Tesi: "Many-Body quantum physics"

1

Jia, Ningyuan. "Quantum Many-Body Physics with Photons". Thesis, The University of Chicago, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10928150.

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Understanding and manipulating quantum materials is a long-sought goal in both the condensed matter and cold atom communities. Photons have recently emerged as a good candidate for studying quantum many-body states due to their fast dynamics and convenient manipulation. Tremendous efforts have been made to engineer single particle Hamiltonian with non-trivial topology. Having individual photons to strongly collide with each other and form an entangled many-body state remained as a challenge in optical domain.

In this thesis, I will first demonstrate how to engineer artificial magnetic field and non-trivial topology for microwave photons. In a classical lumped element circuit, we demonstrate the edge modes for microwave photons within the bulk band, and also show that these modes propagates with topological protection against the local lattice disorder. This work paves the way to synthesize correlated quantum materials in a lattice using microwave photons, combined with circuit QED technique.

Recently, Rydberg-Rydberg interaction has been broadly used in cold atom experiment to generate long-range inter-particle coupling for quantum information processing and quantum material simulation. We combine this technique with cavity electromagnetically induced transparency and create a robust quasi-particle, cavity Rydberg polaritons, which harness the power from both cavity photons with exotic topology and Rydberg atoms with strong interactions. We first demonstrate the interaction in the single quanta level in a quantum dot with single cavity mode and further expand it into multi-mode regime with modulated atomic states.

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2

Bausch, Johannes Karl Richard. "Quantum stochastic processes and quantum many-body physics". Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/269857.

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This dissertation investigates the theory of quantum stochastic processes and its applications in quantum many-body physics. The main goal is to analyse complexity-theoretic aspects of both static and dynamic properties of physical systems modelled by quantum stochastic processes. The thesis consists of two parts: the first one addresses the computational complexity of certain quantum and classical divisibility questions, whereas the second one addresses the topic of Hamiltonian complexity theory. In the divisibility part, we discuss the question whether one can efficiently sub-divide a map describing the evolution of a system in a noisy environment, i.e. a CPTP- or stochastic map for quantum and classical processes, respectively, and we prove that taking the nth root of a CPTP or stochastic map is an NP-complete problem. Furthermore, we show that answering the question whether one can divide up a random variable $X$ into a sum of $n$ iid random variables $Y_i$, i.e. $X=\sum_{i=1}^n Y_i$, is poly-time computable; relaxing the iid condition renders the problem NP-hard. In the local Hamiltonian part, we study computation embedded into the ground state of a many-body quantum system, going beyond "history state" constructions with a linear clock. We first develop a series of mathematical techniques which allow us to study the energy spectrum of the resulting Hamiltonian, and extend classical string rewriting to the quantum setting. This allows us to construct the most physically-realistic QMAEXP-complete instances for the LOCAL HAMILTONIAN problem (i.e. the question of estimating the ground state energy of a quantum many-body system) known to date, both in one- and three dimensions. Furthermore, we study weighted versions of linear history state constructions, allowing us to obtain tight lower and upper bounds on the promise gap of the LOCAL HAMILTONIAN problem in various cases. We finally study a classical embedding of a Busy Beaver Turing Machine into a low-dimensional lattice spin model, which allows us to dictate a transition from a purely classical phase to a Toric Code phase at arbitrarily large and potentially even uncomputable system sizes.

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3

Biella, Alberto. "Many-body physics in open quantum systems". Doctoral thesis, Scuola Normale Superiore, 2016. http://hdl.handle.net/11384/85905.

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4

Besserve, Pauline. "Quantum-classical hybrid algorithms for quantum many-body physics". Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAX086.

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Cette thèse étudie l'apport du calcul quantique bruité pour l’algorithme phare des fortes corrélations, la théorie du champ moyen dynamique (DMFT). Elle vise à mettre à profit les premiers dispositifs de calcul quantique, malgré leurs imperfections liées à un degré de contrôle expérimental encore limité. Dans un premier temps, une version améliorée de la méthode variationnelle de préparation de l'état fondamental du modèle d'impureté est proposée. Elle consiste en la réalisation de mises à jour de la base à une particule dans laquelle est décrit le Hamiltonien d'impureté. Ces mises à jour sont entrelacées avec des optimisations variationnelles de l'état, et guidées par la matrice densité à une particule de l'état variationnel optimisé courant. Cet algorithme nous a permis de réaliser la première implémentation hybride bruitée d'un schéma assimilé à la DMFT avec un système auxiliaire à deux impuretés. Aussi, nous montrons sur plusieurs exemples que cette méthode est capable d'augmenter la capacité d'un circuit variationnel donné à représenter l'état cible. Enfin, nous proposons de combiner les mises à jour de la base à une particule avec un algorithme variationnel dit adaptatif, qui construit le circuit itérativement. Nous montrons que cette approche permet de réduire, à précision donnée sur l'énergie de l'état optimisé, le nombre de portes du circuit. Dans un second temps, nous proposons de mettre à profit la dissipation qui affecte les qubits afin de diminuer les effets de la troncation du bain sur l'ajustement de l'hybridation du bain à celle de la DMFT. Nous montrons qu'une réduction en termes de sites de bain est bien à la portée d'une telle méthode. Cependant, nous faisons l'hypothèse d'un processus dissipatif qui n'est pas réaliste : la méthode doit donc encore être étudiée via un modèle plus proche des conditions expérimentales
This thesis investigates the possibility to leverage noisy quantum computation within the flagship algorithm for strong correlations, the dynamical mean-field theory (DMFT). It aims to take advantage of the first quantum computing devices, despite their imperfections imputable to a still-limited degree of experimental control.Firstly, an improved version of the variational method for preparing the ground state of the impurity model is proposed. It consists in carrying out updates of the single-particle basis in which the impurity Hamiltonian is described. These updates are interwoven with variational optimizations of the state, and guided by the one-particle density matrix of the current optimized variational state. This algorithm has enabled us to carry out the first noisy hybrid implementation of a DMFT-like scheme with a two-impurity auxiliary system. Also, we show on several examples that this method is capable of increasing the ability of a given variational circuit to represent the target state. Finally, we propose to combine single-particle basis updates with an adaptive variational algorithm, which builds the circuit iteratively. We show that this approach can reduce the number of gates in the circuit for a given precision in the energy of the attained state.Secondly, we propose to take advantage of the dissipation affecting the qubits to alleviate the effect of bath truncation onto the fit of the DMFT hybridization. We confirm that a reduction in the count of bath sites is within the reach of such a method. However, we make the assumption of a dissipative process which is not realistic: the method therefore still needs to be studied via a model closer to experimental conditions

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5

Yoshida, Beni. "Studying many-body physics through quantum coding theory". Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/77257.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (p. 133-140).
The emerging closeness between correlated spin systems and error-correcting codes enables us to use coding theoretical techniques to study physical properties of many-body spin systems. This thesis illustrates the use of classical and quantum coding theory in classifying quantum phases arising in many-body spin systems via a systematic study of stabilizer Hamiltonians with translation symmetries. In the first part, we ask what kinds of quantum phases may arise in gapped spin systems on a D-dimensional lattice. We address this condensed matter theoretical question by giving a complete classification of quantum phases arising in stabilizer Hamiltonians at fixed points of RG transformations for D = 1; 2; 3. We found a certain dimensional duality on geometric shapes of logical operators where m-dimensional and (D m)-dimensional logical operators always form anti-commuting pairs (m is an integer). We demonstrate that quantum phases are completely classified by topological characterizations of logical operators where topological quantum phase transitions are driven by non-analytical changes of geometric shapes of logical operators. As a consequence, we argue that topological order is unstable at any nonzero temperature and self-correcting quantum memory in a strict sense may not exist where the memory time is upper bounded by some constant at a fixed temperature, regardless of the system size. Our result also implies that topological field theory is the universal theory for stabilizer Hamiltonians with continuous scale symmetries. In the second part, we ask the fundamental limit on information storage capacity of discrete spin systems. There is a well-known theoretical limit on the amount of information that can be reliably stored in a given volume of discrete spin systems. Yet, previously known systems were far below this theoretical limit. We propose a construction of classical stabilizer Hamiltonians which asymptotically saturate this limit. Our model borrows an idea from fractal geometries arising in the Sierpinski triangle, and is a rare manifestation of limit cycle behaviors with discrete scale symmetries in real-space RG transformations, which may be beyond descriptions of topological field theory.
by Beni Yoshida.
Ph.D.

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6

Young, Carolyn 1979. "Many-body cotunneling in coupled quantum dots". Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=101692.

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The zero-temperature equilibrium conductance of mesoscopic devices due to single-particle resonant tunneling was first described by Landauer [1]. The Landauer formula was later extended to the multi-channel case by Fisher and Lee [2], who reduced the problem of calculating electronic transport properties to the problem of solving for the Green's function for a given system geometry.
In this work, the single-particle formalism is extended to the study of higher-order two-particle cotunneling processes by considering many-body Green's functions. The effect of attaching leads to the system is described in terms of a two-particle self-energy, whose analytical form is written in terms of a Feynman path integral over all possible tunneling processes between the leads and the device. In addition, an efficient numerical technique for the calculation of the fully dressed Green's function of a device region attached to two-particle leads is presented.
The problem of two-particle transport is then approached, and an analogy to single-particle transport on the infinite plane is drawn. It is shown that, for nonspin flip cotunneling processes, the two-particle transport result can be related to the single-particle conductance by way of a simple convolution. Finally, results for the cotunneling contribution to the conductance of double quantum dots, or charge qubits, are presented.

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7

Scarlatella, Orazio. "Driven-Dissipative Quantum Many-Body Systems". Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS281/document.

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Ma thèse de doctorat était consacrée à l'étude des systèmes quantiques à plusieurs corps dissipatifs et pilotés. Ces systèmes représentent des plateformes naturelles pour explorer des questions fondamentales sur la matière dans des conditions de non-équilibre, tout en ayant un impact potentiel sur les technologies quantiques émergentes. Dans cette thèse, nous discutons d'une décomposition spectrale de fonctions de Green de systèmes ouverts markoviens, que nous appliquons à un modèle d'oscillateur quantique de van der Pol. Nous soulignons qu’une propriété de signe des fonctions spectrales des systèmes d’équilibre ne s’imposait pas dans le cas de systèmes ouverts, ce qui produisait une surprenante "densité d’états négative", avec des conséquences physiques directes. Nous étudions ensuite la transition de phase entre une phase normale et une phase superfluide dans un système prototype de bosons dissipatifs forcés sur un réseau. Cette transition est caractérisée par une criticité à fréquence finie correspondant à la rupture spontanée de l'invariance par translation dans le temps, qui n’a pas d’analogue dans des systèmes à l’équilibre. Nous discutons le diagramme de phase en champ moyen d'une phase isolante de Mott stabilisée par dissipation, potentiellement pertinente pour des expériences en cours. Nos résultats suggèrent qu'il existe un compromis entre la fidélité de la phase stationnaire à un isolant de Mott et la robustesse d'une telle phase à taux de saut fini. Enfin, nous présentons des développements concernant la théorie du champ moyen dynamique (DMFT) pour l’étude des systèmes à plusieurs corps dissipatifs et forcés. Nous introduisons DMFT dans le contexte des modèles dissipatifs et forcés et nous développons une méthode pour résoudre le problème auxiliaire d'une impureté couplée simultanément à un environnement markovien et à un environnement non-markovien. À titre de test, nous appliquons cette nouvelle méthode à un modèle simple d’impureté fermionique
My PhD was devoted to the study of driven-dissipative quantum many-body systems. These systems represent natural platforms to explore fundamental questions about matter under non-equilibrium conditions, having at the same time a potential impact on emerging quantum technologies. In this thesis, we discuss a spectral decomposition of single-particle Green functions of Markovian open systems, that we applied to a model of a quantum van der Pol oscillator. We point out that a sign property of spectral functions of equilibrium systems doesn't hold in the case of open systems, resulting in a surprising ``negative density of states", with direct physical consequences. We study the phase transition between a normal and a superfluid phase in a prototype system of driven-dissipative bosons on a lattice. This transition is characterized by a finite-frequency criticality corresponding to the spontaneous break of time-translational invariance, which has no analog in equilibrium systems. Later, we discuss the mean-field phase diagram of a Mott insulating phase stabilized by dissipation, which is potentially relevant for ongoing experiments. Our results suggest that there is a trade off between the fidelity of the stationary phase to a Mott insulator and robustness of such a phase at finite hopping. Finally, we present some developments towards using dynamical mean field theory (DMFT) for studying driven-dissipative lattice systems. We introduce DMFT in the context of driven-dissipative models and developed a method to solve the auxiliary problem of a single impurity, coupled simultaneously to a Markovian and a non-Markovian environment. As a test, we applied this novel method to a simple model of a fermionic, single-mode impurity

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8

Marzolino, Ugo. "Entanglement and decoherence in many-body physics". Doctoral thesis, Università degli studi di Trieste, 2011. http://hdl.handle.net/10077/5827.

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2009/2010
The thesis deals with several features of quantum many-body systems. They are described both in terms of reversible unitary transformations and as an environment interacting with other systems. An introductory part introduces the main ideas of quantum noise and dissipative dynamics. A chapter is also dedicated to some useful aspects of entanglement. The second part of the thesis concerns the orginal results. A chapter describes the dynamics of two qubits interacting with a common environment. This chapter is focused on the derivation of a new Markovian approximation, finer than the standard weak coupling limit, and its application on the dynamical generation of the entanglement. The second topic concerns the developping of some procedures to reconstruct the parameters governing a large class of Markovian and non-Markovian dissipative dynamics of a quantum particle. These procedures are based on the symplectic tomography of the evolved state. The third topic concerns the physics of many identical bosons, with a special focus on Bose-Einstein condensates. The relevance of entanglement and spin squeezing for quantum metrology with high accuracy is discussed in connection with the quantum Fisher information and collective and squeezing inequalities. A third part summerizes the results. Some useful tools are described in the appendices.
XXIII Ciclo
1983

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9

Brell, Courtney Gordon Gray. "Many-body models for topological quantum information". Thesis, The University of Sydney, 2014. http://hdl.handle.net/2123/13539.

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We develop and investigate several quantum many-body spin models of use for topological quantum information processing and storage. These models fall into two categories: those that are designed to be more realistic than alternative models with similar phenomenology, and those that are designed to have richer phenomenology than related models. In the first category, we present a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the perturbative low-energy limits of entirely two-body Hamiltonians. This construction reproduces the target models' behavior using only couplings which are natural in terms of the original Hamiltonians. As an extension of this work, we construct parent Hamiltonians involving only local 2-body interactions for a broad class of Projected Entangled Pair States (PEPS). We define a perturbative Hamiltonian with a finite order low energy effective Hamiltonian that is a gapped, frustration-free parent Hamiltonian for an encoded version of a desired PEPS. For topologically ordered PEPS, the ground space of the low energy effective Hamiltonian is shown to be in the same phase as the desired state to all orders of perturbation theory. We then move on to define models that generalize the phenomenology of several well-known systems. We first define generalized cluster states based on finite group algebras, and investigate properties of these states including their PEPS representations, global symmetries, relationship to the Kitaev quantum double models, and possible applications. Finally, we propose a generalization of the color codes based on finite groups. For non-Abelian groups, the resulting model supports non-Abelian anyonic quasiparticles and topological order. We examine the properties of these models such as their relationship to Kitaev quantum double models, quasiparticle spectrum, and boundary structure.

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10

Nandkishore, Rahul (Rahul Mahajan ). "Quantum many body physics in single and bilayer graphene". Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/79522.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references.
Two dimensional electron systems (2DES) provide a uniquely promising avenue for investigation of many body physics. Graphene constitutes a new and unusual 2DES, which may give rise to unexpected collective phenomena. However, the vanishing density of states in charge neutral single layer graphene suppresses many body effects, and one has to alter the system to observe strongly ordered states. We consider three ways of accessing quantum many body physics using graphene. First, we consider doping single layer graphene to a Van Hove singularity in the density of states. We show that there are strong instabilities to several strongly ordered states, with the leading instability being to a d-wave superconducting state. The superconducting state realizes chiral superconductivity, an exotic form of superconductivity wherein the phase of the order parameter winds by 4[pi] as we go around the Fermi surface. We also discuss the nature of the spin density wave state which is the principal competitor to superconductivity in doped graphene. Next, we study bilayer graphene (BLG), which has a non-vanishing density of states even at charge neutrality. We show that Coulomb interactions give rise to a zero bias anomaly in the tunneling density of states for BLG, which manifests itself at high energy scales. We also show that the quadratic band crossing in BLG is unstable to arbitrarily weak interactions, and estimate the energy scale for formation of strongly ordered states. We show that gapped states in BLG have topological properties, and we classify the various possible gapped and gapless states in terms of symmetries. We study the competition between various ordered states, and discuss how the nature of the ground state may be deduced experimentally. We also discuss recent experimental observations of strongly ordered states in bilayer graphene. Finally, we study bilayer graphene in a transverse magnetic field, focusing on the properties of the quantum Hall ferromagnet (QHF) state. We resolve an apparent discrepancy between the experimentally observed energetics and theory. We close with a discussion of the exotic topological defects that form above the QHF state.
by Rahul Nandkishore.
Ph.D.

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11

Tomadin, Andrea. "Dynamical instabilities in quantum many-body systems". Doctoral thesis, Scuola Normale Superiore, 2010. http://hdl.handle.net/11384/85874.

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from the introduction: "[...] This thesis addresses the problem of the nonequilibrium time-evolution of many-body sistems realized with quantum simulators. We investigate theoretically the relation between the time-evolution and the equilibrium phase diagram in the presence of a quantum phase transition. The long-time evolution of the systems is investigated, both in the case of conservative dynamics and under the action of dissipative processes. The thesis is organized as follows. Chaps. 1-3 contain theoretical and experimental facts that are relevant to the present work. In the Chap. 1 we describe the quantum simulator realized with fermionic cold atoms in the bulk of an optical trap. In the Chap. 2 we describe the microresonators where light and matter are strongly coupled, and we focus on the implementation of a quantum simulator with defect-cavities in photonic crystals. In Chap. 3 several theoretical works concerning the nonequilibrium dynamics of many-body systems are summarized. Chaps. 4{6 contain the original contributions of this thesis. In Chap. 4 we investigate the time-evolution of an ensemble of fermionic atoms after an abrupt change of the interaction strength from a vanishing to a weak attractive value. In Chap. 5 we demonstrate the possibility to measure the quantum phase transition between a super fluid and a Mott-insulator state in an array of microresonators, in the presence of the leakage of photons out of the cavities. In Chap. 6 we study a system of cold bosonic atoms coupled to a tailored bath that dissipatively drives the system into a super fluid or into a thermal state.

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12

Hallnäs, Martin. "Exactly solved quantum many-body systems in one dimension". Licentiate thesis, KTH, Physics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-564.

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This thesis is devoted to the study of various examples of exactly solved quantum many-body systems in one-dimension. It is divided into two parts: the ¯rst provides background and complementary results to the second, which consists of three scienti¯c papers. The ¯rst paper concerns a particu- lar extension, corresponding to the root system CN, of the delta-interaction model. We prove by construction that its exact solution, even in the gen- eral case of distinguishable particles, can be obtained by the coordinate Bethe ansatz. We also elaborate on the physical interpretation of this model. It is well known that the delta-interaction is included in a four parameter family of local interactions. In the second paper we interpret these parameters as cou- pling constants of certain momentum dependent interactions and determine all cases leading to a many-body system of distinguishable particles which can be solved by the coordinate Bethe ansatz. In the third paper we consider the so-called rational Calogero-Sutherland model, describing an arbitrary number of particles on the real line, con¯ned by a harmonic oscillator potential and interacting via a two-body interaction proportional to the inverse square of the inter-particle distance. We construct a novel solution algorithm for this model which enables us to obtain explicit formulas for its eigenfunctions. We also show that our algorithm applies, with minor changes, to all extensions of the rational Calogero-Sutherland model which correspond to a classical root system.

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13

Sengupta, Sanghita. "Quantum Many - Body Interaction Effects In Two - Dimensional Materials". ScholarWorks @ UVM, 2018. https://scholarworks.uvm.edu/graddis/939.

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In this talk, I will discuss three problems related to the novel physics of two-dimensional quantum materials such as graphene, group-VI dichalcogenides family (TMDCs viz. MoS2 , WS2, MoSe2 , etc) and Silicene-Germanene class of materials. The first problem poses a simple question - how do the quantum excitations in a graphene membrane affect adsorption? Using the tools of diagrammatic perturbation theory, I will derive the scattering rates of a neutral atom on a graphene membrane. I will show how this seemingly naive model can serve as a non-relativistic condensed matter analogue of the infamous infrared problem in Quantum Electrodynamics. In the second problem, I will move from the framework of a single atom adsorption to a collective behavior of fluids near graphene and TMDC - interfaces. Following the seminal work of Dzyaloshinskii-Lifshitz-Pitaevskii on van der Waals interactions, I will develop a theory of liquid film growth on 2 dimensional surfaces. Additionally, I will report an exotic phenomenon of critical wetting instability which is a result of the dielectric engineering and discuss experimental and technological implications. Finally, the last problem will see the introduction of spin-orbit coupling effects in the 2D topological insulator family of Silicene-Germanene class of materials. I will present a unified theory for their in-plane magnetic field response leading to "anomalous", i.e electron interaction-dependent spin-flip transition moment. Can this correction to spin-flip transition moment be measured? I will propose magneto-optical experimental techniques that can probe the effects.

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14

Brandao, Fernando G. S. L. "Entanglement theory and the quantum simulation of many-body physics". Thesis, Imperial College London, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491112.

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Quantum mechanics led us to reconsider the scope of physics and its building principles, such as the notions of realism and locality. More recently, quantum mechanics has changed in an equal dramatic manner our understanding of information processing and computation. On one hand, the fundamental properties of quantum systems can be harnessed to transmit, store, and manipulate information in a much more efficient and secure way than possible in the realm of classical physics. On the other hand, the development of systematic procedures to manipulate systems of a large number of particles in the quantum regime, crucial to the implementation of quantum based information processing, has triggered new possibilities in the exploration of quantum many-body physics and related areas. In this thesis, we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement, intrinsically quantum correlations of key importance in quantum information theory, and the exploration of the use of controlled quantum systems to the computation and simulation of quantum many-body phenomena. In the first part we introduce a new approach to the study of entanglement by considering its manipulation under operations not capable of generating entanglement. In this setting we show how the landscape of entanglement conversion is reduced to the simplest situation possible: one unique measure completely specifying which transformations are achievable. This framework has remarkable connections with the foundations of thermodynamics, which we present and explore. On the way to establish our main result, we develop new techniques that are of interest on their own. First, we extend quantum Stein's Lemma, characterizing optimal rates in state discrimination, to the case where the alternative hypothesis might vary over particular sets of possibly correlated (non-LLd) states. Second, we show how recent advances in quantum de Finetti type theorems can be employed to decide when the entanglement contained in non-LLd. sequences of states is distillable by local operations and classical communication. In the second part we discuss the usefulness of a quantum computer to the determination of properties of many-body systems. Our first result is a new quantum procedure, based on the phase estimation quantum algorithm, to calculate additive approximations to partition functions and spectrum densities of quantum local Hamiltonians. We give convincing evidence that quantum computation is superior to classical in solving both problems by showing that they are complete for the class of problems efficiently solved in the one-c1ean-qubit model of quantum computation, which is believe to contain classically hard problems. We then present a negative result on the usefulness of quantum computers and prove that the determination of the ground state energy of local quantum Hamiltonians, with the promise that the gap is larger than an inverse polynomial in the number of sites, is hard for the class QCMA, which is believed to contain intractable problems even for quantum computation. In the third and last part, we approach the problem of quantum simulating many-body systems from a more pragmatic point of view. Based on recent experimental developments on cavity quantum electrodynamics, more specifically on the fabrication of arrays of interacting micro-cavities and on their coupling to atomic-like structures in several physical set-ups, we propose and analyse the realization of paradigmatic condensed matter models in such systems, such as the Bose-Hubbard and the anisotropic Heisenberg models. We presentÃ‚Â· promising properties of such coupled-cavity arrays as simulators of quantum many-body physics, such as the full addressability of individual sites and the access to inhomogeneous models, and discuss the feasibility of an experimental realization with state-of-the-art current technology.

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Chen, Xie Ph D. Massachusetts Institute of Technology. "Many-body entanglement in gapped quantum systems : representation, classification, and application". Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/79515.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 189-205).
Entanglement is a special form of quantum correlation that exists among quantum particles and it has been realized that surprising things can happen when a large number of particles are entangled together. For example, topological orders emerge in condensed matter systems where the constituent 1023 particles are entangled in a nontrivial way; moreover, quantum computers, which can perform certain tasks significantly faster than classical computers, are made possible by the existence of entanglement among a large number of particles. However, a systematic understanding of entanglement in many-body systems is missing, leaving open the questions of what kinds of many-body entanglement exist, where to find them and what they can be used for. In this thesis, I present my work towards a more systematic understanding of many-body entanglement in systems where the particles interact with each other locally and the ground state of the system is separated from the excited states by a finite energy gap. Under such physically realistic locality and gap constraints, I am able to obtain more understanding concerning the efficient representation of many-body entangled states, the classification of such states according to their universal properties and the application of such states in quantum computation. More specifically, this thesis is focused on the tensor network representation of many-body entangled states and studies how the tensors in the representation reflect the universal properties of the states. An algorithm is presented to extract the universal properties from the tensors and certain symmetry constraints are found necessary for the tensors to represent states with nontrivial topological order. Classification of gapped quantum states is then carried out based on this representation. An operational procedure relating states with the same universal properties is established which is then applied to systems in one and higher dimensions. This leads not only to the discovery of new quantum phases but also to a more systematic understanding of them. A more complete understanding of possible many-body entanglement structures enables us to design an experimentally more feasible many-body entangled state for application in measurement-based quantum computation. Moreover, the framework of measurement-based quantum computation is generalized from spin to fermion systems leading to new possibilities for experimental realization.
by Xie Chen.
Ph.D.

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16

Shi, Bowen. "Anyon theory in gapped many-body systems from entanglement". The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587705058308889.

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17

Roumiantsev, Ilia. "Many-body effects in low-order optical nonlinearities of semiconductor quantum wells". Diss., The University of Arizona, 2003. http://hdl.handle.net/10150/280383.

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This dissertation addresses both fundamental aspects of Coulomb correlations in semiconductor quantum wells and more practical aspects of theoretical analysis of semiconductor optoelectronic devices. After introducing the subject, we present and evaluate a state-of-the-art theory of the third order coherent optical response of a semiconductor quantum well based on the Dynamics Controlled Truncation (DCT) scheme. Already in the third order (the so-called chi (3)) regime, semiconductors exhibit a number of many-body Coulomb correlation effects. Their manifestation in various multi-pulse experimental configurations, customarily used in ultrafast semiconductor spectroscopy, has been an important component of this thesis. Coherent optical effects in a semiconductor 3-band system based on the heavy-hole, light-hole and conduction bands were investigated. The quantum beats in the time-integrated differential transmission signal were analyzed and compared with experimental data obtained at the University of Iowa. Fundamental differences from corresponding quantum beats in atomic 3-level systems were found. Also, the analysis of experimental data (obtained at the University of Arizona) of the coupled heavy-hole-light-hole optical Stark shift revealed evidence of intervalence band coherences, an analog of Raman coherences in atomic 3-levels systems. A scheme for realization of electromagnetically-induced transparency (EIT) based on the interference of excitonic and biexcitonic coherences was proposed. Corresponding experiments performed at the University of Oregon showed indeed a considerable coherent reduction of excitonic absorption. Furthermore, an extension of the chi(3) analysis revealed an energy renormalization of the biexciton, in good agreement with the corresponding experiment. A microscopic analysis of polarization dynamics in time-resolved four-wave mixing signals was performed, revealing interesting implications for the biexciton dephasing in addition to the significance of many-body correlations. In the case of four-wave mixing in semiconductor microcavities, our theoretical analysis in conjunction with experimental data obtained at the University of Tokyo gave us indications for a significant shortcoming of the second Born approximation (2nd BA) applied to two-exciton Coulomb correlations in a thin semiconductor quantum well, in agreement with the general knowledge of the qualitative failure of the 2nd BA in systems with short-range interaction in two dimensions. We also analyzed a novel all-optical switching technique based on the nonlinear polarization rotation. Apart from identifying the many-particle processes relevant for the switch operation in the chi(3) regime, we proposed ways to further optimize the switch.

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18

Hallnäs, Martin. "Quantum many-body systems exactly solved by special functions". Doctoral thesis, KTH, Teoretisk fysik, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4416.

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This thesis concerns two types of quantum many-body systems in one dimension exactly solved by special functions: firstly, systems with interactions localised at points and solved by the (coordinate) Bethe ansatz; secondly, systems of Calogero-Sutherland type, as well as certain recently introduced deformations thereof, with eigenfunctions given by natural many-variable generalisations of classical (orthogonal) polynomials. The thesis is divided into two parts. The first provides background and a few complementary results, while the second presents the main results of this thesis in five appended scientific papers. In the first paper we consider two complementary quantum many-body systems with local interactions related to the root systems CN, one with delta-interactions, and the other with certain momentum dependent interactions commonly known as delta-prime interactions. We prove, by construction, that the former is exactly solvable by the Bethe ansatz in the general case of distinguishable particles, and that the latter is similarly solvable only in the case of bosons or fermions. We also establish a simple strong/weak coupling duality between the two models and elaborate on their physical interpretations. In the second paper we consider a well-known four-parameter family of local interactions in one dimension. In particular, we determine all such interactions leading to a quantum many-body system of distinguishable particles exactly solvable by the Bethe ansatz. We find that there are two families of such systems: the first is described by a one-parameter deformation of the delta-interaction model, while the second features a particular one-parameter combination of the delta and the delta-prime interactions. In papers 3-5 we construct and study particular series representations for the eigenfunctions of a family of Calogero-Sutherland models naturally associated with the classical (orthogonal) polynomials. In our construction, the eigenfunctions are given by linear combinations of certain symmetric polynomials generalising the so-called Schur polynomials, with explicit and rather simple coefficients. In paper 5 we also generalise certain of these results to the so-called deformed Calogero-Sutherland operators.
QC 20100712

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19

Keck, Maximilian. "Many-body open quantum systems: from dynamics to thermodynamics". Doctoral thesis, Scuola Normale Superiore, 2019. http://hdl.handle.net/11384/85919.

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This thesis studies problems concerning the dynamics and thermodynamics of manybody quantum systems. We start by introducing the necessary theoretical concepts and tools forming the basis of this manuscript. The research presented can be split in two parts. The first one deals with the dynamics of many-body quantum systems subject to environmental dissipative effects of various forms, while the second one studies topics of thermodynamics in many-body quantum systems. The first part of the research presented studies the effects of an environment inducing dissipation. We establish and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, which thus can help us to study the interplay between non-adiabatic transitions and dissipation in many-body quantum systems. After the adiabatic evolution, we evaluate the excess energy (average value of the Hamiltonian) as a measure of the deviation from reaching the target final ground state. We find a robust evidence of the fact that an optimal working time for the quantum annealing protocol emerges as a result of the competition between the non-adiabatic effects and the dissipative processes. We compare these results with matrix product operator simulations of an Ising system and show that the phenomenology we found applies also for this more realistic case. We then proceed to a scenario in which the environment is not detrimental, but is on the contrary the driving force of the effects studied. We demonstrate that persistent currents can be induced in a quantum system in contact with a structured reservoir, without the need of any applied gauge field. The working principle of the mechanism leading to their presence is based on the extension to the many-body scenario of non-reciprocal Lindblad dynamics. Specifically, we consider an interacting spin/boson model in a ring-shaped one-dimensional lattice coupled to an external bath. By employing a combination of cluster mean-field, exact diagonalization and matrix product operator techniques, we show that solely dissipative effects suffice to engineer steady states with a persistent current that survives in the limit of large systems. We also verify the robustness of such current in the presence of additional dissipative or Hamiltonian perturbation terms. The second part studies many-body quantum systems with a focus on thermodynamics. First, we investigate a quantum battery made of N two-level systems, which is charged by an optical mode via an energy-conserving interaction. We quantify the fraction of energy stored in the battery that can be extracted in order to perform thermodynamic work. We first demonstrate that this fraction is highly reduced by the presence of correlations between the charger and the battery or between the two-level systems composing the battery. We then show that the correlation-induced suppression of extractable energy, however, can be mitigated by preparing the charger in a coherent optical state. We conclude by proving that the charger-battery system is asymptotically free of such locking correlations in the N ! 1 limit. And lastly, we study open questions within the theory of open quantum systems. The Markovian evolution of an open quantum system is characterized by a positive entropy production, while the global entropy gets redistributed between the system and the environmental degrees of freedom. Starting from these premises, we analyse the entropy variation of an open quantum system in terms of two distinct relations: the Clausius inequality, that provides an intrinsic bound for the entropy variation in terms of the heat absorbed by the system, and an extrinsic inequality, which instead relates the former to the corresponding entropy increment of the environment. By modeling the thermalization process with a Markovian collisional model, we compare and discuss the two bounds, showing that the latter is asymptotically saturated in the limit of large interaction time. In this regime not only the reduced density matrix of the system reaches an equilibrium configuration, but it also factorizes from the environmental degrees of freedom.

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20

Kucsko, Georg. "Coupled Spins in Diamond: From Quantum Control to Metrology and Many-Body Physics". Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493597.

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The study of quantum mechanics, together with the ability to coherently control and manipulate quantum systems in the lab has led to a myriad of discoveries and real world applications. In this thesis we present experiments demonstrating precise control of an individual long-lived spin qubit as well as sensing applications for biology and investigation of quantum many-body dynamics. Stable quantum bits, capable both of storing quantum information for macroscopic time scales and of integration inside small portable devices, are an essential building block for an array of potential applications. In the second chapter of this thesis we demonstrate high-fidelity control of a solid-state qubit, which preserves its polarization for several minutes and features coherence lifetimes exceeding 1 second at room temperature. Sensitive probing of temperature variations on nanometer scales is an outstanding challenge in many areas of modern science and technology. In chapter three we show how nitrogen vacancy centers in diamond can be used as a robust, high sensitivity temperature probe. We furthermore demonstrate biological compatibility by introducing nano-sized diamonds into living cells and measuring externally induced sub-cellular temperature gradients. Understanding the dynamics of interacting many-body quantum systems with on-site potential disorder has proven one of the biggest challenges in quantum physics to investigate both in theory and experiment. In chapter four we demonstrate how coherent control techniques can be utilized to probe the many-body dynamics of a strongly interacting NV spin ensemble. Specifically, we show how a long-range interacting dipolar spin system exhibits characteristically slow thermalization in the presence of tunable disorder. The presented works offer up many new areas to investigate, including complex quantum many-body effects of large, disordered spin systems, as well as applications of NV centers as bio-compatible nano-scale temperature probes.
Physics

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21

Beconcini, Michael. "Quantum transport and many-body effects in encapsulated graphene". Doctoral thesis, Scuola Normale Superiore, 2019. http://hdl.handle.net/11384/85922.

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Unlike any other material, graphene is all surface. This means that it is strongly affected by its surroundings, including the substrate it lays upon. In the past few years, it was understood that silicon oxide (SiO2), the most popular substrate material for graphene, limits the performance of graphene devices and obscures interesting physics. Hexagonal boron nitride (hBN) has emerged as “the perfect” substrate that results in graphene devices of astonishing electronic quality. In this Thesis, we explore some peculiar nonlocal effects that are found in such new devices due to quantum transport and electron-electron interactions in the coherent as well as the diffusive regime. Chapters 1-4 are devoted to the introduction of some basic concepts and to the main experimental facts that motivated our work. Since encapsulation in hBN crystals makes graphene practically insusceptible to the environment, electrons can travel micrometer distances without scattering. In Chapter 5, in the framework of the Landauer-Büttiker scattering theory, we have developed a scaling procedure for numerical simulations of tight-binding nonlocal transport in realistic graphene devices. We have tested our method against experimental data on transverse magnetic focusing (TMF). This comparison enables a clear physical interpretation of all the observed features of the TMF signal, including its oscillating sign. Moreover, in graphene/hBN superlattices and in bilayer graphene in a perpendicular electric field, which have broken inversion symmetry, topological currents originating from graphene’s two valleys flow in opposite directions and combine to produce long-range charge neutral flow. This effect translates into a nonlocal voltage at zero magnetic fields in a narrow energy range near Dirac points at distances as large as several micrometers. However, the behavior of the observed long-range nonlocality as a function of temperature, band gap, and carrier concentration remained to be understood. In Chapter 6 and 7, we have showen, using a diffusive theory, that this behavior can be explained with bulk topological transport and Coulomb drag between the electrons belonging to the two different valleys, in good agreement with experimental findings. Finally, in Chapter 8, we have studied the crossed Andreev reflection in a three-terminal hybrid graphene/superconductor system in the quantum Hall regime and its effect on the nonlocal resistances.

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22

Ruiz-Tijerina, David A. "Kondo Physics and Many-Body Effects in Quantum Dots and Molecular Junctions". Ohio University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1385982088.

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23

Dyhdalo, Alexander. "Aspects of the Many-Body Problem in Nuclear Physics". The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524186564591926.

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24

Goldsborough, Andrew M. "Tensor networks and geometry for the modelling of disordered quantum many-body systems". Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/70003/.

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Tensor networks provide a powerful and elegant approach to quantum manybody simulation. The simplest example is the density matrix renormalisation group (DMRG), which is based on the variational update of a matrix product state (MPS). It has proved to be the most accurate approach for the numerical study of strongly correlated one dimensional systems. We use DMRG to study the one dimensional disordered Bose-Hubbard model at fillings N=L = 1=2, 1 and 2 and show that the whole phase diagram for each can be successfully obtained by analysing entanglement properties alone. We �nd that the average entanglement is insufficient to accurately locate all of the phases, however using the standard error on the mean we are able to construct a phase diagram that is consistent with previous studies. It has recently been shown that there is a connection between the geometry of tensor networks and the entanglement and correlation properties that it can encode, which is a generalisation of the so called area law for entanglement entropy. This suggests that whilst gapped quantum systems can be accurately modeled using an MPS, a tensor network with a holographic geometry is natural to capture the logarithmic entanglement scaling and power law decaying correlation functions of critical systems. We create an algorithm for the disordered Heisenberg Hamiltonian that self assembles a tensor network based on the disorder in the couplings. The geometry created is that of a disordered tree tensor network (TTN) that when averaged has the holographic properties characteristic of critical systems. We continue the analysis of holographic tensor network geometry by considering the average length of leaf-to-leaf paths in various tree graphs, which is related to two-point correlation functions in tensor networks. For regular, complete trees we analytically calculate the average path length and all statistical moments, and generalise it for any splitting number. We then turn to the Catalan trees, which is the set of unique binary trees with n vertices, as it has a similar geometry to the disordered TTNs. We calculate the average depth of a leaf and show that it is equal to the average path length. We compare these analytic results with the structures found in the TTN and randomly constructed trees to show that the renormalisation involved in the TTN algorithm is crucial in the selection of the tree structure.

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25

Krauser, Jasper Simon [Verfasser]. "Coherent Spin Dynamics in Fermionic Quantum Gases From Two-Body to Many-Body Physics / Jasper Simon Krauser". München : Verlag Dr. Hut, 2015. http://d-nb.info/1069020494/34.

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26

Mucciolo, Eduardo Rezende. "Universal correlations in the quantum spectra of chaotic systems and exactly solvable many-body problems". Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/35996.

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27

Schiulaz, Mauro. "Ideal quantum glass transitions: many-body localization without quenched disorder?" Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4908.

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In this work the role of disorder, interaction and temperature in the physics of quantum non-ergodic systems is discussed. I first review what is meant by thermalization in closed quantum systems, and how ergodicity is violated in the presence of strong disorder, due to the phenomenon of Anderson localization. I explain why localization can be stable against the addition of weak dephasing interactions, and how this leads to the very rich phenomenology associated with many-body localization. I also briefly compare localized systems with their closest classical analogue, which are glasses, and discuss their similarities and differences, the most striking being that in quantum systems genuine non ergodicity can be proven in some cases, while in classical systems it is a matter of debate whether thermalization eventually takes place at very long times. Up to now, many-body localization has been studies in the region of strong disorder and weak interaction. I show that strongly interacting systems display phenomena very similar to localization, even in the absence of disorder. In such systems, dynamics starting from a random inhomogeneous initial condition are non-perturbatively slow, and relaxation takes place only in exponentially long times. While in the thermodynamic limit ergodicity is ultimately restored due to rare events, from the practical point of view such systems look as localized on their initial condition, and this behavior can be studied experimentally. Since their behavior shares similarities with both many-body localized and classical glassy systems, these models are termed “quantum glasses”. Apart from the interplay between disorder and interaction, another important issue concerns the role of temperature for the physics of localization. In non-interacting systems, an energy threshold separating delocalized and localized states exist, termed “mobility edge”. It is commonly believed that a mobility edge should exist in interacting systems, too. I argue that this scenario is inconsistent because inclusions of the ergodic phase in the supposedly localized phase can serve as mobile baths that induce global delocalization. I conclude that true non-ergodicity can be present only if the whole spectrum is localized. Therefore, the putative transition as a function of temperature is reduced to a sharp crossover. I numerically show that the previously reported mobility edges can not be distinguished from finite size effects. Finally, the relevance of my results for realistic experimental situations is discussed.

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28

Darkwah, Oppong Nelson [Verfasser], e Immanuel [Akademischer Betreuer] Bloch. "Probing many-body physics with multiorbital quantum gases / Nelson Darkwah Oppong ; Betreuer: Immanuel Bloch". München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2021. http://d-nb.info/1233201115/34.

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29

Huillery, Paul. "Few and Many-body Physics in cold Rydberg gases". Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112040/document.

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Au cours de cette thèse, la physique des systèmes en interaction à été étudié expérimentalement à partir de gaz froids d'atomes de Rydberg. Les atomes de Rydberg sont des atomes dans un état fortement excités et ils ont la propriété d'interagir fortement du fait d'interactions électrostatiques à longue portée. Le premier résultat majeur de cette thèse est l'observation expérimentale d'un processus à quatre corps. Ce processus consiste en l'échange d'énergie interne entre quatre atomes de Rydberg induit par leurs interactions mutuelles. Il a été possible, en plus de son observation expérimentale, de décrire théoriquement ce processus, au niveau quantique. L'excitation par laser des gaz d'atomes de Rydberg en forte interaction a aussi été étudiée durant cette thèse. Cette situation donne lieu à de très intéressants comportements à N-corps. Ce sujet d'intérêt fondamental pourrait aussi amener à d'éventuelles applications pour la réalisation de simulateurs quantiques ou de sources de lumière non classiques. Un second résultat majeur de cette thèse est l'observation expérimentale d'une statistique fortement sub-poissonienne, i.e corrélée de l'excitation Rydberg. Ce résultat confirme le caractère à N-corps de tels systèmes. Le troisième résultat majeur de cette thèse est le développement d'un modèle théorique pour l'excitation par laser des gaz d'atomes de Rydberg en forte interaction. En utilisant les états quantiques dit états collectifs de Dicke, il a été possible de mettre au jour de nouveaux mécanismes liés au comportement à N-corps de ces sytèmes atomiques en forte interaction
Uring this thesis, the Physics of interacting systems has been investigated experimentally using Cold Rydberg gases. Rydberg atoms are highly excited atoms and have the property to interact together through long-range electrostatic interactions.The first highlight of this thesis is the direct experimental observation of a 4-body process. This process consists in the exchange of internal energy between 4 Rydbergs atoms due to their mutual interactions. In addition to its observation, it has been possible to describ this process theoretically at a quantum level.The laser excitation of strongly interacting Rydberg gases has been also investigated during this thesis. In this regime, the interactions between Rydberg atoms give rise to very interesting many-body behaviors. In addition to fundamental interest, such systems could be used to realyze quantum simulators or non-classical light sources.A second highlight of this thesis is the experimental observation of a highly sub-poissonian, i.e correlated, excitation statistics. This result confirms the many-body character of the investigated system.The third highlight of this thesis is the development of a theoretical model to describ the laser excitation of strongly interacting Rydberg gases. Using the so-called Dicke collective states it has been possible to point out new mechanismes related to the many-body character of strongly atomic interacting systems

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30

Darmawan, Andrew. "Quantum computational phases of matter". Thesis, The University of Sydney, 2014. http://hdl.handle.net/2123/11640.

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Universal quantum computation can be realised by measuring individual particles in a specially entangled state of many particles, called a universal resource state. This model of quantum computation, called measurement-based quantum computation (MBQC), provides a framework for studying the intrinsic computational power of physical systems. In this thesis I will investigate how universal resource states may arise naturally as ground states of interacting spin systems. In particular, I will describe new 'phases' of quantum matter, which are characterised by having universal resource states as ground states. This direction of research allows us to draw on techniques from both many-body quantum physics and quantum information theory.

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31

Everest, Benjamin. "Dissipation as a resource for constrained dynamics in open many-body quantum systems". Thesis, University of Nottingham, 2017. http://eprints.nottingham.ac.uk/43375/.

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This thesis studies non-equilibrium open quantum systems where the dissipation is crucial to the achievement of novel physical regimes. We focus on atomic systems which allow for the coupling of a ground state to a Rydberg state, relying on the strong interactions between Rydberg atoms to produce the collective behaviour that we aim to investigate. For atoms in an optical lattice undergoing standard dissipation forms, e.g. loss and dephasing, we find these simple settings allow for the production of models contained in the non-equilibrium realm. We start by looking at a system with engineered pair dissipation on a one-dimensional lattice. When the dissipation is strong relative to a tunnelling process it creates a quantum Zeno effect which projects the system onto a Zeno-subspace. This subspace is found to contain complexes which experience a binding due to the dissipation. The properties of these complexes are found to feature spin-orbit coupling and, in certain instances, a flat band. We then study what kinetically constrained models (KCMs) can be reproduced in a lattice system. KCMs are models which typically feature trivial steady states, but a complex relaxation dynamics. These models appear in the fields of glasses and soft matter physics. We find a general framework for the consideration of a quantum Hamiltonian and a classical potential with strong dephasing noise. We then focus on a model mimicking volume excluded KCMs and find characteristic constrained behaviour, such as ergodicity breaking. We apply this framework to the decay of a many-body localised state in an open system with interactions in which we find the decay to be classical in the two interaction limits. For weak interactions, it follows a stretched exponential form due to pair relaxation, while for strong interactions the decay follows a compressed exponential, now being modelled as an Avrami process due to the correlated relaxation. We also find that on-site loss only affects the strong interacting limit. We then move on to the study of universal non-equilibrium behaviour in the directed percolation (DP) class. We consider on-site atomic loss and gain as a substitute for the standard decay channel. We show that this replaces the absorbing state with an enlarged absorbing space, leading to a loss of the DP transition at lower average densities. This class of DP-like systems has received little study, and we present a method of experimentally realising it in current set-ups. We finish with a look at a quantum DP model, where we consider its quantum and classical limits. We find that the transition changes from first to second order as the system becomes more classical, featuring a bi-critical point. We then numerically demonstrate that the same transitions are visible in idealised and Rydberg models.

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32

Bertini, Bruno. "Non-equilibrium dynamics of interacting many-body quantum systems in one dimension". Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:1e2c50b9-73b3-4ca0-a5f3-276f967c3720.

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In this thesis we study three examples of interacting many-body systems undergoing a non equilibrium time evolution. Firstly we consider the time evolution in an integrable system: the sine-Gordon field theory in the repulsive regime. We will focus on the one point function of the semi-local vertex operator e^iβφ(x)/2 on a specific class of initial states. By analytical means we show that the expectation value considered decays exponentially to zero at late times and we determine the decay time. The method employed is based on a form-factor expansion and uses the "Representative Eigenstate Approach" of Ref. [73] (a.k.a. "Quench Action"). In a second example we study the time evolution in models close to "special" integrable points characterised by hidden symmetries generating infinitely many local conservation laws that do not commute with one another, in addition to the infinite commuting family implied by integrability. We observe that both in the case where the perturbation breaks the integrability and when it breaks only the additional symmetries maintaining integrability, the local observables show a crossover behaviour from an initial to a final quasi stationary plateau. We investigate a weak coupling limit, identify a time window in which the effects of the perturbations become significant and solve the time evolution through a mean-field mapping. As an explicit example we study the XYZ spin-1/2 chain with additional perturbations that break integrability. Finally, we study the effects of integrability breaking perturbations on the non-equilibrium evolution of more general many-particle quantum systems, where the unperturbed integrable model is generic. We focus on a class of spinless fermion models with weak interactions. We employ equation of motion techniques that can be viewed as generalisations of quantum Boltzmann equations. We benchmark our method against time dependent density matrix renormalisation group computations and find it to be very accurate as long as interactions are weak. For small integrability breaking, we observe robust prethermalisation plateaux for local observables on all accessible time scales. Increasing the strength of the integrability breaking term induces a "drift" away from the prethermalisation plateaux towards thermal behaviour. We identify a time scale characterising this crossover.

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33

Khan, Imran. "QUANTUM THEORY OF MANY BOSE ATOM SYSTEMS". Connect to Online Resource-OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=Toledo1195507917.

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34

Goldstein, Garry. "Applications of Many Body Dynamics of Solid State Systems to Quantum Metrology and Computation". Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10555.

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This thesis describes aspects of dynamics of solid state systems which are relevant to quantum metrology and computation. It may be divided into three research directions (parts). For the first part, a new method to enhance precision measurements that makes use of a sensor’s environment to amplify its response to weak external perturbations is described. In this method a “central” spin is used to sense the dynamics of surrounding spins, which are affected by the external perturbations that are being measured. The enhancement in precision is determined by the number of spins that are coupled strongly to the central spin and is resilient to various forms of decoherence. For polarized environments, nearly Heisenberg-limited precision measurements can be achieved. The second part of the thesis focuses on the decoherence of Majorana fermions. Specializing to the experimentally relevant case where each mode interacts with its own bath we present a method to study the effect of external perturbations on these modes. We analyze a generic gapped fermionic environment (bath) interacting via tunneling with individual Majorana modes - components of a qubit. We present examples with both static and dynamic perturbations (noise), and derive a rate of information loss for Majorana memories, that depends on the spectral density of both the noise and the fermionic bath. For the third part of the thesis we discuss vortices in topological superconductors which we model as closed finite systems, each with an odd number of real fermionic modes. We show that even in the presence of many-body interactions, there are always at least two fermionic operators that commute with the Hamiltonian. There is a zero mode corresponding to the total Majorana operator [1] as well as additional linearly independent zero modes, one of which is continuously connected to the Majorana mode in the non-interacting limit. We also show that in the situation where there are two or more well separated vortices their zero modes have non-Abelian Ising statistics under braiding.
Physics

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35

Ohliger, Matthias. "Characterizing and measuring properties of continuous-variable quantum states". Phd thesis, Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/6292/.

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We investigate properties of quantum mechanical systems in the light of quantum information theory. We put an emphasize on systems with infinite-dimensional Hilbert spaces, so-called continuous-variable systems'', which are needed to describe quantum optics beyond the single photon regime and other Bosonic quantum systems. We present methods to obtain a description of such systems from a series of measurements in an efficient manner and demonstrate the performance in realistic situations by means of numerical simulations. We consider both unconditional quantum state tomography, which is applicable to arbitrary systems, and tomography of matrix product states. The latter allows for the tomography of many-body systems because the necessary number of measurements scales merely polynomially with the particle number, compared to an exponential scaling in the generic case. We also present a method to realize such a tomography scheme for a system of ultra-cold atoms in optical lattices. Furthermore, we discuss in detail the possibilities and limitations of using continuous-variable systems for measurement-based quantum computing. We will see that the distinction between Gaussian and non-Gaussian quantum states and measurements plays an crucial role. We also provide an algorithm to solve the large and interesting class of naturally occurring Hamiltonians, namely frustration free ones, efficiently and use this insight to obtain a simple approximation method for slightly frustrated systems. To achieve this goals, we make use of, among various other techniques, the well developed theory of matrix product states, tensor networks, semi-definite programming, and matrix analysis.
Die stürmische Entwicklung der Quanteninformationstheorie in den letzten Jahren brachte einen neuen Blickwinkel auf quantenmechanische Probleme. Insbesondere die fundamentale Eigenschaft der Verschränkung von Quantenzuständen spielt hierbei eine Schlüsselrolle. Einstein, Podolsky und Rosen haben 1935 versucht die Unvollständigkeit der Quantenmechanik zu demonstrieren, indem sie zeigten, dass sie keine lokale, realistische Therie ist und der Ausgang einer Messung an einem Ort von Messungen abhängen kann, die an beliebig weit entfernten Orten gemacht wurden. John Bell stellte 1964 eine, später nach ihm benannte, Ungleichung auf, die eine Grenze an mögliche Korrelationen von Messergebnissen in lokalen, realistischen Theorien gibt. Die Vorhersagen der Quatenmechanik verletzen diese Ungleichung, eine Tatsache, die 1981 von Alain Aspect und anderen auch experimentell bestätigt wurde. Solche nicht-lokalen Quantenzustände werden verschränkt'' genannt. In neuerer Zeit wurde Verschränkung nicht mehr nur als mysteriöse Eigenschaft der Quantenmechanik sondern auch als Resource für Aufgaben der Informationsverarbeitung gesehen. Ein Computer, der sich diese Eigenschaften der Quantenmechanik zu nutze macht, ein sogenannter Quantencomputer, würde es erlauben gewisse Aufgaben schnell zu lösen für die normale'' Computer zu lange brauchen. Das wichtigste Beispiel hierfür ist die Zerlegung von großen Zahlen in ihre Primfaktoren, für die Shor 1993 einen Quantenalgorithmus präsentierte. In dieser Arbeit haben wir uns mit den Eigenschaften von Quantensystemen, die durch sogenannte kontinuierliche Variablen beschrieben werden, beschäftigt. Diese sind nicht nur theoretisch sonder auch experimentell von besonderem Interesse, da sie quantenoptische Systeme beschreiben, die sich verhältnismäßig leicht im Labor präparieren, manipulieren und messen lassen. Wenn man eine vollständige Beschreibung eines Quantenzustandes erhalten will, braucht man, auf Grund der Heisenberg'schen Unschärferelation, mehrere Kopien von ihm an denen man dann Messungen durchführt. Wir haben eine Methode, compressed-sensing genannt, eingeführt um die Anzahl der nötigen Messungen substantiell zu reduzieren. Wir haben die theoretische Effizienz dieser Methode bewiesen und durch numerische Simulationen auch ihre Praktikabilität demonstriert. Desweiteren haben wir beschrieben, wie man compressed-sensing für die schon erwähnten optischen Systemen sowie für ultrakalte Atome experimentell realisieren kann. Ein zweites Hauptthema dieser Arbeit war messbasiertes Quantenrechnen. Das Standardmodell des Quantenrechnens basiert auf sogenannten Gattern, die eine genaue Kontrolle der Wechselwirkung zwischen den Bestandteilen des Quantencomputers erfordern. Messbasiertes Quantenrechnen hingegen kommt mit der Präparation eines geeigneten Quantenzustands, Resource genannt, gefolgt von einfachen Messungen auf diesem Zustand aus. Wir haben gezeigt, dass Systeme mit kontinuierlichen Variablen eine vorteilhafte Realisierung eines Quantencomputers in diesem Paradigma erlauben, es jedoch auch wichtige Beschränkungen gibt, die kompliziertere Zustandspräparationen und Messungen nötig machen.

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36

Sun, Deqiang. "Landau-Zener transitions in noisy environment and many-body systems". [College Station, Tex. : Texas A&M University, 2009. http://hdl.handle.net/1969.1/ETD-TAMU-2009-05-773.

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37

Logg, Peter William. "Superconductivity in the proximity of a quantum critical point". Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/248786.

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In a many-body fermionic system, the suppression of continuous transitions to absolute zero can result in a low temperature quantum fluid which deviates strongly from typical metallic behaviour; unconventional superconductivity can be induced by the strange metal region surrounding the zero-temperature phase transition. In this thesis we focus on three systems which demonstrate a highly tunable phase transition, with the aim of pushing them toward the border of a zero-temperature phase transition, and potentially superconductivity. CeAgSb2 is a uniaxial 4f ferromagnet, where physical pressure or a transverse field may be used to tune the magnetic transition towards T = 0 K. Our investigations, however, did not reveal the presence of superconductivity. It is likely that the field tuned transition does not correspond to a true critical point, whilst the high pressure region may be occupied by an antiferromagnetic phase, with the true critical point at higher pressures. However, other interesting features emerge in the electrical resistivity and AC-susceptibility, along with novel thermodynamic signatures linking the magnetisation to the specific heat. The doping series Lu(1-x)YxFe2Ge2 shows an antiferromagnetic transition which is suppressed to absolute zero at a critical concentration x_c=0.2. YFe2Ge2 displays anomalous low temperature behaviour consistent with the proximity to quantum critical fluctuations, along with a superconducting transition which appears in the electrical resistivity beneath a critical temperature of T_c ~ 1.7 K. Using low temperature DC magnetisation measurements, we show that this is a bulk effect, and that the superconductivity in YFe2Ge2 is of type-II. The thermodynamic and BCS properties of the superconducting phase are analysed in line with the parameters we extract experimentally. The superconducting 3-4-13 stannides (Ca,Sr)3Ir4Sn13 show a high temperature structural transition which may be suppressed by the application of hydrostatic pressure or effective chemical pressure. A superconducting dome is found, which appears to peak near where the structural transition extrapolates to zero temperature. Anomalous exponents are seen in the electrical resistivity over a wide temperature range. We investigate the influence of pressure on the superconducting critical temperature in Ca3Ir4Sn13 and the related compound Co3Ca4Sn13, along with an analysis of the upper critical field and flux-line phenomena in Ca3Ir4Sn13 and Sr3Ir4Sn13.

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38

Mazzucchi, Gabriel. "Conditional many-body dynamics and quantum control of ultracold fermions and bosons in optical lattices coupled to quantized light". Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:6c6eddac-41de-476d-851e-6630907965e6.

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We study the atom-light interaction in the fully quantum regime, with the focus on off-resonant light scattering into a cavity from ultracold atoms trapped in an optical lattice. Because of the global coupling between the atoms and the light modes, observing the photons leaking from the cavity allows the quantum nondemolition (QND) measurement of quantum correlations of the atomic ensemble, distinguishing between different quantum states. Moreover, the detection of the photons perturbs the quantum state of the atoms via the so-called measurement backaction. This effect constitutes an unusual additional dynamical source in a many-body strongly correlated system and it is able to efficiently compete with its intrinsic short-range dynamics. This competition becomes possible due to the ability to change the spatial profile of a global measurement at a microscopic scale comparable to the lattice period, without the need of single site addressing. We demonstrate nontrivial dynamical effects such as large-scale multimode oscillations, breakup and protection of strongly interacting fermion pairs. We show that measurement backaction can be exploited for realizing quantum states with spatial modulations of the density and magnetization, thus overcoming usual requirement for a strong interatomic interactions. We propose detection schemes for implementing antiferromagnetic states and density waves and we demonstrate that such long-range correlations cannot be realized with local addressing. Finally, we describe how to stabilize these emerging phases with the aid of quantum feedback. Such a quantum optical approach introduces into many-body physics novel processes, objects, and methods of quantum engineering, including the design of many-body entangled environments for open systems and it is easily extendable to other systems promising for quantum technologies.

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39

Jayatilaka, Frederic William. "Theoretical studies of tunnel-coupled double quantum dots". Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:756add23-aae6-4a71-a22b-087695bc600a.

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We study the low-temperature physics arising in models of a strongly correlated, tunnel-coupled double quantum dot (DQD), particularly the two-impurity Anderson model (2AIM) and the two-impurity Kondo model (2IKM), employing a combination of physical arguments and the Numerical Renormalisation Group. These models exhibit a rich range of Kondo physics. In the regime with essentially one electron on each dot, there is a competition between the Kondo effect and the interdot exchange interaction. This competition gives rise to a quantum phase transition (QPT) between local singlet and Kondo singlet phases in the 2IKM, which becomes a continuous crossover in the 2AIM as a result of the interlead charge transfer present. The 2IKM is known to exhibit two-channel Kondo (2CK) physics at the QPT, and we investigate whether this is also the case for the 2AIM at the crossover. We find that while in principle 2CK physics can be observed in the 2AIM, extremely low temperatures are required, such that it is unlikely that 2CK physics will be observed in an experimental DQD system in the near future. We have studied the effect of a magnetic field on the 2AIM and the 2IKM, finding that both the zero-field QPT in the 2IKM and the zero-field crossover in the 2AIM, persist to finite field. This presents the possibility of observing 2CK physics in an experimental DQD at finite field, but we find that the temperatures required to do so are extremely low. We show that longer even-numbered chains of spins also exhibit QPTs at finite field, and argue that a 2N-spin chain should undergo N QPTs as field is increased (starting deep in the local singlet phase at zero field). We have also carried out a joint theoretical-experimental study of a carbon nanotube based DQD, in collaboration with Dr. Mark Buitelaar et al. The agreement between experimental and theoretical results is good, and the experiments are able to access the crossover present in the 2AIM at finite field. Furthermore, the experiments show the wide range of physics exhibited by DQD systems, and illustrate the utility of such systems in probing correlated electron physics.

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40

Chen, Kuan-Hao. "Creating Extended Landau Levels of Large Degeneracy with Photons". The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1542878428843845.

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41

Jacobson, Leif David. "Approximating Many-Body Induction to Efficiently Describe Molecular Liquids and Clusters With Improved Accuracy". The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1312480919.

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42

Leib, Martin [Verfasser], Michael J. [Akademischer Betreuer] Hartmann e Wilhelm [Akademischer Betreuer] Zwerger. "Many-Body Physics with Circuit Quantum Electrodynamics / Martin Leib. Gutachter: Wilhelm Zwerger ; Michael J. Hartmann. Betreuer: Michael J. Hartmann". München : Universitätsbibliothek der TU München, 2015. http://d-nb.info/1070624292/34.

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43

Xu, Guang-Hui. "Exploratory studies of group theoretic methods in atomic physics". Scholarly Commons, 1989. https://scholarlycommons.pacific.edu/uop_etds/2189.

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The properties of a physical system are determined by its equation of motion, and every such equation admits one-parameter groups which keep the equation invariant. Thus, for a particular system, if one can find the generator of a one-parameter group which keeps the equation and some further function or functional invariant, then one can change this system into others by changing the parameter, while keeping some properties constant. In this way, one can tell why different systems have some common properties. More importantly, one can use this method to find relationships between the physical properties of different systems. In the next section, we will illustrate the group theoretic approach by applying it to systems of two coupled oscillators and the hydrogen molecular ion. In section III of this thesis, we will investigate the helium atom system, considering both classical and quantum cases. In the quantum case our attention will be concentrated on the Schrodinger equation in matrix form. We will use a finite set of wavefunctions as our basis. Hence the results obtained will be approximate.

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44

Hafver, Andreas. "The formalism of non-commutative quantum mechanics and its extension to many-particle systems". Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/5255.

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Thesis (MSc (Physics))--University of Stellenbosch, 2010.
ENGLISH ABSTRACT: Non-commutative quantum mechanics is a generalisation of quantum mechanics which incorporates the notion of a fundamental shortest length scale by introducing non-commuting position coordinates. Various theories of quantum gravity indicate the existence of such a shortest length scale in nature. It has furthermore been realised that certain condensed matter systems allow effective descriptions in terms of non-commuting coordinates. As a result, non-commutative quantum mechanics has received increasing attention recently. A consistent formulation and interpretation of non-commutative quantum mechanics, which unambiguously defines position measurement within the existing framework of quantum mechanics, was recently presented by Scholtz et al. This thesis builds on the latter formalism, extends it to many-particle systems and links it up with non-commutative quantum field theory via second quantisation. It is shown that interactions of particles, among themselves and with external potentials, are altered as a result of the fuzziness induced by non-commutativity. For potential scattering, generic increases are found for the differential and total scattering cross sections. Furthermore, the recovery of a scattering potential from scattering data is shown to involve a suppression of high energy contributions, disallowing divergent interaction forces. Likewise, the effective statistical interaction among fermions and bosons is modified, leading to an apparent violation of Pauli’s exclusion principle and foretelling implications for thermodynamics at high densities.
AFRIKAANSE OPSOMMING: Nie-kommutatiewe kwantummeganika is ’n veralgemening van kwantummeganika wat die idee van ’n fundamentele kortste lengteskaal invoer d.m.v. nie-kommuterende ko¨ordinate. Verskeie teorie¨e van kwantum-grawitasie dui op die bestaan van so ’n kortste lengteskaal in die natuur. Dit is verder uitgewys dat sekere gekondenseerde materie sisteme effektiewe beskrywings in terme van nie-kommuterende koordinate toelaat. Gevolglik het die veld van nie-kommutatiewe kwantummeganika onlangs toenemende aandag geniet. ’n Konsistente formulering en interpretasie van nie-kommutatiewe kwantummeganika, wat posisiemetings eenduidig binne bestaande kwantummeganika raamwerke defineer, is onlangs voorgestel deur Scholtz et al. Hierdie tesis brei uit op hierdie formalisme, veralgemeen dit tot veeldeeltjiesisteme en koppel dit aan nie-kommutatiewe kwantumveldeteorie d.m.v. tweede kwantisering. Daar word gewys dat interaksies tussen deeltjies en met eksterne potensiale verander word as gevolg van nie-kommutatiwiteit. Vir potensiale verstrooi ¨ıng verskyn generiese toenames vir die differensi¨ele and totale verstroi¨ıngskanvlak. Verder word gewys dat die herkonstruksie van ’n verstrooi¨ıngspotensiaal vanaf verstrooi¨ıngsdata ’n onderdrukking van ho¨e-energiebydrae behels, wat divergente interaksiekragte verbied. Soortgelyk word die effektiewe statistiese interaksie tussen fermione en bosone verander, wat ly tot ’n skynbare verbreking van Pauli se uitsluitingsbeginsel en dui op verdere gevolge vir termodinamika by ho¨e digthede.

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45

Fedorov, Aleksey. "Non-conventional Many-body Phases in Ultracold Dipolar Systems". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS580/document.

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Le problème de la détection et de ladescription des nouveaux états quantiquesmacroscopiques, caractérisées par des propriétésexotiques et non-conventionnelles, estd’importance fondamentale dans la physiquemoderne. Ces états offrent des perspectivesfascinantes dans le domaine de traitementd’information, de simulations quantiques et derecherche des nouveaux types des matériaux.Dans ce travail de thèse nous développons unethéorie qui permet de décrire des phases non conventionnellesdans des systèmes des gazultra-froids dipolaires. Ces systèmes sontactivement étudiés expérimentalement enutilisant des atomes à grand-spins, desmolécules polaires et des excitations dipolairesdans des semi-conducteurs. Nous mettonsl'accent sur la révélation du rôle de l’interactiondipôle-dipôle à long porté.Nous considérons l’effet de rotonization dansun système de gaz des bosons dipolaires «tiltés»aux interactions faibles dans une couchehomogène. Nous prédisons l’effet derotonization pour un gaz de Bose faiblementcorrélé des excitons dipolaires dans une couchede semi-conducteur et nous calculons lediagramme de stabilité. Ensuite, nousconsidérons des superfluides d’onde-p desfermions identiques dans des réseaux 2D.Finalement, nous faisons une discussion sur unautre état superfluide intéressant des moléculespolaires fermioniques, qui devrait apparaitredans des systèmes bicouches
The problem of revealing anddescribing novel macroscopic quantum statescharacter- ized by exotic and non-conventionalproperties is of fundamental importance formodern physics. Such states offer fascinatingprospects for potential applications in quantumin- formation processing, quantum simulation,and material research. In the present Thesis wedevelop a theory for describing nonconventionalphases of ultracold dipolar gases.The related systems of large-spin atoms, polarmolecules, and dipolar excitons in semiconductorsare actively studied in experiments.We put the main emphasis on revealing the roleof the long-range character of the dipole-dipoleinteraction.We consider the effect of rotonization for a 2Dweakly interacting gas of tilted dipolar bosonsin a homogeneous layer. We predict the effectof rotonization for a weakly correlated Bosegas of dipolar excitons in a semiconductorlayer and calculate the stability diagram. Wethen consider p-wave superfluids of identicalfermions in 2D lattices. Finally, we discussanother interesting novel superfluid offermionic polar molecules

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46

Rowlands, Daniel Alexander. "Spectral and dynamical properties of disordered and noisy quantum spin models". Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/284393.

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This thesis, divided into two parts, is concerned with the analysis of spectral and dynamical characteristics of certain quantum spin systems in the presence of either I) quenched disorder, or II) dynamical noise. In the first part, the quantum random energy model (QREM), a mean-field spin glass model with a many-body localisation transition, is studied. In Chapter 2, we attempt a diagrammatic perturbative analysis of the QREM from the ergodic side, proceeding by analogy to the single-particle theory of weak localisation. Whilst we are able to describe diffusion, the analogy breaks down and a description of the onset of localisation in terms of quantum corrections quickly becomes intractable. Some progress is possible by deriving a quantum kinetic equation, namely the relaxation of the one-spin reduced density matrix is determined, but this affords little insight and extension to two-spin quantities is difficult. We change our approach in Chapter 3, studying instead a stroboscopic version of the model using the formalism of quantum graphs. Here, an analytic evaluation of the form factor in the diagonal approximation is possible, which we find to be consistent with the universal random matrix theory (RMT) result in the ergodic regime. In Chapter 4, we replace the QREM's transverse field with a random kinetic term and present a diagrammatic calculation of the average density of states, exact in the large-N limit, and interpret the result in terms of the addition of freely independent random variables. In the second part, we turn our attention to noisy quantum spins. Chapter 5 is concerned with noninteracting spins coupled to a common stochastic field; correlations arising from the common noise relax only due to the spins' differing precession frequencies. Our key result is a mapping of the equation of motion of n-spin correlators onto the (integrable) non-Hermitian Richardson-Gaudin model, enabling exact calculation of the relaxation rate of correlations. The second problem, addressed in Chapter 6, is that of the dynamics of operator moments in a noisy Heisenberg model; qualitatively different behaviour is found depending on whether or not the noise conserves a component of spin. In the case of nonconserving noise, we report that the evolution of the second moment maps onto the Fredrickson-Andersen model - a kinetically constrained model originally introduced to describe the glass transition. This facilitates a rigorous study of operator spreading in a continuous-time model, providing a complementary viewpoint to recent investigations of random unitary circuits.

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47

Dargel, Piet. "Spectral functions of low-dimensional quantum systems". Doctoral thesis, Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2012. http://hdl.handle.net/11858/00-1735-0000-000D-F1A3-6.

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48

Waltersson, Erik. "On the role of the electron-electron interaction in two-dimensional quantum dots and rings". Doctoral thesis, Stockholms universitet, Fysikum, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-38862.

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Many-Body Perturbation Theory is put to test as a method for reliable calculations of the electron-electron interaction in two-dimensional quantum dots. We show that second order correlation gives qualitative agreement with experiments on a level which was not found within the Hartree-Fock description. For weaker confinements, the second order correction is shown to be insufficient and higher order contributions must be taken into account. We demonstrate that all order Many-Body Perturbation Theory in the form of the Coupled Cluster Singles and Doubles method yields very reliable results for confinements close to those estimated from experimental data. The possibility to use very large basis sets is shown to be a major advantage compared to Full Configuration Interaction approaches, especially for more than five confined electrons. Also, the possibility to utilize two-electron correlation in combination with tailor made potentials to achieve useful properties is explored. In the case of a two-dimensional quantum dot molecule we vary the interdot distance, and in the case of a two-dimensional quantum ring we vary the ring radius, in order to alter the spectra. In the latter case we demonstrate that correlation in combination with electromagnetic pulses can be used for the realization of quantum logical gates.
At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 5: Manuscript.

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49

D'Alberto, Jacopo. "Study of a 2D Bose-Fermi mixture with quantum Monte Carlo methods". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/24393/.

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Ultracold gases are an exceptionally versatile platform to test novel physical concepts. Thanks to the development of new experimental techniques, they have greatly advanced our understanding of the physics of many-body systems and allowed precision measurements of fundamental constants. Bose-Fermi mixtures can then be introduced in this context. This novel quantum many-body system is essentially an ultracold gas made up by both bosons and fermions, where tunable attractive or repulsive interactions between the components can be introduced. At T = 0 and for weak interactions the bosons condense while the fermions behave as a Fermi liquid. In particular, a recent system of interest is given by two-dimensional Bose-Fermi mixtures with both Bose-Fermi and Bose-Bose repulsive interactions. In the present work, a Quantum Monte Carlo study is conducted, for a fixed value of boson concentration, at zero-temperature from the weak to the strong Bose-Fermi coupling limit. Variational Monte Carlo and Fixed-Node Diffusion Monte Carlo are applied using an optimized Jastrow-Slater wavefunction, extending previous methodology developed for the three-dimensional case. The results are then compared with perturbative predictions, showing very good agreement in the weak coupling region. Variational Monte Carlo agrees with the analytic predictions only for extremely weak coupling, while Diffusion Monte Carlo proves necessary to recover good agreement over the whole perturbative regime. For stronger couplings, our simulations indicate the tendency of the mixture to form bosonic clusters. This finding would definitively deserve further investigation, which is postponed to future works.

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Puertas, Javier. "Interaction lumière-matière dans le régime à N-corps des circuits quantiques supraconducteurs". Thesis, Université Grenoble Alpes (ComUE), 2018. http://www.theses.fr/2018GREAY021/document.

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Comprendre l'interaction lumière-matière est toujours un sujet d'actualité malgré des décennies de recherche intense. Grâce au large couplage lumière-matière présent dans les circuits quantiques supraconducteurs, il est maintenant possible d'effectuer des expériences où la dynamique d'environnements contenant beaucoup de degrés de liberté, devient pertinente. Ainsi, relier la physique à N-corps, généralement réservée à la matières condensée, et l’optique quantique est à portée de main.Dans ce travail, nous présentons un système totalement accordable in-situ pour étudier l'interaction lumière-matière à N-corps (N grand) dans différents régimes de couplage. Le circuit est constitué d'un bit quantique de type transmon (“la matière”) couplé capacitivement à une chaîne de 4700 jonctions Josephson en géométrie squid. Cette chaîne supporte de nombreux modes électromagnétiques ou modes plasma (“la lumière”). Grâce à la grande inductance cinétique des jonctions Josephson, la chaîne présente une impédance caractéristique élevée ce qui augmente significativement le couplage qubit-modes. Les squids dans le transmon et dans la chaîne nous permettent de modifier la force de ce couplage en appliquant un flux magnétique.Avec ce sytème, nous avons les trois ingrédients requis pour explorer la physique à N-corps: un environnement avec une grande densité de modes électromagnétiques, un couplage lumière-matière ultra-fort, et une non linéarité comparable aux autres échelles d'énergie pertinentes. De plus, nous présentons un traitement de l'effet des fluctuations du vide de ce large nombre de degrées de liberté. Ce qui nous permet d'obtenir un modèle quantitatif et sans paramètre libre de ce système complexe. Finalement, à partir du décalage de phase induit par le transmon sur les modes de la chaîne, le transmon phase shift, nous quantifions l’hybridation du qubit transmon avec plusieurs modes de la chaîne (jusqu'à 10 modes) et obtenons la fréquence de résonance du transmon, ainsi que sa largeur, confirmant que nous sommes dans le régime de couplage ultra-fort.Ce travail démontre que les circuits quantiques sont un outil puissant pour explorer l'optique quantique à N-corps de manière totalement contrôlée. Combiner des métamatériaux supraconducteurs et des qubits devrait permettre de mettre en évidence des effets à N-corps qualitatifs, comme le décalage de Lamb géant, d’observer des états non-classiques de la lumière ou la production de particules ou encore de simuler des problèmes d’impuretés quantiques (par exemple le modèle de Kondo ou celui de Sine-Gordon) et des transitions de phase quantiques dissipatives
Understanding the way light and matter interact remains a central topic in modern physics despite decades of intensive research. Owing to the large light-matter interaction in superconducting circuits, it is now realistic to think about experiments where the dynamics of environments containing many degrees of freedom becomes relevant. It suggests that bridging many-body physics, usually devoted to condensed matter, and quantum optics is within reach.In this work we present a fully tunable system for studying light-matter interaction with many bodies at different coupling regimes. The circuit consists of a transmon qubit (“the matter”) capacitively coupled to an array of 4700 Josephson junctions in a squid geometry, sustaining many electromagnetic or plasma modes (“the light”). Thanks to the large kinetic inductance of Josephson junctions, the array shows a high characteristic impedance that enhances the qubit-modes coupling. The squids in the transmon and in the array allow us to tune the strength of this coupling via an external magnetic flux.We observe the three required ingredients to explore many-body physics: an environment with a high density of electromagnetic modes, the ultra-strong light-matter coupling regime and a non-linearity comparable to the other relevant energy scales. Moreover, we present a method to treat the effect of the vacuum fluctuations of all these degrees of freedom. Thus we provide a quantitative and parameter-free model of this large quantum system. Finally, from the phase shift induced by the transmon on the modes of the array, the transmon phase shift, we quantify the hybridization of the transmon qubit with several modes in the array (up to 10) and obtain the transmon resonance frequency and its width, demonstrating that we are in the ultra-strong coupling regime.This work demonstrates that quantum circuits are a very powerful platform to explore many-body quantum optics in a fully controlled way. Combining superconducting metamaterials and qubits could allow us to observe qualitative many-body effects such as giant lambshift, non-classical states of light and particle productions or to simulate quantum impurity problems (such as the Kondo model or the sine-Gordon model) and dissipative quantum phase transitions

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