Teses / dissertações sobre o tema "Drive and dissipation"

La simulation des Hamiltoniens de réseaux dans les plateformes photoniques a permis de mieux comprendre les nouvelles propriétés de transport et de localisation dans le contexte de la physique de l'état solide. En particulier, les exciton-polaritons constituent un système polyvalent permettant d'étudier ces propriétés dans des réseaux avec des structures de bande intrigantes en présence de pertes et de gains, et d'interactions entre particules. Les polaritons sont des quasi-particules hybrides lumière-matière résultant du couplage fort entre les photons et les excitons dans les microcavités semi-conductrices, dont les propriétés peuvent être directement accessibles dans les expériences de photoluminescence. Dans cette thèse, nous étudions premièrement les caractéristiques des réseaux en nid d'abeille déformés, composés de résonateurs de polaritons couplés, à haut contenu photonique. Dans un réseau déformé de façon critique, nous mettons en évidence à la fois un transport semi-Dirac et une localisation anisotrope des photons. Deuxièmement, nous montrons qu'un forçage judicieux dans des réseaux de résonateurs à pertes permet l'apparition de nouveaux modes localisés. En utilisant des réseaux de polaritons sous un forçage résonant par plusieurs faisceaux optiques, nous démontrons la possibilité de localiser la lumière sur différentes géométries, voir jusqu'à un seul site. Enfin, nous profitons de l'interaction de polaritons dépendant de la polarisation pour démontrer un effet optique de type Zeeman dans un seul micropilier. En combinant le couplage spin-orbite optique, inhérent aux microstructures semi-conductrices, avec l'effet Zeeman, induit par l'interaction, nous montrons l'émission de faisceaux de vortex avec une chiralité bien définie. Cette thèse met en lumière la puissance des plateformes de polaritons pour étudier les Hamiltoniens de réseaux avec des propriétés sans précédent. Elle apporte également un premier pas vers la génération, entièrement optique, de phases topologiques dans les réseaux
The simulation of lattice Hamiltonians in photonic platforms has been enlightening in the understanding of novel transport and localization properties in the context of solid-state physics. In particular, exciton-polaritons provide a versatile system to investigate these properties in lattices with intriguing band structures in the presence of gain and loss, and particle interactions. Polaritons are hybrid light-matter quasiparticles arising from the strong coupling between photons and excitons in semiconductor microcavities, whose properties can be directly accessed in photoluminescence experiments. In this thesis, we firstly study the features of strained honeycomb lattices made of coupled polariton resonators having high photonic content. In a critically strained lattice, we evidence both a semi-Dirac transport and an anisotropic localization of photons. Secondly, we show that a judicious driving in lattices of lossy resonators allows the appearance of novel localized modes. Using polariton lattices driven resonantly with several optical beams, we demonstrate the localization of light in at-will geometries down to a single site. Finally, we take advantage of the polarization-dependent polariton interaction to demonstrate an optical Zeeman-like effect in a single micropillar. In combination with optical spin-orbit coupling inherent to semiconductor microstructures, the interaction-induced Zeeman effect results in emission of vortex beams with a well-defined chirality. This thesis brings to light the power of polariton platforms to study lattice Hamiltonians with unprecedented properties and it also provides a first step towards the fully-optical generation of topological phases in lattices

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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Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq
Diversas relações entre física e teoria de informação foram estabelecidas desde o trabalho de Shannon. Entropia é um elemento essencial nesta conexão, quantificando a informação transferida em um experimento. Mecânica estatística está conectada à teoria de informação através do princípio de máxima entropia, definindo as distribuições de probabilidade de estados de equilíbrio como aquelas que maximizam a entropia sujeita as condições físicas apropriadas. A energia dissipada em um processo clássico está conectada a divergência de Kullback-Leibler. Recentemente, Still e colaboradores mostraram que a ineficiência energética em um processo estocástico Markoviano é equivalente a ineficiência do modelo, definida como a diferença em informação que o estado do sistema compartilha com as variáveis externas no futuro e passado. Isto sugere que imprevisibilidade e ineficiência energética estejam relacionadas no âmbito da física clássica. O objetivo deste trabalho é estabelecer uma relação entre o comportamento randômico de sistemas clássicos, quantificado pela entropia de Kolmogorov-Sinai, com a ineficiência energética.
Many connections between physics and information theory have been revealed since the development of classical information theory by Shannon. A key concept in this connection is entropy, which represents the amount of information transferred to the observer who performs measurements in an experiment. Statistical mechanics is a physical theory deeply connected to information by Jaynes’ Maximum Entropy principle, which defines equilibrium probability distributions as the ones that maximizes entropy under some physical constraints. In this way, these distributions are the less unbiased probabilities that can be assignment to an event. Following this path, the dissipated energy in a classical Hamiltonian process (also known as the thermodynamic entropy production) was connected to the relative entropy between the forward and backward probability densities. A recent work by Still et al. has revealed that energetic inefficiency and model inefficiency are equivalent concepts in Markovian processes, where the latter is defined as the difference in mutual information that the system’s state shares with the future and past environmental variables. This raises the question whether model unpredictability and energetic inefficiency are connected in the framework of classical physics. The aim of this study is to connect the concepts of random behavior of a classical Hamiltonian system with its energetic inefficiency. The random behavior of a classical system is quantified by the Kolmogorov-Sinai entropy associated with its dynamics, an information-theoretic approach to chaos, whereas energetic inefficiency is measured by the dissipated work.

Bose-Einstein condensation is a collective quantum phenomenon where a macroscopic number of bosons occupies the lowest quantum state. For fixed temperature, bosons condense above a critical particle density. This phenomenon is a consequence of the Bose-Einstein distribution which dictates that excited states can host only a finite number of particles so that all remaining particles must form a condensate in the ground state. This reasoning applies to thermal equilibrium. We investigate the fate of Bose condensation in nonisolated systems of noninteracting Bose gases driven far away from equilibrium. An example of such a driven-dissipative scenario is a Floquet system coupled to a heat bath. In these time-periodically driven systems, the particles are distributed among the Floquet states, which are the solutions of the Schrödinger equation that are time periodic up to a phase factor. The absence of the definition of a ground state in Floquet systems raises the question, whether Bose condensation survives far from equilibrium. We show that Bose condensation generalizes to an unambiguous selection of multiple states each acquiring a large occupation proportional to the total particle number. In contrast, the occupation numbers of nonselected states are bounded from above. We observe this phenomenon not only in various Floquet systems, i.a. time-periodically-driven quartic oscillators and tight-binding chains, but also in systems coupled to two baths where the population of one bath is inverted. In many cases, the occupation numbers of the selected states are macroscopic such that a fragmented condensation is formed according to the Penrose-Onsager criterion. We propose to control the heat conductivity through a chain by switching between a single and several selected states. Furthermore, the number of selected states is always odd except for fine-tuning. We provide a criterion, whether a single state (e.g., Bose condensation) or several states are selected. In open systems, which exchange also particles with their environment, the nonequilibrium steady state is determined by the interplay between the particle-number-conserving intermode kinetics and particle-number-changing pumping and loss processes. For a large class of model systems, we find the following generic sequence when increasing the pumping: For small pumping, no state is selected. The first threshold, where the stimulated emission from the gain medium exceeds the loss in a state, is equivalent to the classical lasing threshold. Due to the competition between gain, loss and intermode kinetics, further transitions may occur. At each transition, a single state becomes either selected or deselected. Counterintuitively, at sufficiently strong pumping, the set of selected states is independent of the details of the gain and loss. Instead, it is solely determined by the intermode kinetics like in closed systems. This implies equilibrium condensation when the intermode kinetics is caused by a thermal environment. These findings agree well with observations of exciton-polariton gases in microcavities. In a collaboration with experimentalists, we observe and explain the pump-power-driven mode switching in a bimodal quantum-dot micropillar cavity
Die Bose-Einstein-Kondensation ist ein Quantenphänomen, bei dem eine makroskopische Zahl von Bosonen den tiefsten Quantenzustand besetzt. Die Teilchen kondensieren, wenn bei konstanter Temperatur die Teilchendichte einen kritischen Wert übersteigt. Da die Besetzungen von angeregten Zuständen nach der Bose-Einstein-Statistik begrenzt sind, bilden alle verbleibenden Teilchen ein Kondensat im Grundzustand. Diese Argumentation ist im thermischen Gleichgewicht gültig. In dieser Arbeit untersuchen wir, ob die Bose-Einstein-Kondensation in nicht wechselwirkenden Gasen fern des Gleichgewichtes überlebt. Diese Frage stellt sich beispielsweise in Floquet-Systemen, welche Energie mit einer thermischen Umgebung austauschen. In diesen zeitperiodisch getriebenen Systemen verteilen sich die Teilchen auf Floquet-Zustände, die bis auf einen Phasenfaktor zeitperiodischen Lösungen der Schrödinger-Gleichung. Die fehlende Definition eines Grundzustandes wirft die Frage nach der Existenz eines Bose-Kondensates auf. Wir finden eine Generalisierung der Bose-Kondensation in Form einer Selektion mehrerer Zustände. Die Besetzung in jedem selektierten Zustand ist proportional zur Gesamtteilchenzahl, während die Besetzung aller übrigen Zustände begrenzt bleibt. Wir beobachten diesen Effekt nicht nur in Floquet-Systemen, z.B. getriebenen quartischen Fallen, sondern auch in Systemen die an zwei Wärmebäder gekoppelt sind, wobei die Besetzung des einen invertiert ist. In vielen Fällen ist die Teilchenzahl in den selektierten Zuständen makroskopisch, sodass nach dem Penrose-Onsager Kriterium ein fragmentiertes Kondensat vorliegt. Die Wärmeleitfähigkeit des Systems kann durch den Wechsel zwischen einem und mehreren selektierten Zuständen kontrolliert werden. Die Anzahl der selektierten Zustände ist stets ungerade, außer im Falle von Feintuning. Wir beschreiben ein Kriterium, welches bestimmt, ob es nur einen selektierten Zustand (z.B. Bose-Kondensation) oder viele selektierte Zustände gibt. In offenen Systemen, die auch Teilchen mit der Umgebung austauschen, ist der stationäre Nichtgleichgewichtszustand durch ein Wechselspiel zwischen der (Teilchenzahl-erhaltenden) Intermodenkinetik und den (Teilchenzahl-ändernden) Pump- und Verlustprozessen bestimmt. Für eine Vielzahl an Modellsystemen zeigen wir folgendes typisches Verhalten mit steigender Pumpleistung: Zunächst ist kein Zustand selektiert. Die erste Schwelle tritt auf, wenn der Gewinn den Verlust in einer Mode ausgleicht und entspricht der klassischen Laserschwelle. Bei stärkerem Pumpen treten weitere Übergänge auf, an denen je ein einzelner Zustand entweder selektiert oder deselektiert wird. Schließlich ist die Selektion überraschenderweise unabhängig von der Charakteristik des Pumpens und der Verlustprozesse. Die Selektion ist vielmehr ausschließlich durch die Intermodenkinetik bestimmt und entspricht damit den oben beschriebenen geschlossenen Systemen. Ist die Kinetik durch ein thermisches Bad hervorgerufen, tritt wie im Gleichgewicht eine Grundzustands-Kondensation auf. Unsere Theorie ist in Übereinstimmung mit experimentellen Beobachtungen von Exziton-Polariton-Gasen in Mikrokavitäten. In einer Kooperation mit experimentellen Gruppen konnten wir den Modenwechsel in einem bimodalen Quantenpunkt-Mikrolaser erklären

Superconducting circuits provide an architecture upon which cavity quantum electrodynamics (QED) can be implemented at microwave frequencies in a highly tunable environment. Known as circuit QED, these systems can achieve larger nonlinearities, stronger coupling and greater controllability than can be achieved in cavity QED, all in a customisable, solid state device, making this technology an exciting test bed for both quantum optics and quantum information processing. These new parameter regimes open up new avenues for quantum technology, while also allowing older quantum optics results to finally be tested. In particular is is now possible to experimentally produce nonclassical states, such as squeezed and Schr\"odinger cat states, relatively simply in these devices. Using open quantum systems methods, in this thesis we investigate four problems which involve the use of nonclassical states in circuit QED. First we investigate the effects of a Kerr nonlinearity on the ability to preserve transported squeezed states in a superconducting cavity, and whether this setup permits us to generate, and perform tomography, of a highly squeezed field using a qubit, with possible applications in the characterisation of sources of squeezed microwaves. Second, we present a novel scheme for the amplification of cat states using a coupled qubit and external microwave drives, inspired by the stimulated Raman adiabatic passage. This scheme differs from similar techniques in circuit QED in that it is deterministic and therefore compatible with a protocol for stabilising cat states without the need for complex dissipation engineering. Next we use solutions of Fokker-Planck equations to study the exact steady-state response of two nonlinear systems: a transmon qubit coupled to a readout resonator, where we find good agreement with experiments and see simultaneous bistability of the cavity and transmon; and a parametrically driven nonlinear resonator, where we compare the classical and quantum phases of the system and discuss applications in the generation of squeezed states and stabilisation of cat states. Finally, we investigate the use of two different types of superconducting qubits in a single experiment, seeing that this enables engineering of the self- and cross-Kerr effects in a line of cavities. This could provide a valuable means of entangling cavity states, in addition to a resource for quantum simulation.

Collective quantum phenomena are fascinating, as they repeatedly challenge our comprehension of nature and its underlying mechanisms. The qualification ``quantum'' can be attributed to a generic many-body system whenever the interference effects related to the underlying wave nature of its elementary constituents can not be neglected anymore, and a naive classical description in terms of interacting billiard balls fails to catch its most essential features. This interference phenomenon called ``quantum degeneracy'' which occurs at weak temperatures, leads to spectacular collective behaviours such as the celebrated Bose-Einstein Condensation (BEC) phase transition, where a macroscopic fraction of a bosonic system of particles collapses below a critical temperature T_c on a single-particle state. Quantum coherence, when combined with inter-particle interactions, gives rise to highly non-classical frictionless hydrodynamic behaviours such as superfluidity (SF) and superconductivity (SC). Even more exotic quantum phases emerge in presence of important interactions as matter reaches a ``strongly correlated regime'' dominated by quantum fluctuations, where each particle is able to affect significantly the surrounding fluid: characteristic examples are the so-called Mott-Insulator (MI) quantum phase where particles are localized on a lattice due to a strong interaction-induced blockade, along with the Tonks-Girardeau (TG) gas where impenetrable bosons in one-dimension acquire effective fermionic statistics up to a unitary transformation, and the Fractional Quantum Hall (FQH) effect which occurs in presence of a gauge field, and features a special type of elementary excitation possessing a fractional charge and obeying to fractional statistics called `anyon'. These quantum many-body effects were explored in a first place in systems well isolated from the external environment such as ultra-cold atomic gases or electrons in solid-state systems, within a physical context well described by ``equilibrium statistical mechanics''. Yet, over the last two decades a broad community has started investigating the possibility of stabilizing interacting quantum phases in novel nonlinear quantum optics architectures, where interacting photons have replaced their atomic and electronic counterpart. Thanks to their high level of controllability and flexibility, and the possibility of reaching the quantum degeneracy regime at exceptionally high temperatures, these platforms appear as extremely promising candidates for the ``quantum simulation'' of the most exotic many-body quantum problems: while the precursors experiments in semiconductor exciton-polariton already allow to reach the Bose-Einstein Condensation and superfluid regimes, novel platforms such as superconducting circuits, coupled cavity arrays or photons coupled to Rydberg EIT (Electromagnetically induced Transparency) atoms have entered the so-called `photon blockade' where photons behave as impenetrable particles, and open a encouraging pathway toward the future generation of strongly correlated phases with light. A specificity of quantum optics devices is their intrinsic ``non-equilibrium'' nature: the interplay between the practically unavoidable radiative and non-radiative losses and the external drive needed to replenish the photon gas leads the many-body system toward a steady-state presenting important non-thermal features. One one hand, an overwhelmingly large quantity of novel quantum phenomena is expected in the non-equilibrium framework, as breaking the thermal equilibrium condition releases severe constraints on the state of a quantum system and on the nature of its surrounding environment. On the other hand, we do not benefit yet of an understanding of non-equilibrium statistical mechanics comparable with its well-established equilibrium counterpart, which relies on strong historical foundations. Understanding how to tame (and possibly exploit) non-equilibrium effects in order to stabilize interesting quantum phases in a controlled manner often reveals a hard challenge. In that prospect, an important conceptual issue in the non-equilibrium physics of strongly interacting photons regards the possibility of stabilizing ``incompressible quantum phases'' such as the Mott-Insulator or Fractional Quantum Hall states, and more generally to stabilize the ground-state of a given particle-number conserving Hamiltonian, in a physical context where dissipative losses can not be neglected. While being able to quantum simulate those emblematic strongly correlated quantum phases in this novel experimental context would strongly benefit to the quantum optics community, gaining such a kind of flexibility would also contribute to fill an important bridge between the equilibrium and the non-equilibrium statistical physics of open quantum systems, allowing to access in a controlled manner a whole new phenomenology at the interface between the two theories. In this thesis I address those questions, which I reformulate in the following manner: -What are the conditions for the emergence of analogue equilibrium properties in open quantum systems in contact with a non-thermal environment ? -In particular, is it possible to stabilize strongly correlated quantum phases with a perfectly defined particle number in driven-dissipative photonic platforms, in spite of environment-induced losses and heating effects ? The structure of the thesis is the following. [Chapter 1.] We give an overview of the physics of many-body photonic systems. As a first step we address the weakly interacting regime in the physical context of exciton-polaritons: after describing the microscopic aspects of typical experiments, we move to the discussion of non-equilibrium Bose-Einstein Condensation and the various mechanisms related to the emergence of thermal signatures at steady-state. The second part of this Chapter is dedicated to strongly interacting fluids. After drawing a quick overview of several experimental platforms presenting a good potential for the study of such physics in a near future, we discuss the relative performance of several schemes proposed in order to replenish the photonic population [Chapter 2.] We investigate the potential of a non-Markovian pump scheme with a narrow bandpass (Lorentzian shaped) emission spectrum for the generation of strongly correlated states of light in a Bose-Hubbard lattice. Our proposal can be implemented by mean of embedded inverted two-level emitters with a strong incoherent pumping toward the excited state. Our study confirms in a single cavity the possibility of stabilizing photonic Fock states in a single configuration, and strongly localized n=1 Mott-Insulator states in a lattice with n=1 density. We show that a relatively moderate hopping is responsible for a depletion of the Mott-state, which then moves toward a delocalized state reminiscent of the superfluid regime. Finally, we proceed to a mean-field analysis of the phase diagram, and unveil a Mott-to-Superfluid transition characterized by a spontaneous breaking of the U(1) symmetry and incommensurate density. The results of this Chapter are based on the following publications: - J. Lebreuilly, M. Wouters and I. Carusotto, ``Towards strongly correlated photons in arrays of dissipative nonlinear cavities under a frequency-dependent incoherent pumping'', C. R. Phys., 17(8), 836, 2016. - A. Biella, F. Storme, J. Lebreuilly, D. Rossini, R. Fazio, I. Carusotto and C. Ciuti, ``Phase diagram of incoherently driven strongly correlated photonic lattice'', Phys. Rev. A, 96, 023839, 2017. [Chapter 3.] In view of improving the performance of the scheme introduced in last chapter, and reproducing in particular the equilibrium zero temperature phenomenology in driven-dissipative photonic lattices, we develop a fully novel scheme based on the use of non-Markovian reservoirs with tailored broadband spectra which allows to mimick the effect of tunable chemical potential. Our proposal can be implemented by mean of a small number of emitters and absorbers and is accessible to current technologies. We first analyse the case of a frequency-dependent emission with a square spectrum and confirm the possibility of stabilizing Mott insulator states with arbitrary integer density. Unlike the previous proposal the Mott state is robust against both losses and tunneling. A sharp transition toward a delocalized superfluid-like state can be induced by strong values of the tunneling or a change in the effective chemical potential. While an overall good agreement is found with the T=0 predictions, our analysis highlights small deviations from the equilibrium case in some parts of the parameters space, which are characterized by a non-vanishing entropy and the kinetic generation of doublon excitations. We finally consider an improved scheme involving additional frequency-dependent losses, and show in that case that the Hamiltonian ground-state is fully recovered for any choice of parameters. Our proposal, whose functionality relies on generic energy relaxation mechanisms and is not restricted to the Bose-Hubbard model, appears as a promising quantum simulator of zero temperature physics in photonic devices. The results of this Chapter are based on the following publication: - J. Lebreuilly, A. Biella, F. Storme, D. Rossini, R. Fazio, C. Ciuti and I. Carusotto, ``Stabilizing strongly correlated photon fluids with non-Markovian reservoirs'', Phys. Rev. A 96, 033828 (2017). [Chapter 4.] We adopt a broader perspective, and analyse the conditions for the emergence of analogous thermal properties in driven-dissipative quantum systems. We show that the impact of an equilibrated environment can be mimicked by several non-Markovian and non-equilibrated reservoirs. Chapter 2 already features a preliminary result in that direction, showing that in presence of a broad reservoir spectral density a given quantum system will evolve toward a Gibbs ensemble with an artificial chemical potential and temperature. In this chapter we develop a broader analysis focusing as a counterpart part on the exactly solvable model of a weakly interacting Bose Gas in the \acs{BEC} regime. Our formalism based on a quantum Langevin model, allows in particular to access both static and dynamical properties: remarkably, we demonstrate not only the presence of an equilibrium static signature, but also the validity of the fluctuation-dissipation theorem. While our results apply only for low-energy excitations for an arbitrary choice of reservoir spectral densities, we predict that a fine tuned choices of reservoirs mimicking the so-called Kennard Stepanov condition will lead to a full apparent equilibration. Such effect that we call ``pseudo-thermalization'' implies that under very specific conditions, an open quantum system can present all the properties of an equilibrated one in spite of the presence of an highly non equilibrated environment. The results of this Chapter are based on the following paper: - J. Lebreuilly, A. Chiocchetta and I. Carusotto, ``Pseudo-thermalization in driven-dissipative non-Markovian open quantum systems'', arXiv:1710.09602 (submitted for publication).

Durch eine Modellierung der Energiekaskade gewinnt man wertvolle Einsichten in die Dynamik turbulenter Strömungen. In dieser Arbeit werden multiplikative Kaskadenprozesse untersucht und mit verschiedenen experimentellen Zeitreihen der Energiedissipation verglichen. Zur Berechnung der Energiedissipation ist es unvermeidlich auf eine Hilfskonstruktion zurückzugreifen, die die nicht gemessenen Komponenten des Geschwindigkeitsfeldes ersetzt. Der Schwerpunkt des Vergleichs zwischen Modell und Experiment liegt auf Zweipunktkorrelationen, weil andere Observablen, wie z. B. integrale Momente, durch diese Hilfskonstruktion der Dissipation verfälscht werden. Es werden explizite Ausdrücke für die Zweipunktkorrelationen abgeleitet, die auch Korrekturen, die von einem endlichen Skalierungsbereich stammen,berücksichtigen. Mit diesen Ausdrücken ist es möglich, auch Datensätze mit niedrigen oder moderaten Reynoldszahlen zu fitten und genaue Werte für die Skalierungsexponenten zu bestimmen. Mit einer umfassenden Datenanalyse wird versucht, die freien Parameter des Kaskadengenerators zu bestimmen. Die verfügbare Statistik der Daten ist zu gering, um genauere Aussagen zu treffen, als dass die Verteilung des Kaskadengenerators ähnlich einer log-normal Verteilung sein wird. Mit dem Intermittenzexponenten, der der fundamentalste Skalierungsexponent des Dissipationsfeldes ist, lassen sich die Daten charakterisieren. Die untersuchten Daten teilen sich in zwei Gruppen auf: Die Daten, die aus Luftströmungen gewonnen wurden, weisen einen mit der Reynoldszahl steigenden Intermittenzexponenten auf, der für hohe Reynoldszahlen gegen den konstanten Wert 0.2 konvergiert. Die Daten aus einem Helium-Freistrahl andererseits können am besten mit einem konstanten Intermittenzexponenten 0.1 charakterisiert werden. Diese Unterschiede können nicht vollständig erklärt werden.Um diesen Sachverhalt genauer zu untersuchen wird ein neues Modell vorgeschlagen, das die Kramers-Moyal-Koeffizienten des Geschwindigkeitsfeldes in ein Dissipationsfeld übersetzt, um den Intermittenzexponenten aus einer anderen Perspektive zu berechnen.Schließlich wird eine dynamische Verallgemeinerung des Kaskadenprozesses,die kürzlich vorgestellt wurde, getestet. Das dynamische Modell macht Vorhersagen für allgemeine n-Punktkorrelationen. Die analytischen Ausdrücke für Dreipunktkorrelationen werden mit experimentellen Daten verglichen. Die Übereinstimmung zwischen Modellvorhersage und Experiment ist überzeugend
Modelling the turbulent energy cascade gives valuable insight into the dynamics of a turbulent flow. In this work, random multiplicative cascade processes are studied and compared with dissipation time series obtained from various experiments. The emphasis of this comparison is laid on the two-point correlation function because the unavoidable surrogacy of the dissipation field, i.e.the substitution of the multi-component expression by a single component of the velocity signal, corrupts the scaling behaviour of other observables such as integral moments. Finite-size expressions for the two-point correlation function are derived, which make it possible to fit data obtained at moderate or low Reynolds numbers and extract accurate values of scaling exponents. A comprehensive data analysis attempts to determine the free parameters of the cascade generator. The statistics are too limited to claim more than that the cascade generator will be close to having a log-normal distribution. The most basic scaling exponent of the dissipation field is called intermittency exponent and can be used to characterise the data. The investigated data fall into two groups. One set of data obtained from measurements with air show an increasing intermittency exponent with an increasing Reynolds number and saturate for high Reynolds numbers to a value of 0.2. The other set, obtained in a helium jet is best characterised with a constant intermittency exponent of 0.1. The differences are not fully understood. To investigate this issue further, a new construction is suggested, that translates the Kramers-Moyal coefficients of the velocity field into a dissipation field in order to calculate the intermittency exponent from different perspective. Finally, a dynamical generalisation of the cascade process, introduced recently, is tested. The dynamical model makes predictions for point correlation functions. The analytical expressions for three-point correlation functions are compared with their counterparts obtained from experimental data and show remarkable agreement

Micro and nanoscale systems are rapidly evolving to improve the resolution of experimental measurements. Experiments involving such small scale devices are difficult and expensive, and the available analytical theory to describe their dynamics is idealized. The dynamics of microscopic cantilevers in fluid are complicated and include significant contributions from many sources in an actual experiment. Some examples are: complex cantilever geometries, near-wall effects, thermal and external actuation techniques, and a variety of measurement techniques. Numerical simulations are a powerful approach to describe the dynamics of micro and nanoscale systems for the precise conditions of experiment. This thesis provides a numerical approach capable of addressing these inherent challenges and quantifies the dynamics of microscopic cantilevers in fluid for experimentally relevant conditions. A thermodynamic approach based upon the fluctuation-dissipation theorem allows for the calculation of stochastic dynamics from deterministic dynamics. Using numerical simulations, the thermal motion can be described for the precise conditions of experiment. It is found that the measured dynamics of cantilevers differs depending on the quantity being measured. In particular, the dynamics of displacement and angle of the cantilever tip distribute energy differently to the higher flexural modes. The externally driven dynamics of microscale cantilevers in fluid are also considered. The driven dynamics are calculated using numerical simulations of the cantilever response to a force impulse. It is found that the driven dynamics depend upon the type of actuation in addition to the quantity measured. A comparison of the driven dynamics to the corresponding stochastic dynamics yields insight into the nature of the Brownian force acting on the cantilever. Another experimentally relevant condition is the use of cantilevers with V-shaped planforms in fluid. The resulting flow field is three-dimensional and complex in contrast to what is found for a long and slender rectangular cantilever. Despite the flow complexity, the stochastic and driven dynamics of the fundamental mode can be predicted using a two-dimensional model with an appropriately chosen length scale. An experimentally motivated magnetomotive actuation technique is investigated. Results show that this approach generates power spectra nearly equivalent to the noise spectra. Furthermore, the case of a V-shaped cantilever in fluid and oscillating in proximity of a solid boundary is investigated. In the presence of a solid surface the fluid damping and added mass of fluid on the cantilever are larger than for a cantilever far from boundaries. This results in a lower frequency and quality factor for the fundamental resonance. This can impede experimental efforts because broad peaks lack distinct features that can be used to identify experimental signals. An option to overcome the large viscous damping is to take advantage of higher modes of cantilever oscillation. The higher frequency oscillations of the higher modes generate a smaller viscous boundary layer and have a reduced added mass. As a result, the quality factor increases with increasing mode number. The frequency dependence of the fluid dynamics around a fluctuating microscale cantilever is also studied. The mass of fluid entrained by the cantilever and the viscous damping quantify the interaction of a cantilever with the surrounding fluid and are computed. Analytical expressions for these parameters are derived for moderate mode number. The techniques and findings of this thesis have broad applicability to a wide range of micro and nanotechnologies that rely upon understanding the dynamics of small scale structures in fluid.
Ph. D.

Les matériaux mous impliquant des interfaces liquides présentent un grand intérêt scientifique en raison des multiples forces faibles en jeu qui dictent leur disposition et leur comportement, souvent surprenants. Dans cette thèse, nous avons étudié de nouveaux phénomènes et principes d'actuation pour le contrôle de la structure (organisation) et de la dynamique (mouvement) des systèmes de matière molle aux interfaces liquides, de l'assemblage dirigé de particules solides à la manipulation de gouttes flottantes. Nous avons établi une méthode pour adsorber et cristalliser des particules, de taille micro- ou nanométrique, à l'interface air/eau, mettant en évidence un nouveau rôle des tensioactifs pour contrôler l'organisation bidimensionnelle (2D) des particules à une concentration de tensioactif extraordinairement faible. Nous avons ensuite programmé ces assemblages en 2D afin de contrôler l'organisation des particules avec la lumière, en élaborant deux stratégies innovantes. L'utilisation de particules absorbant la lumière nous a permis de construire des structures ordonnées reconfigurables. Avec des particules ordinaires et des surfactant photosensibles, nous avons démontré un nouveau type de cristaux 2D dissipatifs (organisation induite par la lumière grâce à un apport constant en énergie). En parallèle, nous avons conçu une nouvelle méthode d'actuation magnétique pour la manipulation de petites entités liquides (gouttes, billes liquides) au moyen de substrats liquides paramagnétiques déformables, permettant de diriger, à l'aide de simples aimants permanents, le mouvement de gouttes d'huile ou d'eau
Soft materials interacting at/with liquid interfaces are of great scientific interest because of the multiple weak forces at play that dictate their, often surprising, arrangement and behaviour. In this thesis, we studied novel phenomena and actuating principles for the control of the structure (organization) and dynamics (motion) of soft matter systems at liquid interfaces, from the directed assembly of thousands of solid particles, to the manipulation of small floating drops. We established the first method to both adsorb and crystallise nm- to µm-sized particles at air/water interface, evidencing a new role of surfactants to control two-dimensional (2D) particle organization at extremely low surfactant concentration. We then programmed such 2D assemblies in order to control particle organization with light stimulation, devising two innovative strategies. Using light-absorbing particles allowed us to construct reconfigurable ordered structures (light-controlled inter-particle distance and disassembly). With ordinary particles and photosensitive surfactant, we demonstrated a new kind of dissipative 2D crystals (light-induced organization through continuous consumption of energy). In parallel, we conceived a novel magnetic actuation method for the manipulation of small liquid entities (drops, liquid marbles) by means of deformable paramagnetic liquid substrates, shaping the liquid surface with small permanent magnets and in turn directing the motion of water and oil drops in a user-defined fashion

Motivated by the sustained interest in Bose Einstein condensates and the recent progress in the understanding of topological phases in condensed matter systems, we study quantum condensates and possible topological phases of bosons in coupled light-matter excitations, so-called polaritons. These bosonic quasi-particles emerge if electronic excitations (excitons) couple strongly to photons. In the first part of this thesis a polariton Bose Einstein condensate in the presence of disorder is investigated. In contrast to the constituents of a conventional condensate, such as cold atoms, polaritons have a finite life time. Then, the losses have to be compensated by continued pumping, and a non-thermal steady state can build up. We discuss how static disorder affects this non-equilibrium condensate, and analyze the stability of the superfluid state against disorder. We find that disorder destroys the quasi-long range order of the condensate wave function, and that the polariton condensate is not a superfluid in the thermodynamic limit, even for weak disorder, although superfluid behavior would persist in small systems. Furthermore, we analyze the far field emission pattern of a polariton condensate in a disorder environment in order to compare directly with experiments. In the second part of this thesis features of polaritons in a two-dimensional quantum spin Hall cavity with time reversal symmetry are discussed. We propose a topological invariant which has a nontrivial value if the quantum spin Hall insulator is topologically nontrivial. Furthermore, we analyze emerging polaritonic edge states, discuss their relation to the underlying electronic structure, and develop an effective edge state model for polaritons.

博士
國立交通大學
電子物理系
88
We have studied a mesoscopic ring threaded by a magnetic flux that increases linearly with time. The ring is partially coherent such that conduction electrons in the ring will encounter incoherent scatterings. Besides, we have also considered the behavior of the ring when the electrons encounter elastic scatterings due to the presence of an impurity in the ring. We have adopted a S-matrix model, as proposed by Buttiker, for the incoherent scatterings in this time-dependent situation. This allows us to treat the incoherent scatterings, the elastic scatterings and the coherent inelastic processes on the same footing. We have solved exactly the problem that the coherent inelastic processes caused by the time-varying magnetic flux. Our results demonstrate unequivocally that, 1.When there is no impurity, for the electrons emanating out of incoherent scatterings, the lower the energies of these electrons, the greater will be their net contribution to the dc component of the induced current. 2. When there is an impurity : (a)In the case of a weak impurity, the lower the energies of the electrons that emanate out of incoherent scatterings, the greater will be their net contribution to the dc component I_{dc} of the induced current just like the situation of no impurity. (b)In the case of a strong impurity, however, I_{dc} alternates between regions of zero and nonzero values as the chemical potential \mu increases. The peak value of I_{dc} in the nonzero region increases with \mu. We find that these regions of zero I_{dc}, and nonzero I_{dc}, correspond closely with the gaps, and the bands, respectively, of a one dimensional energy band. These characteristics arise from the fact that the electrons traversing the ring have their {\it energies} shifted gradually until their {\it energies} fall upon a forbidden region, where they suffer total reflection. This kind of total reflection does not occur in a ring with a constant flux. Our results thus contain the nonadiabatic effects of the changing flux on the dissipation in a partially coherent ring. The evolution of these nonadiabatic features in the intermediate impurity regime is also investigated.

碩士
國立臺灣大學
應用力學研究所
85
The present study investigates the ambient fluid situation for the laterally driven oscillating microstructure , which is frequently used in MEMS. We also investigate fluid viscous dissipation and the quality factor of the present microstructure. We obstain a more reality and meanful result in compare with Cho's and experiment result. According to the present study, one can easily evaulate the dissipation energy and the quality factor of this microstructure. Besides the flow situation, we also investigets the tempature and rarefied gas effect. the result shows that when using this microstructure, the tempature effect will influnce the quality factor and the dissipation energy.

碩士
淡江大學
電機工程學系碩士在職專班
99
Due to the productivity growth of computer relevant products and based on the nowadays environment of respecting to the energy conservation, low power dissipation of computer chipset becomes one of the development goals. This paper is to address a new type of CMOS buffer which can be compatible in all the chipset design in computer relevant products. This new type of CMOS buffer has two main features. Firstly, this Feedback- controlled Split-path CMOS Buffer can distinguish the output signals, and then depart the path. In another words, it would eliminate the power dissipation of output short-current if the CMOS buffer has this inverted-delay-unit. Secondly, it has Bootstrapping Low-Voltage Driver features. This driver is to combine bootstrapping large capacitor to the MOSFET switch speed more than fast, it would eliminate the power-delay product dissipation. The simulated environment in this paper is based on the manufacture process of 0.35μm in TSMC and Intel ICH10 Chipset (14MHz, 33MHz and 48MHz) as main simulated frequency. The simulated range of voltage is from 3.3V to 1.8V (0.5V is the interval.). The simulated range of temperature is from -40℃ to 140℃ (10℃ is the interval.). As compared this CMOS buffer with others in 14MHz, 33MHz and 48MHz. At 1.8V this new type of CMOS buffer than the best of power-delay product dissipation and its value were 10.3%, 10.8%, 9.1%.

Obesity-induced diabetes affects over 400 million people worldwide. Obesity is a complex metabolic disease and is associated with several co-morbidities, all of which negatively affect the individual’s quality of life. It is commonly considered that obesity is a result of a positive energy misbalance, as increased food intake and lower expenditure eventually lead to the development of this disease. Moreover, the pathology of obesity is attributed to several genetic and epigenetic factors that put an individual at high risk compared to another. Adipose tissue is the main site of the organism’s energy storage. During the time when the nutrients are available in excess, adipocytes acquire triglycerides, which are released during the time of food deprivation in the process of lipolysis (free fatty acids and glycerol released from adipocytes). Uncontrolled lipolysis is the consequent event that contributes to the development of diabetes and paradoxically obesity. To identify the genetic factors aiming for future therapeutic avenues targeting this pathway, we performed a high-throughput screen and identified the Extracellular-regulated kinase 3 (ERK3) as a hit. We demonstrate that β-adrenergic stimulation stabilizes ERK3 leading to the formation of a complex with the co-factor MAP kinase-activated protein kinase 5 (MK5) thereby driving lipolysis. Mechanistically, we identify a downstream target of the ERK3/MK5 pathway, the transcription factor FOXO1, which promotes the expression of the major lipolytic enzyme ATGL. Finally, we provide evidence that targeted deletion of ERK3 in mouse adipocytes inhibits lipolysis, but elevates energy dissipation, promoting lean phenotype and ameliorating diabetes. Moreover, we shed the light on our pharmacological approach in targeting ERK3/MK5 pathways using MK5 specific inhibitor. Already after 1 week of administering the inhibitor, mice showed signs of improvement of their metabolic fitness as showed here by a reduction in induced lipolysis and the elevation in the expression of thermogenic genes. Taken together, our data suggest that targeting the ERK3/MK5 pathway, a previously unrecognized signaling axis in adipose tissue, could be an attractive target for future therapies aiming to combat obesity-induced diabetes
Adipositas-induzierter Diabetes betrifft weltweit über 400 Millionen Menschen. Adipositas ist eine komplexe Stoffwechselerkrankung und geht mit mehreren Komorbiditäten einher, die sich alle negativ auf die Lebensqualität der Betroffenen auswirken. Es wird generell angenommen, dass Adipositas aus einem positiven Energieungleichgewicht resultiert, da eine erhöhte Nahrungsaufnahme und ein geringerer Verbrauch zu der Ausbildung dieser Krankheit führen. Darüber hinaus ist die Pathologie von Adipositas auf mehrere genetische und epigenetische Faktoren zurückzuführen, wodurch Individuen einem erhöhtem Risiko ausgesetzt sein können. Das Fettgewebe ist der vorwiegende Energiespeicher des Organismus. In Zeiten eines Nährstoffüberschusses speichern Adipozyten Triglyceride, die im Falle eines Nahrungsmangels durch den Prozess der Lipolyse in Form von freien Fettsäuren und Glycerin freigesetzt werden. Unkontrollierte Lipolyse ist ein Folgeereignis, welches zur Entwicklung von Diabetes und paradoxerweise zu Adipositas beiträgt. Um die genetischen Faktoren zu identifizieren, die in Zukunft therapeutische Angriffspunkte darstellen könnten, haben wir ein Hochdurchsatz-Screening durchgeführt und die extrazellulär regulierte Kinase 3 (ERK3) als Treffer identifiziert. Wir zeigen, dass β-adrenerge Stimulation ERK3 stabilisiert, was zur Bildung eines Komplexes mit dem Cofactor MAP-Kinase-aktivierte Proteinkinase 5 (MK5) führt und dadurch die Lipolyse vorantreibt. Mechanistisch identifizieren wir den Transkriptionsfaktor FOXO1, der dem ERK3/MK5-Signalweg nachgeschaltet ist und die Expression des wichtigsten lipolytischen Enzyms ATGL fördert. Darüber hinaus belegen wir, dass die gezielte Deletion von ERK3 in Maus-Adipozyten die Lipolyse hemmt, aber die Energiedissipation erhöht, den mageren Phänotyp fördert und Diabetes lindert. Außerdem nutzen wir einen pharmakologischen Ansatz durch Verwendung eines MK5 spezifischen Inhibitors, um auf den ERK3/MK5-Signalweg abzuzielen. Bereits eine Woche nach Verabreichung des Inhibitors zeigen Mäuse Anzeichen einer verbesserten metabolischen Fitness, die sich durch einer Verringerung der induzierten Lipolyse und eine verstärkte Expression von thermogenen Genen auszeichnet. Zusammenfassend legen unsere Daten nahe, dass der ERK3/MK5-Signalweg, eine zuvor nicht erkannte Signalachse im Fettgewebe, ein attraktiver Ansatzpunkt für zukünftige Therapien zur Bekämpfung von Adipositas-induziertem Diabetes sein könnte

Bose-Einstein condensation is a collective quantum phenomenon where a macroscopic number of bosons occupies the lowest quantum state. For fixed temperature, bosons condense above a critical particle density. This phenomenon is a consequence of the Bose-Einstein distribution which dictates that excited states can host only a finite number of particles so that all remaining particles must form a condensate in the ground state. This reasoning applies to thermal equilibrium. We investigate the fate of Bose condensation in nonisolated systems of noninteracting Bose gases driven far away from equilibrium. An example of such a driven-dissipative scenario is a Floquet system coupled to a heat bath. In these time-periodically driven systems, the particles are distributed among the Floquet states, which are the solutions of the Schrödinger equation that are time periodic up to a phase factor. The absence of the definition of a ground state in Floquet systems raises the question, whether Bose condensation survives far from equilibrium. We show that Bose condensation generalizes to an unambiguous selection of multiple states each acquiring a large occupation proportional to the total particle number. In contrast, the occupation numbers of nonselected states are bounded from above. We observe this phenomenon not only in various Floquet systems, i.a. time-periodically-driven quartic oscillators and tight-binding chains, but also in systems coupled to two baths where the population of one bath is inverted. In many cases, the occupation numbers of the selected states are macroscopic such that a fragmented condensation is formed according to the Penrose-Onsager criterion. We propose to control the heat conductivity through a chain by switching between a single and several selected states. Furthermore, the number of selected states is always odd except for fine-tuning. We provide a criterion, whether a single state (e.g., Bose condensation) or several states are selected. In open systems, which exchange also particles with their environment, the nonequilibrium steady state is determined by the interplay between the particle-number-conserving intermode kinetics and particle-number-changing pumping and loss processes. For a large class of model systems, we find the following generic sequence when increasing the pumping: For small pumping, no state is selected. The first threshold, where the stimulated emission from the gain medium exceeds the loss in a state, is equivalent to the classical lasing threshold. Due to the competition between gain, loss and intermode kinetics, further transitions may occur. At each transition, a single state becomes either selected or deselected. Counterintuitively, at sufficiently strong pumping, the set of selected states is independent of the details of the gain and loss. Instead, it is solely determined by the intermode kinetics like in closed systems. This implies equilibrium condensation when the intermode kinetics is caused by a thermal environment. These findings agree well with observations of exciton-polariton gases in microcavities. In a collaboration with experimentalists, we observe and explain the pump-power-driven mode switching in a bimodal quantum-dot micropillar cavity.
Die Bose-Einstein-Kondensation ist ein Quantenphänomen, bei dem eine makroskopische Zahl von Bosonen den tiefsten Quantenzustand besetzt. Die Teilchen kondensieren, wenn bei konstanter Temperatur die Teilchendichte einen kritischen Wert übersteigt. Da die Besetzungen von angeregten Zuständen nach der Bose-Einstein-Statistik begrenzt sind, bilden alle verbleibenden Teilchen ein Kondensat im Grundzustand. Diese Argumentation ist im thermischen Gleichgewicht gültig. In dieser Arbeit untersuchen wir, ob die Bose-Einstein-Kondensation in nicht wechselwirkenden Gasen fern des Gleichgewichtes überlebt. Diese Frage stellt sich beispielsweise in Floquet-Systemen, welche Energie mit einer thermischen Umgebung austauschen. In diesen zeitperiodisch getriebenen Systemen verteilen sich die Teilchen auf Floquet-Zustände, die bis auf einen Phasenfaktor zeitperiodischen Lösungen der Schrödinger-Gleichung. Die fehlende Definition eines Grundzustandes wirft die Frage nach der Existenz eines Bose-Kondensates auf. Wir finden eine Generalisierung der Bose-Kondensation in Form einer Selektion mehrerer Zustände. Die Besetzung in jedem selektierten Zustand ist proportional zur Gesamtteilchenzahl, während die Besetzung aller übrigen Zustände begrenzt bleibt. Wir beobachten diesen Effekt nicht nur in Floquet-Systemen, z.B. getriebenen quartischen Fallen, sondern auch in Systemen die an zwei Wärmebäder gekoppelt sind, wobei die Besetzung des einen invertiert ist. In vielen Fällen ist die Teilchenzahl in den selektierten Zuständen makroskopisch, sodass nach dem Penrose-Onsager Kriterium ein fragmentiertes Kondensat vorliegt. Die Wärmeleitfähigkeit des Systems kann durch den Wechsel zwischen einem und mehreren selektierten Zuständen kontrolliert werden. Die Anzahl der selektierten Zustände ist stets ungerade, außer im Falle von Feintuning. Wir beschreiben ein Kriterium, welches bestimmt, ob es nur einen selektierten Zustand (z.B. Bose-Kondensation) oder viele selektierte Zustände gibt. In offenen Systemen, die auch Teilchen mit der Umgebung austauschen, ist der stationäre Nichtgleichgewichtszustand durch ein Wechselspiel zwischen der (Teilchenzahl-erhaltenden) Intermodenkinetik und den (Teilchenzahl-ändernden) Pump- und Verlustprozessen bestimmt. Für eine Vielzahl an Modellsystemen zeigen wir folgendes typisches Verhalten mit steigender Pumpleistung: Zunächst ist kein Zustand selektiert. Die erste Schwelle tritt auf, wenn der Gewinn den Verlust in einer Mode ausgleicht und entspricht der klassischen Laserschwelle. Bei stärkerem Pumpen treten weitere Übergänge auf, an denen je ein einzelner Zustand entweder selektiert oder deselektiert wird. Schließlich ist die Selektion überraschenderweise unabhängig von der Charakteristik des Pumpens und der Verlustprozesse. Die Selektion ist vielmehr ausschließlich durch die Intermodenkinetik bestimmt und entspricht damit den oben beschriebenen geschlossenen Systemen. Ist die Kinetik durch ein thermisches Bad hervorgerufen, tritt wie im Gleichgewicht eine Grundzustands-Kondensation auf. Unsere Theorie ist in Übereinstimmung mit experimentellen Beobachtungen von Exziton-Polariton-Gasen in Mikrokavitäten. In einer Kooperation mit experimentellen Gruppen konnten wir den Modenwechsel in einem bimodalen Quantenpunkt-Mikrolaser erklären.

Quantum systems that are in weak contact with a thermal heat bath will ultimately relax to an equilibrium state which is characterized by the temperature of the environment only. This state is independent of the specific properties of the bath and of how it is coupled to the system. This changes completely, when the system is additionally driven. Such a driven-dissipative situation can emerge, for example, due to an additional time-periodic modulation of the system, or when it is brought into contact with a second bath of different temperature. Then, the system will run into a well-defined nonequilibrium steady state. This state, however, will depend on the very details of the environment and its coupling to the system. We study whether this freedom can be used to engineer interesting properties of quantum systems, which are not found in their equilibrium states, i.e. in the absence of a drive. We focus on bosonic quantum many-body systems. We investigate when far-from-equilibrium ideal gases feature Bose condensation in a group of single-particle states, as opposed to situations where Bose condensation is completely absent in the nonequilibrium steady state. We show that Bose condensation can be induced in a finite one-dimensional ideal gas by the competition of two heat baths whose temperatures both lie well above the equilibrium condensation temperature. This setup also allows to engineer condensation in excited single-particle states. We discuss first ideas to study similar setups in weakly interacting Bose gases. Describing the microscopic dynamics of interacting many-body systems coupled to thermal baths is extremely challenging, due to the fact that generally the full many-body spectrum is inaccessible. Using ideas from semiclassics, we develop an approximation to the dynamics that yields good results at high and intermediate bath temperatures. We also investigate the transient dynamics of driven-dissipative quantum systems. Our studies are motivated by a result that is well known for isolated quantum systems: for a system whose dynamics is generated by a time-periodic Hamiltonian, the stroboscopic dynamics (observed at integer multiples of the driving period) can always be understood as if it would stem from a time-independent Hamiltonian, the Floquet Hamiltonian. For open quantum systems in contact with an environment, we ask if a similar mapping to an effective generator, the Floquet Lindbladian, is always possible. For a simple qubit model we show that there are two extended parameter regions, one in which the Floquet Lindbladian exists, and one in which it does not. We discuss problems of analytical expansions that can give rise to this Floquet Lindbladian and discuss how we can interpret the region where it does not exist. These results are important for dissipative Floquet engineering and open up new perspectives for the control of open quantum systems via time-periodic driving.:1. Introduction 2. Master equation for open quantum systems 3. Existence of the Floquet Lindbladian 4. Number of Bose-selected modes in driven-dissipative ideal Bose gases 5. High-temperature nonequilibrium Bose condensation induced by a hot needle 6. Weakly interacting Bose gases far from thermal equilibrium 7. Summary and outlook
Quantensysteme, die in schwacher Wechselwirkung mit einem thermischen Wärmebad stehen, relaxieren stets in einen Gleichgewichtszustand, welcher allein durch die Temperatur der Umgebung beschrieben ist. Dieser Zustand ist unabhängig von den spezifischen Eigenschaften des Bades, und davon wie dieses an das System gekoppelt ist. Dies ändert sich, wenn das System zusätzlich angetrieben wird. Ein solches getrieben-dissipatives Szenario kann beispielsweise durch einen zusätzlichen zeitperiodischen Antrieb entstehen, oder wenn das System mit einem zweiten Bad unterschiedlicher Temperatur in Kontakt gebracht wird. In diesem Fall läuft das System in einen wohldefinierten stationären Nichtgleichgewichtszustand. Dieser Zustand hängt jedoch von den Details der Umgebung, und davon wie diese an das System gekoppelt ist, ab. Es wird untersucht ob diese Freiheit genutzt werden kann um interessante Eigenschaften von Quantensystemen zu konstruieren, die in deren Gleichgewichtszuständen, d.h. in Abwesenheit des Antriebs, nicht zu finden sind. Der Fokus der Arbeit liegt auf bosonischen Quantenvielteilchensystemen. Es wird ergründet unter welchen Bedingungen ideale Gase fernab des thermischen Gleichgewichts Bose Kondensation in einer Gruppe von Einteilchenzuständen aufweisen, im Gegensatz zu Szenarien in denen überhaupt keine Bose Kondensation im stationären Nichtgleichgewichtszustand auftritt. Weiterhin wird gezeigt, dass Bose Kondensation in einem eindimensionalen idealen Gas durch das Wechselspiel zweier Wärmebäder induziert werden kann. Die Temperatur beider Bäder liegt dabei weit über der Kondensationstemperatur des Gleichgewichts. Diese Anordnung erlaubt außerdem kontrollierte Kondensation in angeregten Einteilchenzuständen. Erste Ideen für das theoretische Studium ähnlicher Anordnungen für schwach wechselwirkende Bosegase werden diskutiert. Eine Beschreibung der mikroskopischen Dynamik wechselwirkender Vielteilchensysteme ist extrem anspruchsvoll, da typischerweise das volle Vielteilchenspektrum unzugänglich ist. Unter Zurhilfenahme semiklassischer Ideen wird eine Näherung der Dynamik entwickelt, welche eine gute Beschreibung für hohe und intermediäre Temperaturen liefert. Weiterhin wird die transiente Dynamik getrieben-dissipativer Quantensysteme untersucht. Die Motivation bietet ein bekanntes Resultat für abgeschlossene Quantensysteme: Für ein System, dessen Dynamik durch einen zeitperiodischen Hamiltonoperator bestimmt ist, kann die stroboskopische Dynamik (unter Beobachtung zu Zeiten, die Vielfache der Antriebsperiode sind) immer so verstanden werden als würde sie von einem zeitunabhängigen Hamiltonoperator, dem Floquet Hamiltonian, induziert. Für offene Quantensysteme im Kontakt mit einer Umgebung wird untersucht ob eine ähnliche Abbildung auf einen effektiven Generator, den Floquet Lindbladian, existiert. Für ein einfaches Qubit Modell wird gezeigt, dass es zwei ausgedehnte Parameterregionen gibt, eine in welcher der Floquet Lindbladian existiert und eine weitere in der dieser nicht existiert. Es werden Probleme von analytischen Entwicklungen des Floquet Lindbladian diskutiert. Auch wird eine Interpretation der Region gegeben, in der dieser nicht existiert. Diese Resultate sind maßgeblich für dissipatives Floquetengineering und eröffnen neue Blickwinkel auf die zeitperiodische Kontrolle offener Quantensysteme.:1. Introduction 2. Master equation for open quantum systems 3. Existence of the Floquet Lindbladian 4. Number of Bose-selected modes in driven-dissipative ideal Bose gases 5. High-temperature nonequilibrium Bose condensation induced by a hot needle 6. Weakly interacting Bose gases far from thermal equilibrium 7. Summary and outlook

碩士
國立中山大學
電機工程學系研究所
94
The first topic of this thesis proposes a neural stimulation, recording and impedance measuring system for implantable applications. It includes a stimulation DAC, a instrumentation amplifier, an ADC, and a digital controller which decides the operation of each block according to the required functions. The function provided by the system include micro-stimulation, neural signal recording, or impedance measurement. The second topic is to describe a dual-OPA coil driver for SOC heat dissipation. It includes two class AB complementary output drivers which can drive an inductance load, such as micro motors and fans. It also discusses the feasibility of a bipolar transistor in CMOS process.

Motivated by the sustained interest in Bose Einstein condensates and the recent progress in the understanding of topological phases in condensed matter systems, we study quantum condensates and possible topological phases of bosons in coupled light-matter excitations, so-called polaritons. These bosonic quasi-particles emerge if electronic excitations (excitons) couple strongly to photons. In the first part of this thesis a polariton Bose Einstein condensate in the presence of disorder is investigated. In contrast to the constituents of a conventional condensate, such as cold atoms, polaritons have a finite life time. Then, the losses have to be compensated by continued pumping, and a non-thermal steady state can build up. We discuss how static disorder affects this non-equilibrium condensate, and analyze the stability of the superfluid state against disorder. We find that disorder destroys the quasi-long range order of the condensate wave function, and that the polariton condensate is not a superfluid in the thermodynamic limit, even for weak disorder, although superfluid behavior would persist in small systems. Furthermore, we analyze the far field emission pattern of a polariton condensate in a disorder environment in order to compare directly with experiments. In the second part of this thesis features of polaritons in a two-dimensional quantum spin Hall cavity with time reversal symmetry are discussed. We propose a topological invariant which has a nontrivial value if the quantum spin Hall insulator is topologically nontrivial. Furthermore, we analyze emerging polaritonic edge states, discuss their relation to the underlying electronic structure, and develop an effective edge state model for polaritons.