velocities according to the full wave function, is replaced with a stochastic one that approximates the velocity of a subset of coordinates according to the reduced density matrix. In such a way, the quantum fluctuations induced by the environment are taken into account. The advantage of this method concerns its capability of describing quantum systems, including open quantum systems, in terms of a quantum trajectory. This could allow the understanding of the molecular motion during a spectroscopical experiment. The possibility of investigating reactive systems, such as conformational changes, is particularly interesting. As a matter of fact, chemical reactions can be completely characterised only through the particles motion and we define the suit- able quantum methodology providing a self-consistent description of the molecular motion.
La teoria di Bohm è una formulazione della Meccanica Quantistica che caratterizza lo stato di un sistema quantistico attraverso sia la funzione d’onda, come la teoria standard, sia le coordinate (le posizioni) di tutte le particelle che evolvono nel tempo secondo traiettorie quantistiche continue. Inoltre, un ensemble statistico di tutte le possibile traiettorie, che deriva dall’impossibilità di conoscere la posizione iniziale di tutte le particelle, stabilisce l’esatta corrispondenza con la Meccanica Quantistica tradizionale. Da un punto di vista computazionale, la teoria di Bohm è stata impiegata in Chimica Fisica principalmente per sviluppare nuove strategie risolutive dell’equazione di Schrödinger o nuove approssimazioni semi-classiche della Meccanica Quantistica. Da un punto di vista teorico, la caratteristica più attraente della teoria di Bohm è quella di essere il contesto naturale per definire un mappa concettuale tra il formalismo quantistico e la nostra rappresentazione dei sistemi chimici. I sistemi chimici sono composti di molecole, ma l’idea stessa di molecola è associata ad una specifica posizione spaziale delle particelle, i.e., i nuclei degli atomi. La descrizione statistica della Meccanica Quantistica convenzionale, sulla base della sola funzione d’onda, è insufficiente per definire una chiara corrispondenza con questa immagine delle molecole. Infatti, i chimici fanno spesso affidamento alla Meccanica Classica per aggirare questa difficoltà della teoria quantistica standard. Tuttavia, se la posizione delle particelle è inclusa nel formalismo quantistico, così come fa la teoria di Bohm, la corrispondenza può essere definita in modo autoconsistente. In altre parole, la teoria di Bohm sembra essere il contesto formale idoneo per rappresentare quantisticamente le molecole e il loro moto. Comunque, la raffigurazione chimica dei sistemi molecolari corrisponde ad una singola traiettoria di Bohm dato che si assume implicitamente che i componenti delle molecole abbiano una specifica posizione spaziale indipendentemente dal fatto che essa sia nota o meno. Di conseguenza, si è sviluppata una metodologia quantistica che si basa sull’assunzione che una singola traiettoria di Bohm, cioè una traiettoria molecolare quantistica, descrive correttamente i sistemi molecolari e il moto molecolare. In primo luogo, viene esaminata la corrispondenza tra una singola traiettoria di Bohm e la Meccanica Quantistica convenzionale dato che si rinuncia all’ensemble di traiettorie. Si verifica che tale corrispondenza esiste attraverso un esperimento numerico e si dimostra formalmente che le proprietà statistiche di una singola traiettoria spiegano la descrizione probabilistica della Meccanica Quantistica. Una volta che la coerenza di questa metodologia è stata verificata, vengono esaminate accuratamente le sue previsioni. Per esempio, si prendono in considerazione le costanti del moto (come l’energia) associate all’evoluzione temporale delle particelle e il comportamento di semplici sistemi chimici, e.g., il moto vibrazionale di singole molecole che interagiscono con un campo esterno risonante. In questo modo, proprietà inaspettate del moto molecolare emergono naturalmente. In secondo luogo, si considera la sfida di descrivere sistemi a molti componenti (quali sono i sistemi chimici in condizioni ordinarie). È ben noto che il calcolo della traiettoria di Bohm e della funzione d’onda è molto costoso computazionalmente. Comunque, le proprietà statistiche della traiettoria di Bohm permettono di derivare teorie stocastiche per esaminare la dinamica di sistemi quantistici aperti, come qualche molecola (o qualche grado di libertà) interagente con l’ambiente (le altre molecole). Uno dei metodi stocastici sviluppati correla la dinamica della matrice densità ridotta, per i gradi di libertà di interesse, all’evoluzione delle corrispondenti coordinate di Bohm. In altre parole, l’equazione di Bohm, che determina la velocità delle particelle attraverso la funzione d’onda, è sostituita da un’equazione stocastica che approssima la velocità di un sott’insieme di coordinate attraverso la matrice densità ridotta. In questo modo, le fluttuazioni quantistiche indotte dall’ambiente sono prese in considerazione. Il vantaggio del metodo riguarda la sua capacità di descrivere i sistemi quantistici, compresi quelli aperti, in termini di una traiettoria quantistica. Questo potrebbe permettere la comprensione del moto molecolare durante un esperimento spettroscopico. Di particolare interesse è la possibilità di esaminare sistemi reattivi, come quelli in cui avvengono cambi conformazionali. Come è ben noto, le reazioni chimiche possono essere totalmente caratterizzate solo attraverso il moto delle particelle e in questa tesi viene definita esattamente una metodologia quantistica che fornisce una descrizione autoconsistente del moto molecolare.

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Buercklin, Samuel Adam. "Optimal trajectories for fast quantum harmonic transport." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/121733.

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Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2019
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 85-88).
The transport of atomic ions trapped within a harmonic potential arises necessarily in the course of building a trapped ion quantum computer. We may define this problem in terms of a differential equation and its corresponding boundary conditions to satisfy which are sufficient to guarantee the motional quantum state of the ion is unaltered. However, the solution space to this problem is uncountably large, and the various solutions differ in many qualitative and quantitative aspects. We present an easily-computed functional of transport trajectories with intuitively interpretable terms which may be used to compare solutions to the quantum harmonic transport problem, but does not require an expensive quantum-mechanical simulation of the ion dynamics. Furthermore, we prove the convexity of this cost function under easily satisfied conditions in a Fourier Series parameterization of the problem. We then numerically optimize the cost function to discover optimal trajectories for the quantum harmonic transport problem.
by Samuel Adam Buercklin.
S.M.
S.M. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science

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Koch, Werner. "Non-Markovian Dissipative Quantum Mechanics with Stochastic Trajectories." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-63671.

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All fields of physics - be it nuclear, atomic and molecular, solid state, or optical - offer examples of systems which are strongly influenced by the environment of the actual system under investigation. The scope of what is called "the environment" may vary, i.e., how far from the system of interest an interaction between the two does persist. Typically, however, it is much larger than the open system itself. Hence, a fully quantum mechanical treatment of the combined system without approximations and without limitations of the type of system is currently out of reach. With the single assumption of the environment to consist of an internally thermalized set of infinitely many harmonic oscillators, the seminal work of Stockburger and Grabert [Chem. Phys., 268:249-256, 2001] introduced an open system description that captures the environmental influence by means of a stochastic driving of the reduced system. The resulting stochastic Liouville-von Neumann equation describes the full non-Markovian dynamics without explicit memory but instead accounts for it implicitly through the correlations of the complex-valued noise forces. The present thesis provides a first application of the Stockburger-Grabert stochastic Liouville-von Neumann equation to the computation of the dynamics of anharmonic, continuous open systems. In particular, it is demonstrated that trajectory based propagators allow for the construction of a numerically stable propagation scheme. With this approach it becomes possible to achieve the tremendous increase of the noise sample count necessary to stochastically converge the results when investigating such systems with continuous variables. After a test against available analytic results for the dissipative harmonic oscillator, the approach is subsequently applied to the analysis of two different realistic, physical systems. As a first example, the dynamics of a dissipative molecular oscillator is investigated. Long time propagation - until thermalization is reached - is shown to be possible with the presented approach. The properties of the thermalized density are determined and they are ascertained to be independent of the system's initial state. Furthermore, the dependence on the bath's temperature and coupling strength is analyzed and it is demonstrated how a change of the bath parameters can be used to tune the system from the dissociative to the bound regime. A second investigation is conducted for a dissipative tunneling scenario in which a wave packet impinges on a barrier. The dependence of the transmission probability on the initial state's kinetic energy as well as the bath's temperature and coupling strength is computed. For both systems, a comparison with the high-temperature Markovian quantum Brownian limit is performed. The importance of a full non-Markovian treatment is demonstrated as deviations are shown to exist between the two descriptions both in the low temperature cases where they are expected and in some of the high temperature cases where their appearance might not be anticipated as easily.

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Kuipers, Jack Anton. "Correlated Trajectories in Semiclassical Approaches to Quantum Chaos." Thesis, University of Bristol, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486392.

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This thesis is concerned with the application and extension of semiclassical methods, involving correlated trajectories, that were recently developed to explain the observed universal statistics of classically chaotic quantum systems. First we consider systems that depend on an external parameter that does not change the symmetry of the system. 'Ve study correlations between the spectra at different values of the param~ter, a scaled distance x apart, via the parametric spectral form factor K(r, x). Using a semiclassical periodic orbit expansion, we obtain a small r expansion that agrees with random matrix theory for systems with and without time reversal symmetry. Then we consider correlations of the Wigner time delay in open systems. We study a form factor K (r, x, y, M) that depends on the number of scattering channels M, the non-symmetry breaking parameter difference x and also a symmetry breaking parameter y. TheWigner time delay can be expressed semiclassically in terms of the trapped periodic orbits of the system, and using a periodic orbit expansion we obtain several terms in the small r expansion of the form factor that are identical to those calculated from random matrix theory. The Wigner time delay can also be expressed in terms of scattering trajectories that enter and leave the system. Starting from this picture, we derive all terms in the periodic orbit formula and therefore show how the two pictures of the time delay are related on a semiclassical level. A new type of trajectory correlation is derived which recreates the terms from the trapped periodic orbits. This involves two trajectories approaching the same trapped periodic orbit closely - one trajectory approaches the orbit and follows it for several traversals, while its partner approaches in almost the same way but follows the periodic orbit an additional number of times.

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Sutcliffe, Julia H. "Quantum studies of molecular dynamics." Thesis, University of Nottingham, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282566.

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Lopreore, Courtney Lynn. "Recent applications of the quantum trajectory method." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3034933.

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Duprey, Quentin. "Valeurs Faibles, Trajectoires Faibles et Interferométrie." Thesis, Cergy-Pontoise, 2019. http://www.theses.fr/2019CERG1049.

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La théorie de la mesure, basée sur la mesure projective, constitue un aspect fondamental de la mécanique quantique. La mesure faible diffère de la mesure projective traditionnelle sur laquelle les axiomes élémentaires de la physique quantique sont bâtis. Bien que définie dans le cadre de la théorie quantique standard, les mesures faibles sont encore mal comprises. Le travail de thèse s'inscrit dans une large démarche qui vise à comprendre les implications conceptuelles et pratiques d'une telle mesure et à la comprendre dans le cadre de la théorie quantique.Le chapitre 1 est une introduction détaillée à la mesure faible et à la valeur faible. Ensuite, nous étudierons les "trajectoires faibles" dans un interféromètre à fentes d'Young. Nous abordons au chapitre 3 les implications de l'annulation d'une valeur faible au regard de l'apparition de trajectoires faibles dans des interféromètres de Mach-Zender imbriqués. Enfin, le chapitre 4 traite des critiques théoriques et expérimentales présentes dans la littérature concernant l'effet du Chat du Cheshire quantique qui est défini dans le cadre de mesures faibles
Measurement theory, based on projective measurements, is a fundamental aspect of quantum mechanics. Weak measurements differ from standard projective measurements on which the elementary axioms of quantum physics are built. Although weak measurement framework is defined within standard quantum mechanics, its implications are still poorly understood. The thesis work is part of a broad reflexion that aims to understand the conceptual and practical implications of such a measurement and to understand it in the context of quantum theory.Chapter 1 is a detailed introduction to weak measurements and weak values. Next, we will study the "weak trajectories" in a two slit interferometer. In Chapter 3, we discuss the implications of a cancellation of a weak value with respect to the observation of weak trajectories in nested Mach-Zender interferometers. Finally, Chapter 4 deals with the theoretical and experimental criticisms in the literature of the effect of the Cheshire Cat that is defined in the framework of weak measurement

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Hemphill, Patrick A. "Intensity auto- and cross-correlations and other properties of a 85Rb atom coupled to a driven, damped two-mode optical cavity." Oxford, Ohio : Miami University, 2009. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=miami1248371234.

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Tilloy, Antoine. "Mesure continue en mécanique quantique : quelques résultats et applications." Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLEE010/document.

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Cette thèse est consacrée à l’étude des trajectoires quantiques issues de la théorie desmesures continues en mécanique quantique non relativiste. On y présente de nouveaux résultatsthéoriques ainsi que des exemples d’applications. Sur le front théorique, on étudie principalementla limite de mesure «forte» dans laquelle on met en évidence l’émergence de sauts quantiques etd’échardes quantiques, deux phénomènes dont on précise la statistique. Hors de la limite forte, onpropose une méthode d’extraction optimale d’information pour un registre de qubits. Sur le frontdes applications, on introduit une méthode originale de contrôle utilisant l’intensité de la mesurecomme unique variable et on explique la transition balistique-diffusif dans les marches aléatoiresquantiques ouvertes; deux sous produits de l’étude théorique préalable des situations de mesureforte. On s’intéresse aussi au problème de la gravité semi-classique et montre que la théorie desmesures continues peut permettre d’en construire un modèle cohérent à la limite newtonienne. Onsuggère enfin quelques extensions possibles de la théorie à l’estimation a posteriori et d’éventuellesgénéralisations des résultats théoriques à des situations de mesures répétées discrètes. Dans laprésentation des résultats, l’accent est mis davantage sur l’explicitation des liens entre les multiplespoints de vue possibles sur les trajectoires quantiques (parallèles avec la théorie classique du filtrageet les modèles de collapse objectif utilisés dans les fondements) que sur la rigueur mathématique
This thesis is devoted to the study of the quantum trajectories obtained from thetheory of continuous measurement in non relativistic quantum mechanics. New theoretical resultsas well as examples of applications are presented. On the theoretical front, we study mostly thelimit of «strong» measurement where we put forward the emergence of quantum jumps and quantumspikes, two phenomena we characterize in detail. Out of the strong measurement limit, weinvestigate a method to extract information from a register of qubits optimally. On the applicationfront, we introduce an original method to control quantum systems exploiting only the freedomof changing the measurement intensity and we explain the transition between a ballistic and adiffusive behavior in open quantum random walks; two byproduct of the theoretical study of thestrong measurement regime. We further study the problem of semi-classical gravity and show thatcontinuous measurement theory allows to construct a consistent model in the Newtonian regime.We eventually suggest possible extensions of the formalism to a posteriori estimation and hint atgeneralizations of the results for the strong measurement limit in the wider context of discreterepeated measurements. In the course of our presentation, we emphasize the link with other approachesto the theory of continuous measurement (parallels with stochastic filtering and collapsemodels in foundations) rather than aim for mathematical rigor

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Oxtoby, Neil Paul. "Keeping it real': A Quantum Trajectory Approach to Realistic Measurement of Solid-State Quantum Systems." Thesis, Griffith University, 2007. http://hdl.handle.net/10072/365770.

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To obtain information about a system of interest a measurement has to be made. In experiments that probe the quantum nature of our world, the system itself is, in general, necessarily affected by the act of measurement. If the system is weakly coupled to its bath and the dynamics are such that information concerning the system is spread throughout the many degrees of freedom of the bath, and the bath is being measured then a stochastic master equation for the conditioned state of the system can be found. This is termed a quantum trajectory equation. Realistic detectors are not perfect. Information is lost in the conversion to a signal that the observer can use. This loss may occur in the detector itself, in the circuit containing the detector (described by a response time and electronic noise) or at the circuit output (electronic output noise). In order to obtain a true quantum trajectory for the experiment, the observer must condition the state of the quantum system on results that are available in the laboratory rather than on the microscopic events considered previously in quantum trajectories. A method for treating this was first proposed by Warszawski, Wiseman and Mabuchi [Phys. Rev. A 65, 023802 (2002)], in which the quantum system is embedded within a supersystem that also contains the state of the detector. They applied their theory to photodetectors of various sorts. Warszawski has also done the preliminary work on applying this theory to detecting the state of a pair of quantum dots using a SET (single-electron transistor) [MSc. Thesis, Griffith University (2001)]. The resulting theory is termed 'realistic' quantum trajectory theory. In this thesis, the approach of Warszawski, et al.is applied to various solidstate readout devices. These include the SET, the QPC (quantum point contact), and the RF-QPC (radio-frequency QPC). Numerically obtained realistic quantum trajectories for the QPC agree with heuristic results. In particular, in certain limits, the realistic quantum trajectories can take on the appearance of ideal quantum trajectories. This thesis also resolves a problem in solid-state continuous quantum measurement theory by deriving a quantum trajectory model for a SET-monitored charge qubit, that guarantees physically meaningful qubit states. The particular limit necessary to achieve this is discussed, and the SET measurement quality is analysed using techniques borrowed from quantum optics. Conditions for which the SET can approach operation at the limit allowed by quantum mechanics are given. This is also done for the QPC, for which the results agree with previous work.
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Science
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Cotton, Stephen Joshua. "Symmetrical Windowing for Quantum States in Quasi-Classical Trajectory Simulations." Thesis, University of California, Berkeley, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3686249.

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An approach has been developed for extracting approximate quantum state-to-state information from classical trajectory simulations which "quantizes" symmetrically both the initial and final classical actions associated with the degrees of freedom of interest using quantum number bins (or "window functions") which are significantly narrower than unit-width. This approach thus imposes a more stringent quantization condition on classical trajectory simulations than has been traditionally employed, while doing so in a manner that is time-symmetric and microscopically reversible.

To demonstrate this "symmetric quasi-classical" (SQC) approach for a simple real system, collinear H + H₂ reactive scattering calculations were performed [S.J. Cotton and W.H. Miller, J. Phys. Chem. A 117, 7190 (2013)] with SQC-quantization applied to the H₂ vibrational degree of freedom (DOF). It was seen that the use of window functions of approximately 1/2-unit width led to calculated reaction probabilities in very good agreement with quantum mechanical results over the threshold energy region, representing a significant improvement over what is obtained using the traditional quasi-classical procedure.

The SQC approach was then applied [S.J. Cotton and W.H. Miller, J. Chem. Phys. 139, 234112 (2013)] to the much more interesting and challenging problem of incorporating non-adiabatic effects into what would otherwise be standard classical trajectory simulations. To do this, the classical Meyer-Miller (MM) Hamiltonian was used to model the electronic DOFs, with SQC-quantization applied to the classical "electronic" actions of the MM model—representing the occupations of the electronic states—in order to extract the electronic state population dynamics. It was demonstrated that if one ties the zero-point energy (ZPE) of the electronic DOFs to the SQC windowing function's width parameter this very simple SQC/MM approach is capable of quantitatively reproducing quantum mechanical results for a range of standard benchmark models of electronically non-adiabatic processes, including applications where "quantum" coherence effects are significant. Notably, among these benchmarks was the well-studied "spin-boson" model of condensed phase non-adiabatic dynamics, in both its symmetric and asymmetric forms—the latter of which many classical approaches fail to treat successfully.

The SQC/MM approach to the treatment of non-adiabatic dynamics was next applied [S.J. Cotton, K. Igumenshchev, and W.H. Miller, J. Chem. Phys., 141, 084104 (2014)] to several recently proposed models of condensed phase electron transfer (ET) processes. For these problems, a flux-side correlation function framework modified for consistency with the SQC approach was developed for the calculation of thermal ET rate constants, and excellent accuracy was seen over wide ranges of non-adiabatic coupling strength and energetic bias/exothermicity. Significantly, the "inverted regime" in thermal rate constants (with increasing bias) known from Marcus Theory was reproduced quantitatively for these models—representing the successful treatment of another regime that classical approaches generally have difficulty in correctly describing. Relatedly, a model of photoinduced proton coupled electron transfer (PCET) was also addressed, and it was shown that the SQC/MM approach could reasonably model the explicit population dynamics of the photoexcited electron donor and acceptor states over the four parameter regimes considered.

The potential utility of the SQC/MM technique lies in its stunning simplicity and the ease by which it may readily be incorporated into "ordinary" molecular dynamics (MD) simulations. In short, a typical MD simulation may be augmented to take non-adiabatic effects into account simply by introducing an auxiliary pair of classical "electronic" action-angle variables for each energetically viable Born-Oppenheimer surface, and time-evolving these auxiliary variables via Hamilton's equations (using the MM electronic Hamiltonian) in the same manner that the other classical variables—i.e., the coordinates of all the nuclei—are evolved forward in time. In a complex molecular system involving many hundreds or thousands of nuclear DOFs, the propagation of these extra "electronic" variables represents a modest increase in computational effort, and yet, the examples presented herein suggest that in many instances the SQC/MM approach will describe the true non-adiabatic quantum dynamics to a reasonable and useful degree of quantitative accuracy.

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Clemens, James Peter. "Collective spontaneous emission in the framework of quantum trajectory theory /." view abstract or download file of text, 2003. http://wwwlib.umi.com/cr/uoregon/fullcit?p3102158.

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Thesis (Ph. D.)--University of Oregon, 2003.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 129-135). Also available for download via the World Wide Web; free to University of Oregon users.

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18

Oriols, Pladevall Xavier. "Quantum Monte Carlo simulation of tunnelling devices using wavepackets and Bohm trajectories." Doctoral thesis, Universitat Autònoma de Barcelona, 1999. http://hdl.handle.net/10803/5353.

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Alarcón, Pardo Alfonso. "Quantum many-particle electron transport in time-dependent systems with Bohmian trajectories." Doctoral thesis, Universitat Autònoma de Barcelona, 2011. http://hdl.handle.net/10803/42002.

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Es conocido que a escalas nanométricas se debe tratar con en el problema de muchas partículas a la hora de estudiar dispositivos electrónicos. Es estos escenarios, la ecuación de Schrödinger dependiente del tiempo para muchas partículas solo se puede resolver para unos pocos grados de libertad. En este sentido, diferentes formalismos han sido desarrollados en la literatura (tales como time-dependent Density Functional Theory, Green's functions técnicas o Quantum Monte Carlo técnicas) para tratar sistemas cuánticos de muchos electrones. Estas aproximaciones modelizan de forma razonable el transporte electrónico en sistemas de muchas partículas. Una propuesta alternativa ha sido desarrollada por el Dr. Oriols para descomponer la ecuación de Schrödinger de N-partículas en un sistema de N-ecuaciones de Schrödinger para una sola partícula usando trayectorias (cuánticas) de Bohm. Basado en esta propuesta se presenta un 3D, general, versátil y dependiente del tiempo simulador de transporte de dispositivos electrónicos llamado BITLLES (Bohmian Interacting Transport for non-equiLibrium eLEctronic Structures). Las novedades que aporta el simulador BITLLES se basan en dos puntos. El primero, éste representa un modelo de transporte cuántico de electrones para muchas partículas en el cual se tiene en cuenta de forma explicita las correlaciones de Coulomb y de intercambio entre electrones usando trayectorias de Bohm. En segundo lugar, el simulador proporciona una completa información de los momentos de la corriente (i.e., DC, AC, fluctuaciones o incluso momentos mayores). A continuación resumimos las contribuciones que esta tesis aporta al desarrollo del simulador BITLLES. De esta forma, introducimos de forma explicita la interacción de intercambio entre electrones. En este contexto, mostramos como la interacción de intercambio es la responsable final para determinar la corriente total a través del sistema. Además presentamos una nueva aproximación para estudiar sistemas de muchas partículas donde los espines de los electrones tienen diferente orientación. Hasta donde llega nuestro conocimiento, es la primera vez que la interacción de intercambio es introducida de forma práctica en un simulador de transporte de electrones. Además presentamos la computación de la corriente total dependiente del tiempo en un contexto de alta frecuencia donde se tienen que tener en cuenta las variaciones del campo eléctrico dependientes del tiempo (i.e., la corriente de desplazamiento) para asegurar la conservación de la corriente. También discutimos el cálculo de la corriente total (conducción más desplazamiento) usando los teoremas de Ramo-Shockley-Pellegrini. Diferentes capacidades del simulador BITLLES como AC y fluctuaciones de la corriente se presentan para el diodo túnel resonante. También hemos usado el simulador BITLLES para testear un nuevo tipo de dispositivo nanoeléctronico diseñado para procesar señales dentro del espectro de los THz. Hemos llamado a este dispositivo Driven Tunneling Device. Se trata de un dispositivo de tres terminales donde la conductancia entre el drain y el source se controla por el terminal del gate el cual oscila a frecuencias de THz. También presentamos ejemplos prácticos de la funcionalidad de este dispositivo como un rectificador y un multiplicador de frecuencia. Finalmente, hemos desarrollado una aproximación numérica para resolver la ecuación de Schrödinger usando el modelo de tight-binding con el propósito de mejorar la descripción de la estructura de bandas del simulador BITLLES.
It is known that at nanoscale regime we must deal with the many-particle problem in order to study electronic devices. In this scenario, the time-dependent many-particle Schrödinger equation is only directly solvable for very few degrees of freedom. However, there are many electrons (degrees of freedom) in any electron device. In this sense, many-particle quantum electron formalisms (such as time-dependent Density Functional Theory, Green's functions techniques or Quantum Monte Carlo techniques) have been developed in the literature to provide reasonable approximations to model many-particle electron transport. An alternative proposal has been developed by Dr. Oriols to decompose the N-particle Schrödinger equation into a N-single particle Schrödinger equation using Bohmian trajectories. Based on this proposal a general, versatile and time-dependent 3D electron transport simulator for nanoelectronic devices, named BITLLES (Bohmian Interacting Transport for non-equiLibrium eLEctronic Structures) is presented. The novelty of the BITLLES simulator is based on two points. First, it presents a many-particle quantum electron transport model taking into account explicitly the Coulomb and exchange correlations among electrons using Bohmian trajectories. Second, it provides full information of the all current distribution moments (i.e. DC, AC, fluctuations and even higher moments). We summarize the important contributions of this thesis to the development of BITLLES simulator. Thus, we introduce explicitly the exchange correlations among electrons. In this context, we show how exchange interaction is the final responsible for determining the total current across the system. We also present a new approximation to study many-particle systems with spin of different orientations. Some practical examples are studied taking into account the exchange interaction. To the best of our knowledge, it is the first time that the exchange interaction is introduced explicitly (imposing the exchange symmetry properties directly into the many-particle wavefunction) in practical electron transport simulators. We present the computation of the time-dependent total current in the high-frequency regime where one has to compute time-dependent variations of the electric field (i.e. the displacement current) to assure current conservation. We discuss the computation of the total (conduction plus displacement) current using Bohmian trajectories and the Ramo-Shockley-Pellegrini theorems. Different capabilities of BITLLES simulator such as AC and current fluctuations are presented for Resonant Tunneling Devices. We have used the BITLLES simulator to test a new type of nanoelectronic device designed to process signals at THz regime named Driven Tunneling Device. It is a three terminal device where the drain-source conductance is controlled by a gate terminal that can oscillate at THz frequencies. We also present practical examples on the functionality of this device such as rectifier and frequency multiplier. Finally, we have developed a numerical approximation to solve the Schrödinger equation using tight-binding model to improve the band structure description of the BITLLES simulator.

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McNally, Douglas M. II. "A NEW ALGORITHM FOR THE TIME EVOLUTION OF QUANTUM TRAJECTORY SIMULATIONS AND PHYSICALLY MOTIVATED ERROR MODELS IN 1D QUANTUM CELLULAR AUTOMATA." Miami University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=miami1407344625.

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Jacobs, Andrew. "Probe Spectra and Photon Statistics in a Weakly-Driven Cavity Optomechanical System." Miami University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=miami1344150680.

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22

Sarno, Giorgio. "A numerical approach to spin foam models of quantum gravity." Thesis, Aix-Marseille, 2020. http://www.theses.fr/2020AIXM0231.

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Les modèles de mousse de spin proposent une définition covariante de Lorentz de la dynamique de la gravité quantique en boucle.C'est une approche non-perturbative qui a déjà obtenu un résultat important, reproduire la Relativité Générale discrétisée dans une limite semi-classique. Cependant, la complexité analytique des modèles est telle que des questions clés concernant leur cohérence théorique et leurs prédictions physiques restent ouvertes. Dans cette thèse, j'introduis un cadre systématique pour effectuer des calculs numériques dans ce domaine. La thèse contient une introduction aux théories de mousse de spin d’un point de vue théorique et numérique, en particulier au modèle EPRL. Je présente ensuite quatre des six articles que j'ai publiés au cours de mon doctorat, où le cadre numérique a été utilisé pour étudier des problèmes critiques ouverts dans le domaine. Il s'agit notamment de l'étude numérique du modèle semi-classique limite d'un 4-simplexe, en récupérant son action de Regge et en confirmant des calculs analytiques connus ; une étude des mousses de spin non-simplexes pour offrir un aperçu de la limite du continuum de la théorie ; une nouvelle approche pour étudier les triangulations étendues et leur limite semi-classique. Appliquée à une amplitude de transition particulière, la nouvelle approche m'a permis de retrouver des configurations géométriques compatibles avec des paramètres de bord courbes, et d'argumenter contre un litige important dans la littérature appelé flatness-problem. Ces résultats ouvrent une fenêtre pour les calculs dans les théories de mousse de spin et ils fournissent une nouvelle voie pour aborder leur questions encore non résolues
Spin foam models provide a Lorentz-covariant definition of the dynamics of loop quantum gravity. They offer a background-independent and non-perturbative quantization of gravity, and in their semiclassical limit, they are related to discretized General Relativity. However, the analytic complexity of the models is such that key questions concerning their theoretical consistency and physical predictions are still open. In this thesis, I introduce a systematic framework to perform numerical computations in this domain, to go beyond the limitations of the analytical techniques. The thesis contains an introduction to spin foam theories from a theoretical and a numerical standpoint, in particular to the EPRL model. I then present four of the six papers I published during my Ph.D., where the numerical framework was used to study critical open problems in the field. These include the numerical study of the semiclassical limit of a 4-simplex, recovering its Regge action and confirming known analytical computations ; a study of non-simplicial spin foams to offer an insight into the continuum limit of the theory ; a new approach to investigate extended triangulations and their semiclassical limit. Applied to a particular transition amplitude, the new approach allowed me to recover geometrical configurations compatible with curved boundary data, and to argue against an important dispute in the literature referred to as flatness problem. These results open a window for calculations in spin foam theories and they provide a new path to address their still unresolved questions

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Lees, Eitan Jacob. "Suppression of Collective Quantum Jumps of Rydberg Atoms due to Collective Spontaneous Emission from Atoms in Free Space." Miami University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=miami1438276591.

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Cruz, Rodriguez Lidice. "Méthodes de dynamique quantique ultrarapide basées sur la propagation de trajectoires." Thesis, Toulouse 3, 2018. http://www.theses.fr/2018TOU30254/document.

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Dans cette thèse, différentes méthodes de dynamique quantique basées sur la propagation de trajectoires sont développées. La première approche consiste en une développer global des champs hydrodynamiques sur une base de polynômes de Chebyshev. Ce schéma est utilisé pour étudier la dynamique vibrationnelle unidimensionnelle de paquets d'ondes dans des potentiels harmoniques et anharmoniques. Par la suite, une méthodologie différente est développée, qui, à partir d'un paramétrage précédemment proposé pour la densité quantique, permet de construire des potentiels d'interaction effectifs entre les pseudo-particules représentant la densité. Dans le cadre de cette approche, plusieurs problèmes de modélisation sont étudiés et des effets quantiques importants sont décrits, tels que l'énergie de point zéro, l'effet tunnel, la diffusion et la réflexion sur une barrière. La même approximation est utilisée pour l'étude de l'ionisation des atomes par laser. Dans une troisième approche, un potentiel quantique approximatif à plusieurs corps est dérivé pour décrire des matrices d'argon et de krypton contenant une impureté de sodium. Il est obtenu en proposant un ansatz approprié pour la fonction d'onde de l'état fondamental du solide. Le potentiel est utilisé dans les simulations de dynamique moléculaire pour obtenir les spectres d'absorption de l'atome de Na isolé dans les matrices cryogéniques
In this thesis different trajectory-based methods for the study of quantum mechanical phenomena are developed. The first approach is based on a global expansion of the hydrodynamic fields in Chebyshev polynomials. The scheme is used for the study of one-dimensional vibrational dynamics of bound wave packets in harmonic and anharmonic potentials. Furthermore, a different methodology is developed, which, starting from a parametrization previously proposed for the density, allows the construction of effective interaction potentials between the pseudo-particles representing the density. Within this approach several model problems are studied and important quantum mechanical effects such as, zero point energy, tunneling, barrier scattering and over barrier reflection are founded to be correctly described by the ensemble of interacting trajectories. The same approximation is used for study the laser-driven atom ionization. A third approach considered in this work consists in the derivation of an approximate many-body quantum potential for cryogenic Ar and Kr matrices with an embedded Na impurity. To this end, a suitable ansatz for the ground state wave function of the solid is proposed. This allows to construct an approximate quantum potential which is employed in molecular dynamics simulations to obtain the absorption spectra of the Na impurity isolated in the rare gas matrix

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Saller, Maximilian A. C. "Sampling minimal, adaptive basis sets for multidimensional, nuclear quantum dynamics using simple, semi-classical trajectories." Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/97217/.

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Methods for the study of nuclear quantum dynamics can be categorised by the nature of the basis set expansion they employ. The wavefunction can be expanded in a static set of time-independent basis functions, the time evolution being described solely via the expansion coefficients. Alternatively, basis functions can be propagated in time, along with the coefficients, via equations of motion for their parameters. Time-independent basis sets are plagued by exponential scaling, while the equations of motion for time-dependent basis functions are challenging to integrate and, if not derived variationally, can violate energy conservation laws. This work presents a novel basis set sampling method which represents a compromise between these two categories. A set of sampling trajectories, evolving on the potential energy surface of the system, are used to place basis functions in regions of phase space, relevant to wavefunction propagation. These functions then act as a time-independent basis set, the wavefunction being evolved via exact, variational equations of motion for the expansion coefficients. This approach is applied to a challenging quantum dynamics benchmark, namely the relaxation dynamics of photoexcited pyrazine, and yields highly encouraging results. In order to address divergence from exact dynamics at longer timescales, which is attributed to the classical sampling trajectories being a sound approximation to quantum propagation of the wavefunction only in the short-time limit, a modification of this method is proposed. Shorter iterations of trajectory sampling and wavefunction propagation are used, linked by a minimisation algorithm that continuously optimises the basis set, preventing unfavourable scaling. This adaptive sampling approach is again applied to the pyrazine benchmark with a significant increase in performance and accuracy. Highly encouraging results are also obtained for a quantum tunnelling benchmark system, which are improved upon even further, and at little extra cost, by the use of path integral sampling trajectories.

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CILLUFFO, Dario. "(Un)conditioned open dynamics in quantum optics." Doctoral thesis, Università degli Studi di Palermo, 2021. http://hdl.handle.net/10447/500775.

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The study of the dynamics of open quantum systems sheds light on dissipative processes in quantum mechanics. Any system under continuous measurement is open and the act of measuring induces abrupt changes of the system’s state (collapses). The evolution conditioned to measurement records generates the so-called quantum trajectories. A continuous (unconditioned) evolution of the system is recovered by averaging over a large number of trajectories. Historically this kind of evolution has been the main focus of theoretical investigations. In this dissertation we consider both conditional and unconditional dynamics of quantum optical systems. Unconditioned dynamics is studied through the collision model paradigm. The formalism is described in detail and used for describing generic systems featuring many quantum emitters coupled to a usually one-dimensional field. The negligible-delay regime is widely explored. Collision models are used to unveil the mechanisms underlying the decoherence-free evolution regime typical of these systems, which has received considerable attention in the last years. Then we investigate conditioned dynamics by broadening the study of statistics of quantum trajectories. Specifically, we exploit the information about the emission’s full-counting statistics from large deviations to define a nonclassicality witness. Finally we come back to collision models in order to extend the theory of biased quantum trajectories from Lindblad-like dynamics to sequences of arbitrary dynamical maps, providing at once a transparent physical interpretation.

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Baldwin, Charles H. "Cavity QED with Center of Mass Tunneling." Miami University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=miami1312237577.

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Silva, Fernando Luis Semião da. "Interações de sistemas físicos com aplicações em óptica e informação quântica." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/277313.

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Orientador: Antonio Vidiella Barranco
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica "Gleb Wataghin"
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Resumo: A presente tese é dedicada à utilização de conhecidos sistemas quânticos em aplicações de interesse em óptica e informação quântica. Motivados pelos recentes avanços experimentais em sistemas formados por íons aprisionados interagindo com lasers e na eletrodinâmica quântica de cavidades, nós focamos grande parte de nossas propostas nestes sistemas. Mais especificamente, nós estudamos a interação de íons e campos quantizados na chamada eletrodinâmica quântica de cavidades com íons aprisionados. Neste contexto, iniciamos nossos trabalhos com uma proposta de geração de superposições mesoscópicas no movimento do íon. Uma vez que tais superposições são muito sensíveis à decoerência, incluímos perdas na cavidade para tratar uma situação mais realista. Através da observação de quantum jumps, ou fóton-contagens fora da cavidade, mostramos um esquema de geração de estados com características quânticas muito similares aos encontrados no caso da cavidade ideal, sem perdas. Neste aspecto, encontramos um modo de usar a dissipação a nosso favor, fato de grande interesse experimental devido às imperfeições dos espelhos reais. Apresentamos também uma proposta de implementação de uma interação do tipo Kerr em íons como uma alternativa ao uso de cristais não-lineares que apresentam baixíssima eficiência para esse tipo de efeito. Essa proposta abre novas possibilidades para o uso de íons em medidas não demolidoras e computação quântica. Nossos estudos na área de eletrodinâmica quântica com íons aprisionados terminam com a análise dos efeitos do movimento do íon na dinâmica das transições multi-fotônicas. Esse é um estudo mais fundamental e está relacionado com o entendimento da interação da radiação com a matéria. Na última parte desta tese são apresentados resultados sobre o uso de sistemas de muitos corpos para a distribuição de informação quântica. O objetivo de se estudar estes sistemas mais complexos é a busca de implementação de protocolos quânticos em larga escala. Neste sentido, poderíamos pensar numa cadeia de osciladores harmônicos acoplados como ocorre em sistemas típicos da física da matéria condensada. Em particular, nós estudamos como aumentar a eficiência na transmissão de emaranhamento nestas cadeias. Propusemos um esquema que funciona como um tipo de quantum data bus, ou ônibus quântico para transportar e distribuir emaranhamento com alta eficiência
Abstract: This thesis is concerned with the use of firmly established quantum systems for applications in quantum optics and quantum information. Having been driven by recent experimental advances in laser-manipulated trapped ions and cavity quantum electrodynamics, we concentrated more on proposals to be implemented in those systems. Being more specific, we have studied the interaction between trapped ions and quantized fields in the so-called cavity quantum electrodynamics with trapped ions. In this context, we began with a proposal to generate mesoscopic superpositions in the motion of the ion. Since these superpositions are extremely sensitive to decoherence, we have included cavity losses in order to make the situation slightly more realistic. We showed that the observation of quantum jumps, or photon detection outside the cavity, would generate quantum states with properties close to that generated in the ideal lossless case. In spite of the normally destructive effect of dissipation, we found a way to use it in our favor which turns out to be of great experimental importance due to always present mirror imperfections. We also showed how to mimic cross-Kerr nonlinearities in the cavity-ion system as a feasible alternative to the use of nonlinear crystals whose intensity of that non-linearity is too weak. This proposal opens up new possibilities for the use of trapped ions in non-demolition measurements and quantum computing. We finish our work in cavity electrodynamics with trapped ions with the study of the effect of the ionic motion on the dynamics of multiphotonic transitions. This is a more fundamental issue that is related to the understanding of matter-field interaction. In the last part of this thesis, we present results on the use of many-body systems for quantum information distribution. It was our goal to study more complex systems for the implementation of quantum protocols in large scale. In this sense, one could think of a chain of coupled harmonic oscillators as commonly found in condensed matter physics. Particularly, we dealt with the efficiency of entanglement transmission through the chain, trying to improve it. We ended up with a scheme which acts as a quantum data bus able to transport and distribute entanglement around quite efficiently
Doutorado
Física
Doutor em Ciências

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Métillon, Valentin. "Tomographie par trajectoires d'états délocalisés du champ micro-onde de deux cavités." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLEE051.

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La reconstruction d'états quantiques, ou tomographie, joue un rôle central dans les technologies quantiques, afin de caractériser les opérations effectuées et d'extraire de l'information sur les états résultats de traitements d'information quantique. Les méthodes répandues de tomographie reposent généralement sur des mesures idéales, effectuées une seule fois sur chaque préparation de l'état d'intérêt. Dans ce travail, nous utilisons une nouvelle méthode, appelée tomographie par trajectoires, qui consiste à enregistrer, pour chaque réalisation de l'état, la trajectoire quantique suivie par le système à l'aide d'une série de mesures successives du système, en présence d'imperfections expérimentales et de décohérence. On extrait alors plus d'information sur l'état à reconstruire et on est capable, à partir d'un ensemble de mesures accessibles données, de créer des mesures plus générales. À l'aide des techniques de l'électrodynamique quantique en cavité, nous avons préparé des états intriqués de photons micro-onde délocalisés sur deux modes distants. Nous avons ensuite reconstruit ces états par tomographie par trajectoires, dans un espace de Hilbert de grande dimension. Nous montrons que cette méthode permet de reconstruire l'état, de développer des stratégies de mesure adaptées pour accélérer l'extraction d'information sur les cohérences quantiques d'intérêt et qu'elle fournit une estimation de l'incertitude sur les coefficients de la matrice densité reconstruite
Quantum state estimation, or tomography, is a key component of quantum technologies, allowing to characterise quantum operations and to extract information on the results of quantum information processes. The usual tomography techniques rely on ideal, single-shot measurements of the unknown state. In this work, we use a new approach, called trajectory quantum tomography, where the quantum trajectory of each realization of the state is recorded through a series of measurements, including experimental imperfections and decoherence. This strategy increases the extracted amount of information and allows to build new measurements for a set of feasible measurements.Using the tools of cavity quantum eletrodynamics, we have prepared entangled states of microwave photons spread on two separated modes. We have then performed a trajectory tomography of these states, in a large Hilbert space. We have proved that this method allows to estimate the state, to develop faster strategies for extracting information on specific coherences of the state and to compute error bars on the components of the estimated density matrix

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Alonso, Castaneda Jose Joaquin [Verfasser], and Eric [Gutachter] Lutz. "Thermodynamics along classical and quantum trajectories under feedback control / Jose Joaquin Alonso Castaneda ; Gutachter: Eric Lutz." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2017. http://d-nb.info/1150964367/34.

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Hemphill, Patrick A. "Intensity Auto- and Cross-Correlations and Other Properties of a ⁸⁵Rb Atom Coupled to a Driven, Damped Two-Mode Optical Cavity." Miami University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=miami1248371234.

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Benseny, Cases Albert. "Trapping and ionising atoms with light: wave and trajectory dynamics of quantum-optical processes." Doctoral thesis, Universitat Autònoma de Barcelona, 2013. http://hdl.handle.net/10803/129127.

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La mecànica quàntica va néixer a començaments del segle passat per a explicar fenòmens que els models de l'època no podien explicar. Des de llavors n'han aparegut diferents formalismes i interpretacions, cadascun amb les seves peculiaritats, que permeten proposar solucions diferents a alguns problemes quàntics o ajudar a descriure’n la dinàmica. Al mateix temps, l'estudi de la llum ha seguit de prop el desenvolupament de la teoria quàntica: des del seu inici amb la descripció que va fer Albert Einstein de l'efecte fotoelèctric fins al desenvolupament de les font de llum làser. De fet, la llum làser ha demostrat ser una eina molt útil per a induir, manipular i mesurar el comportament quàntic de la matèria. Per exemple, els làsers han permès el desenvolupament de tècniques per a refredar, capturar i manipular àtoms neutres. Les ones de matèria atòmica en potencials òptics, elèctrics i magnètics s'han utilitzat per a posar a prova els principis de la mecànica quàntica i crear-ne aplicacions en, per exemple, el processat d'informació quàntica o l'atomtrònica, on els àtoms atrapats constitueixen dispositius anàlegs als díodes i transistors electrònics. D’altra banda, durant els últims cinquanta anys la intensitat de les fonts de llum ha experimentat un creixement gairebé exponencial. Aquests desenvolupaments han desafiat la física a trobar una descripció per als processos bàsics en la interacció entre la llum i la matèria, molt més complexos que l'efecte fotoelèctric d'Einstein, provocant fenòmens com la ionització multifotònica o l'emissió de radiació d'harmònics d'ordre alt. El punt de partida d’aquesta tesi és la narració del desenvolupament de la mecànica quàntica, després de la qual presentem els dos formalismes matemàtics de la teoria quàntica que usarem: la interpretació estàndard, que ens permet representar la dinàmica ondulatòria de la matèria, i la de de Broglie-Bohm, on la dinàmica es descriu a partir de trajectòries. La tesi tracta sobre dos sistemes òptics quàntics diferents, és a dir, sobre la interacció de la llum i la matèria a nivell quàntic. El primer sistema que estudiem és la manipulació coherent d'àtoms ultrafreds atrapats en potencials òptics. En particular, estudiem l'anàleg per a àtoms en un potencial amb tres trampes òptiques de la transferència adiabàtica Raman estimulada (STIRAP, de les sigles en anglès) de l'òptica quàntica. Gràcies al formalisme de de Broglie-Bohm, demostrem que la descripció d'aquest transport per a un àtom individual (o un condensat de Bose-Einstein) necessita correccions relativistes en alguns règims de paràmetres corresponents a realitzacions molt lentes del procés. A més, presentem pel cas de múltiples àtoms una tècnica per a transportar trampes buides en una fila de trampes òptiques i dissenyem dispositius atomtrònics per al control del flux d'ones de matèria. El segon sistema que estudiem és la ionització de l'hidrogen mitjançant polsos làser ultraintensos. Usem les trajectòries de de Broglie-Bohm per a obtenir informació sobre la dinàmica i proposar mètodes per a calcular, en un model unidimensional, els espectres de ionització per sobre del llindar i de generació d'harmònics. També estudiem la dinàmica d’ionització d'un àtom d'hidrogen interaccionant amb un feix de llum que porta moment angular orbital mitjançant càlculs tridimensionals, demostrant que és possible transmetre el moment angular orbital de la llum als electrons. Les trajectòries de de Broglie-Bohm de la dinàmica del procés permeten una visualització molt clara de l'absorció de moment angular per part dels electrons.
Quantum mechanics was born at the beginning of the twentieth century to account for facts that the physical models at the time could not explain. Since then, many different formalisms and interpretations for it have appeared, each one with its particularities that allow it to provide different solutions for some quantum problems or to help describe particular quantum systems. Simultaneously, the study of light has always followed closely the development of quantum physics: from its inception in Albert Einstein's description of the photoelectric effect to the development of laser sources. In fact, laser light has proven to be a very useful tool to induce, manipulate, and measure the quantum behaviour of matter. For instance, lasers have allowed for the development of techniques to cool down, trap, and manipulate individual neutral atoms. Atomic matter waves in optical, electric, and magnetic potentials have been used for both testing the principles of quantum mechanics and developing applications such quantum information processing or atomtronics, where the trapped atoms constitute the building blocks of coherent diode and transistor-like devices. On the other hand, the last fifty years have witnessed an almost exponential increase in the intensity of light sources. These developments have challenged physics to find a description for the basic processes of light-matter interactions, much more complex than Einstein's photoelectric effect, yielding effects such as above-threshold or multiphoton ionisation or the emission of high-order harmonic radiation. The starting point of this thesis is a historical account of the development of quantum mechanics, after which we present the two mathematical formalisms of quantum mechanics that we use: the standard interpretation, which allows to represent the wave dynamics of matter, and the de Broglie-Bohm interpretation, where the quantum dynamics are described in terms of trajectories. The thesis deals with two different quantum-optical systems, i.e., regarding the interaction of light and matter at the quantum level. The first system under investigation is the coherent manipulation of ultracold atoms trapped in optical potentials. In particular, we study the atomic analogue technique in triple-well optical potentials of the stimulated Raman adiabatic passage (STIRAP) quantum-optical technique. Thanks to the de Broglie-Bohm formalism, we show that the description of this transport for a single atom (or a Bose-Einstein condensate) requires relativistic corrections in certain parameter regimes corresponding to very slow realisations of the process. Furthermore, we present for the case of multiple atoms a technique to transport empty sites in a row of optical microtraps, and extend it to develop atomtronic devices to control the flow of atomic matter waves. The second system we study is the ionisation of hydrogen by ultrastrong light pulses. We have used de Broglie-Bohm trajectories to obtain information about the dynamics and to propose methods for the calculation of the above-threshold ionisation and harmonic-generation spectra in a simple one-dimensional model. We also study the ionisation dynamics of a hydrogen atom interacting with a light beam carrying orbital angular momentum in full three-dimensional calculations, showing that it is possible to transmit the orbital angular momentum of the light to the electron dynamics. The associated de Broglie-Bohm trajectories of the process give a very clear visualisation of the absorption of angular momentum by the electrons.

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Vadapalli, Ravi K. "Accuracy study of a free particle using quantum trajectory method on message passing architecture." Master's thesis, Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-11062002-142043.

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Lolli, Jared. "Quantum Measurement and Feedback Control of highly nonclassical Photonic States." Thesis, Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCC223/document.

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Ces dernières années, les progrès réalisés dans le contrôle de l'interaction lumière-matière au niveau quantique ont conduit à de nombreuses avancées en optique quantique, en particulier dans l'étude de phénomènes quantiques fondamentaux, dans la conception de systèmes quantiques artificiels et dans les applications en information quantique. Il a notamment été possible d'augmenter considérablement l'intensité de l'interaction lumière-matière et de contrôler le couplage de systèmes quantiques à leur environnement, afin d'obtenir des états non conventionnels et fortement non classiques. Cependant, pour exploiter ces états quantiques en vue d'applications technologiques, il est crucial de pouvoir mesurer et contrôler ces systèmes avec précision. Dans ce contexte, ce travail de thèse est consacré à l'étude de nouveaux protocoles pour la mesure et le contrôle de systèmes quantiques dans lesquels des fortes interactions et des symétries particuliers conduisent à la génération d'états fortement non classiques. Nous nous intéressons dans un premier temps au régime de couplage ultra-fort de l'électrodynamique quantique en cavité (et de circuit). Plus précisément, l'état de fondamental n'est plus le vide standard, car il devient énergiquement favorable qu'il contienne des photons.Dans ce régime on peut même obtenir des chat de Schrödinger comme état fondamental.En revanche, pour assurer la conservation de l'énergie, les photons contenus dans ce vide exotique sont liés à la cavité et ne peuvent pas s'échapper dans l'environnement. Cela signifie qu'ils ne peuvent être mesurés par simple photodétection. Nous proposons dans ce travail un protocole spécialement conçu pour surmonter cette difficulté. Nous montrons qu'il est possible de déduire les propriétés photoniques de l'état fondamental à partir du déplacement de Lamb d'un système à deux niveaux auxiliaire.Les résonateurs optiques à paires de photons constituent une autre classe de systèmes dans lesquels la symétrie de parité conduit à des états quantiques non conventionnels. Grâce à "l'ingénierie de réservoir", il est aujourd'hui possible de contrôler l'interaction d'un système avec son environnement, de façon à le stabiliser dans des états quantiques particulièrement intéressants. En particulier, quand un résonateur (une cavité optique) est couplé à l'environnement par échange de paires de photons, il est possible de créer de chats de Schrödinger optiques dans la dynamique transitoire du système. Les corrélations quantiques de ces états sont par contre rapidement perdues en raison de la présence inévitable de dissipation à un photon. Protéger le système contre cette perturbation est le but du protocole de feedback basé sur la parité que nous présentons dans cette thèse
In recent years, the field of quantum optics has thrived thanks to the possibility of controlling light-matter interaction at the quantum level.This is relevant for the study of fundamental quantum phenomena, the generation of artificial quantum systems, and for quantum information applications.In particular, it has been possible to considerably increase the intensity of light-matter interaction and to shape the coupling of quantum systems to the environment, so to realise unconventional and highly nonclassical states.However, in order to exploit these quantum states for technological applications, the question of how to measure and control these systems is crucial.Our work is focused on proposing and exploring new protocols for the measurement and the control of quantum systems, in which strong interactions and peculiar symmetries lead to the generation of highly nonclassical states.The first situation that we consider is the ultrastrong coupling regime in cavity (circuit) quantum electrodynamics.In this regime, it becomes energetically favourable to have photons and atomic excitations in the ground state, that is no more represented by the standard vacuum.In particular, in case of parity symmetry, the ground state is given by a light-matter Schrödinger cat state.However, according to energy conservation, the photons contained in these exotic vacua are bound to the cavity, and cannot be emitted into the environment.This means that we can not explore and control them by simple photodetection.In our work we propose a protocol that is especially designed to overcome this issue.We show that we can infer the photonic properties of the ground state from the Lamb shift of an ancillary two-level system.Another class of systems in which the fundamental parity symmetry leads to very unconventional quantum states is given by two-photon driven-dissipative resonators.Thanks to the reservoir engineering, it is today possible to shape the interaction with the environment to stabilize the system in particularly interesting quantum states.When a resonator (an optical cavity) exchanges with the environment by pairs of photons, it has been possible to observe the presence of optical Schrödinger cat states in the transient dynamics of the system.However, the quantum correlations of these states quickly decays due to the unavoidable presence of one-photon dissipation.Protecting the system against this perturbation is the goal of the parity triggered feedback protocol that we present in this thesis

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Woldekristos, Habtom G. "Tripartite Entanglement in Quantum Open Systems." Miami University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=miami1250185666.

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Tarbox, Grayson J. "Simulations of Electron Trajectories in an Intense Laser Focus for Photon Scattering Experiments." BYU ScholarsArchive, 2015. https://scholarsarchive.byu.edu/etd/5828.

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An experiment currently underway at BYU is designed to test whether the size of a free electron wave packet affects the character of scattered radiation. Using a semi-classical argument wherein the wave packet is treated as a diffuse charge distribution, one would expect strong suppression of radiation in the direction perpendicular to the propagating field as the wave packet grows in size to be comparable to the wavelength of the driving field. If one disallows the interaction of the wave packet with itself, as is the case when calculating the rate of emission using QED, then regardless of size, the electron wave packet radiates with the strength of a point-like emitter. In support of this experiment, we explore a variety of physical parameters that impact the rate of scattered photons. We employ a classical model to characterize the exposure of electrons to high-intensity laser light in a situation where the electrons are driven by strong ponderomotive gradients. Free electrons are modeled as being donated by low-density helium, which undergoes strong-field ionization early on in the pulse or during a pre-pulse. When exposed to relativistic intensities (i.e. intensities sufficient to cause a Lorentz drift at a significant fraction of c), free electrons experience a Lorentz drift that causes redshifting of the scattered 800 nm laser light. This redshift can be used as a key signature to discern light scattered from the more intense regions of the focus. We characterize the focal volume of initial positions leading to significant redshifting, given a peak intensity of 2 x 10^18 W/cm 2 , which is sufficient to cause a redshift in scattered light of approximately 100 nm. Under this scenario, the beam waist needs to be larger than several wavelengths for a pulse duration of 35 fs in order to ensure free electrons remain in the focus sufficiently long to experience intensities near the peak pulse intensity despite strong ponderomotive gradients. We compute the rate of redshifted scattered photons from an ensemble of electrons distributed throughout the focus and relate the result to the scattered-photon rate of a single electron. We also estimate to what extent the ionization process may produce unwanted light in the redshifted spectral region that may confound the measurement of light scattered from electrons experiencing intensities greater than 1.5 x 10^18 W/cm^2.

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Colijn, Caroline. "The de Broglie-Bohm Causal Interpretation of Quantum Mechanics and its Application to some Simple Systems." Thesis, University of Waterloo, 2003. http://hdl.handle.net/10012/1044.

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The de Broglie-Bohm causal interpretation of quantum mechanics is discussed, and applied to the hydrogen atom in several contexts. Prominent critiques of the causal program are noted and responses are given; it is argued that the de Broglie-Bohm theory is of notable interest to physics. Using the causal theory, electron trajectories are found for the conventional Schrödinger, Pauli and Dirac hydrogen eigenstates. In the Schrödinger case, an additional term is used to account for the spin; this term was not present in the original formulation of the theory but is necessary for the theory to be embedded in a relativistic formulation. In the Schrödinger, Pauli and Dirac cases, the eigenstate trajectories are shown to be circular, with electron motion revolving around the z-axis. Electron trajectories are also found for the 1s-2p0 transition problem under the Schrödinger equation; it is shown that the transition can be characterized by a comparison of the trajectory to the relevant eigenstate trajectories. The structures of the computed trajectories are relevant to the question of the possible evolution of a quantum distribution towards the standard quantum distribution (quantum equilibrium); this process is known as quantum relaxation. The transition problem is generalized to include all possible transitions in hydrogen stimulated by semi-classical radiation, and all of the trajectories found are examined in light of their implications for the evolution of the distribution to the standard distribution. Several promising avenues for future research are discussed.

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Cayayan, Lyndon Mark D. "Collective Quantum Jumps of Rydberg Atoms Undergoing Two-Channel Spontaneous Emission." Miami University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=miami1470410030.

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Botheron, Pierre. "Approches classique, quantique et bohmienne de la dynamique électronique de systèmes atomiques en champ fort." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14201/document.

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On s'intéresse à la dynamique électronique de systèmes atomiques soumis à une impulsion laser brève et intense ou à l'impact d'un ion positivement chargé. On procède alors à une comparaison détaillée des descriptions classique et quantique de ces interactions. Sur la base de cette comparaison, on développe une méthode auto-cohérente de trajectoires quantiques, basée sur l'approche hydrodynamique de Bohm. Cette méthode permet d'obtenir des observables très précises tout en conservant le caractère illustratif des méthodes de trajectoires classiques
We are interested in the electronic dynamic of atomic system under influence of a short and intense laser pulse or induced by impact of positively charged ion. We then proceeds in a deeper comparative study of classical and quantal description of these interactions. On the basis of this study, we developped a self-consistent quantum trajectory method, based on the hydrodynamical formulation of Bohm. This method allow to obtain very precise observable while retaining the illustrative character of classical trajectory method

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Yip, Ka Wa. "Optical pumping of multiple atoms in the single photon subspace of two-mode cavity QED." Miami University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=miami1438288697.

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Mazzoni, Michele. "Generalized hydrodynamics of a (1+1)-dimensional integrable scattering theory with roaming trajectories." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23209/.

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The emergence of hydrodynamic features in off-equilibrium (1 + 1)-dimensional integrable quantum systems has been the object of increasing attention in recent years. In this Master Thesis, we combine Thermodynamic Bethe Ansatz (TBA) techniques for finite-temperature quantum field theories with the Generalized Hydrodynamics (GHD) picture to provide a theoretical and numerical analysis of Zamolodchikov’s staircase model both at thermal equilibrium and in inhomogeneous generalized Gibbs ensembles. The staircase model is a diagonal (1 + 1)-dimensional integrable scattering theory with the remarkable property of roaming between infinitely many critical points when moving along a renormalization group trajectory. Namely, the finite-temperature dimensionless ground-state energy of the system approaches the central charges of all the minimal unitary conformal field theories (CFTs) M_p as the temperature varies. Within the GHD framework we develop a detailed study of the staircase model’s hydrodynamics and compare its quite surprising features to those displayed by a class of non-diagonal massless models flowing between adjacent points in the M_p series. Finally, employing both TBA and GHD techniques, we generalize to higher-spin local and quasi-local conserved charges the results obtained by B. Doyon and D. Bernard [1] for the steady-state energy current in off-equilibrium conformal field theories.

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Grigolo, Adriano 1986. "Multiconfigurational trajectory-guided quantum dynamics with generalized coherent states = Dinâmica quântica multiconfiguracional guiada por trajetórias com estados coerentes generalizados." [s.n.], 2017. http://repositorio.unicamp.br/jspui/handle/REPOSIP/330489.

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Orientador: Marcus Aloizio Martinez de Aguiar
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin
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Resumo: Uma versão generalizada do método 'coupled coherent states' é desenvolvida para estados coerentes associados a grupos de Lie arbitrários. Em contraste com a abordagem original, restrita a funções de base gaussianas, o método estendido é adequado para propagação de estados quânticos de sistemas exibindo propriedades físicas destituídas de análogo clássico, tais como graus de liberdade de spin ou indistinguibilidade de partículas. A formulação para o caso de sistemas com um número fixo de partículas idênticas interagentes é examinada em detalhe, sendo este um caso relevante descrito em termos de estados coerentes do grupo especial unitário. A técnica é ilustrada com aplicações simples, envolvendo modelos de Hubbard bosônicos e fermiônicos. Diversos aspectos da implementação numérica são discutidos
Abstract: A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original approach, which is restricted to frozen-Gaussian basis sets, the extended method is suitable for propagating quantum states of systems featuring non-classical physical properties, such as spin degrees of freedom or particle interchange symmetry. The formulation for the relevant case of number-conserving systems of interacting identical particles, most adequately described in terms of coherent states of the special unitary group, is studied in detail. The technique is illustrated with applications to simple Hubbard-like models for both bosons and fermions. Several aspects of the numerical implementation are discussed
Doutorado
Física
Doutor em Ciências
2011/20065-4
141338/2011-3
FAPESP
CNPQ

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Collet, François. "Short scale study of 4-simplex assembly with curvature, in euclidean Loop Quantum Gravity." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4076/document.

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Une étude d'un assemblage symétrique de trois 4-simplex en géométrie classique, de Regge et quantique. Nous étudions les propriétés géométriques et surtout la présence de courbure. Nous montrons que les géométries classique et de Regge de l'assemblage ont une courbure qui évolue en fonction de ses paramètres de bordure. Pour la géométrie quantique, une version euclidienne du modèle EPRL est utilisé avec une valeur pratique du paramètre Barbero-Immirzi pour définir l'amplitude de transition de l'ensemble et de ses composants. Un code C ++ est conçu pour calculer les amplitudes et étudier numériquement la géométrie quantique. Nous montrons qu'une géométrie classique, avec une courbure, émerge déjà à bas spin. Nous reconnaissons également l'apparition de configurations dégénérées et de leurs effets sur la géométrie attendue
A study of symmetrical assembly of three euclidean 4-simplices in classical, Regge and quantum geometry. We study the geometric properties and especially the presence of curvature. We show that classical and Regge geometry of the assembly have curvature which evolves in function of its boundary parameters. For the quantum geometry, a euclidean version of EPRL model is used with a convenient value of the Barbero-Immirzi parameter to define the transition amplitude of the assembly and its components. A C++ code is design for compute the amplitudes and study numerically the quantum geometry. We show that a classical geometry, with curvature, emerges already at low spin. We also recognize the appearance of the degenerate configurations and their effects on the expected geometry

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44

López, José G. "Theoretical studies of the dynamics and spectroscopy of weakly bound systems." The Ohio State University, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=osu1127220592.

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Jack, Michael Wong. "Non-Markovian Quantum Trajectories." 1999. http://hdl.handle.net/2292/2237.

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The technique of quantum trajectories (stochastic Schrödinger equations or Monte Carlo wave functions) for open systems is generalized to the non-Markovian regime. I consider a microscopic model of an open system consisting of a boson field coupled linearly (with an excitation preserving coupling) to a localized system. The model allows for a field with an arbitrary dispersion relation and an arbitrary mode-dependent coupling to the system. The trajectories are formulated as continuous measurements of the output field from the system. For a general dispersive field these measurements must be distributed in space for this formulation to be possible. The result of this formulation is a non-Markovian equation for the system conditioned on the measurements. A method of numerically simulating this equation has been determined and implemented in some test cases. Numerical simulation is possible if one can introduce a finite memory time for the evolution of the reduced system. As an illustration, the method is applied to the spectral detection of the emission from a driven two-level atom and also to an atom radiating into an electromagnetic field where the free space modes of the electromagnetic field are altered by the presence of a cavity. In both cases the non-Markovian behaviour arises from the uncertainty in the time of emission of a photon that is later detected (or reabsorbed), although, in the second case, the non-Markovian behaviour is intrinsic to the system environment coupling whereas, in the spectral detection case, it is a consequence of the choice of measurement process. The generalization of the techniques of quantum trajectories to the non-Markovian regime promises to make a range of open system problems where the Born-Markov approximation is invalid tractable to numerical simulation.
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Coffey, Timothy Michael 1970. "Non-dynamical quantum trajectories." Thesis, 2010. http://hdl.handle.net/2152/ETD-UT-2010-12-2235.

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Commonly held opinion is that particle trajectory descriptions are incompatible with quantum mechanics. Louis de Broglie (1926) first proposed a way to include trajectories in quantum mechanics, but the idea was abandoned until David Bohm (1952) re-invented and improved the theory. Bohm interprets the particle trajectories as physically real; for example, an electron actually is a particle moving on a well defined trajectory with a position and momentum at all times. By design, Bohm's trajectories never make predictions that differ from standard quantum mechanics, and their existence cannot be experimentally verified. Three new methods to obtain Bohm's particle trajectories are presented. The methods are non-dynamical, and utilize none of Bohm's equations of motion; in fact, two of the methods have no equations for a particle's trajectory. Instead, all three methods use only the evolving probability density ρ=ψ*ψ to extract the trajectories. The first two methods rest upon probability conservation and density sampling, while the third method employs the informational or geometrical construction of centroidal Voronoi tessellations. In one-dimension all three methods are proved to be equivalent to Bohm's particle trajectories. For higher dimensional configuration spaces, the first two methods can be used in limited situations, but the last method can be applied in all cases. Typically, the resulting higher dimensional non-dynamical trajectories are also identical to Bohm. Together the three methods point to a new interpretation of Bohm's particle trajectories, namely, the Bohm trajectories are simply a kinematic portrayal of the evolution of the probability density. In addition, the new methods can be used to measure Schrödinger's wave function and Planck's constant.
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Chou, Chia-Chun. "Analytical study of complex quantum trajectories." Thesis, 2009. http://hdl.handle.net/2152/ETD-UT-2009-05-36.

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Quantum trajectories are investigated within the complex quantum Hamilton-Jacobi formalism. A unified description is presented for complex quantum trajectories for one-dimensional time-dependent and time-independent problems. Complex quantum trajectories are examined for the free Gaussian wave packet, the coherent state in the harmonic potential, and the the barrier scattering problems. We analyze the variations of the complex-valued kinetic energy, the classical potential, and the quantum potential along the complex quantum trajectories. For one-dimensional time-independent scattering problems, we demonstrate general properties and similar structures of the complex quantum trajectories and the quantum potentials. In addition, it is shown that a quantum vortex forms around a node in the wave function in complex space, and the quantized circulation integral originates from the discontinuity in the real part of the complex action. Although the quantum momentum field displays hyperbolic flow around a node, the corresponding Polya vector field displays circular flow. Moreover, local topologies of the quantum momentum function and the Polya vector field are thoroughly analyzed near a stagnation point or a pole (including circular, hyperbolic, and attractive or repulsive structures). The local structure of the quantum momentum function and the Polya vector field around a stagnation point are related to the first derivative of the quantum momentum function. However, the magnitude of the asymptotic structures for these two fields near a pole depends only on the order of the node in the wave function. Finally, quantum interference is investigated and it leads to the formation of the topological structure of quantum caves in space-time Argand plots. These caves consist of the vortical and stagnation tubes originating from the isosurfaces of the amplitude of the wave function and its first derivative. Complex quantum trajectories display helical wrapping around the stagnation tubes and hyperbolic deflection near the vortical tubes. Moreover, the wrapping time for a specific trajectory is determined by the divergence and vorticity of the quantum momentum field. The lifetime for interference features is determined by the rotational dynamics of the nodal line in the complex plane. Therefore, these results demonstrate that the complex quantum trajectory method provides a novel perspective for analysis and interpretation of quantum phenomena.
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Rowland, Bradley Allen 1979. "Complex quantum trajectories for barrier scattering." Thesis, 2007. http://hdl.handle.net/2152/3811.

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We have directed much attention towards developing quantum trajectory methods which can accurately predict the transmission probabilities for a variety of quantum mechanical barrier scattering processes. One promising method involves solving the complex quantum Hamilton-Jacobi equation with the Derivative Propagation Method (DPM). We present this method, termed complex valued DPM (CVDPM(n)). CVDPM(n) has been successfully employed in the Lagrangian frame to accurately compute transmission probabilities on 'thick' one dimensional Eckart and Gaussian potential surfaces. CVDPM(n) is able to reproduce accurate results with a much lower order of approximation than is required by real valued quantum trajectory methods, from initial wave packet energies ranging from the tunneling case (E[subscript o]=0) to high energy cases (twice the barrier height). We successfully extended CVDPM(n) to two-dimensional problems (one translational degree of freedom representing an Eckart or Gaussian barrier coupled to a vibrational degree of freedom) in the Lagrangian framework with great success. CVDPM helps to explain why barrier scattering from "thick" barriers is a much more well posed problem than barrier scattering from "thin" barriers. Though results in these two cases are in very good agreement with grid methods, the search for an appropriate set of initial conditions (termed an 'isochrone) from which to launch the trajectories leads to a time-consuming search problem that is reminiscent of the rootsearching problem from semi-classical dynamics. In order to circumvent the isochrone problem, we present CVDPM(n) equations of motion which are derived and implemented in the arbitrary Lagrangian-Eulerian frame for a metastable potential as well as the Eckart and Gaussian surfaces. In this way, the isochrone problem can be circumvented but at the cost of introducing other computational difficulties. In order to understand why CVDPM may give better transmission probabilities than real valued counterparts, much attention we have been studying and applying numerical analytic continuation techniques to visualize complex-extended wave packets as well as the complex-extended quantum potential. Numerical analytic continuation techniques have also been used to analytically continue a discrete real-valued potential into the complex plane for CVDPM with very promising results.

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Yen-JiunChen and 陳彥均. "Quantum Chaos Control by Complex Trajectories." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/23849657514169077641.

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碩士
國立成功大學
航空太空工程學系碩博士班
98
In recent years, analysis and control of quantum chaos is increasingly important, but the lack of the concept of trajectory makes it impossible to analyze quantum chaos by the methods used in classical chaos. The aim of this thesis is to connect the Newton’s world to the quantum world by the complex mechanics so that quantum chaos can be analyzed and controlled by the complex-extended Newtonian mechanics. Through the bridge of complex mechanics, in this thesis we model quantum motions for 2D charged anisotropic harmonic oscillator by complex-valued dynamic equations based on which quantum chaos can be analyzed by using well-known methods used in classical chaos. With the established quantum dynamic model, we then apply the sliding-mode control method to control the chaotic quantum behavior of the considered quantum system. The simulation results show that chaotic motions can be changed into periodic motions by the proposed chaos control and meanwhile, chaos synchronization can be achieved in the presence of variations of initial conditions. Several signatures of chaos are introduced here to justify the chaos to periodicity process under the sliding-mode control law.

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Wei, Chia-Hung, and 魏嘉宏. "A Study on Quantum Chaos and Quantum Probability from the Viewpoint of Complex Quantum Trajectories." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/88220137415754845449.

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博士
國立成功大學
航空太空工程學系碩博士班
97
On the basis of quantum Hamilton mechanics, several issues are addressed in this dissertation. First of all, we study the multi-path behavior of quantum systems by virtue of the complex trajectory interpretation of quantum mechanics. It is shown that Feynman’s path-integral trajectories can be represented by the complex trajectories and then parameterized within the framework of quantum Hamilton mechanics. Next, two simplified physical systems, a 1D harmonic oscillator and a 2D charged anisotropic harmonic oscillator in a uniform magnetic field, are demonstrated to exhibit chaos from the viewpoint of particle-like behavior. While conventional quantum mechanics and Bohmian mechanics both predict that 1D harmonic oscillator shows no signature of chaotic behavior, we find that in quantum Hamilton mechanics this system exhibits both regular and chaotic behavior, depending on the composition of wavefunctions and on the particle’s initial position. We continue to investigate chaotic behavior in a 2D charged anisotropic harmonic oscillator. Even the possibility of chaos in eigenstates has been ruled out from Bohm’s trajectory interpretation, we still find obvious chaotic features in eigenstates of this 2D quantum oscillator. The territory of quantum chaos indeed can be enlarged via the complex-extended dynamics. Finally, we point out that the complex chaotic dynamics may be the origin of the probability interpretation of quantum mechanics. In view of the generality of quantum chaos, it is impossible to predict the final states from the initial states for quantum systems. However, the statistical invariability of chaotic behavior offers another route for us to understand quantum systems. In this dissertation, the comparison between the distribution of complex quantum trajectories on the real coordinate space and the theoretic probability density function determined from the wavefunction shows that a chaotic quantum particle which seems to move irregularly is indeed guided by the wavefunction and attempts to appear somewhere with a statistical regularity. We also examine this tendency for Bohmian trajectories, however, no analogue of the complex trajectories can be found.

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Dissertations / Theses on the topic 'Quantum trajectorie'

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