Dissertations / Theses on the topic 'Quantum Dissipative Systems'

This thesis consists of five scientific papers in the field of condensed matter physics. In all papers we employ large scale Monte Carlo simulations to investigate quantum critical behavior in systems coupled to an environment. Special attention is paid to possible anisotropies between spatial fluctuations and fluctuations in imaginary time. Implications of the results to the loop current theory of cuprates are discussed.

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

In the first part of this thesis, a new method is proposed to circumvent the relaxation bottleneck that prevents high-temperature Bose-Einstein condensation of microcavity polaritons. This is achieved by relaxing polaritons with a coherent beam of phonons that is pumped in the growth direction of the quantum well. By tuning the frequency of these phonons to the energy difference between the bottleneck distribution and the ground state, resonant scattering relaxes the exciton reservoir very efficiently. Within a simple rate equation model, it is shown that above a threshold phonon intensity, an unstable and faster-than-exponential instability of the ground state population occurs, with macroscopic occupation possible on sub-picosecond timescales. Numerical results for GaAs and CdTe are presented, confirming that this method could be highly effective in alleviating the bottleneck effect. The second part addresses the problem of decoherence in the sub-Ohmic spin boson model. This previously unimportant model has recently attracted attention due to the discovery of several new physical realisations. Using Silbey and Harris’ variational method, a zero-temperature phase transition between coherent and incoherent ground states is found. The critical spin-bath coupling is extracted, and found to agree well with numerical calculations. Calculations at finite temperatures also yield transitions between coherent and incoherent spin dynamics at a critical temperature. Considering the dynamics of the variational Hamiltonian, it is shown that fluctuations of the bath lead to damping of the coherent spin-dynamics. Approaching the incoherence transition, these dynamics become highly non-Markovian. This chapter also contains a formal demonstration that an alternative variational state, the displaced-squeezed state (DSS), leads to incorrect results in the thermodynamic limit.

Strong coupling between a quantum system and its many-body environment is becoming an increasingly important topic for many branches of physics. Numerous systems of experimental and technological relevance demonstrate strong system-environment coupling, leading to complex dynamical behaviour. This thesis is concerned with two particular examples of such systems, namely quantum dots (QDs) and excitonic energy transfer (EET) in molecular systems. Traditional quantum optics treatments are often insufficient to describe the transient, steady state, and optical properties of QDs due to system-environment correlations. In contrast, we present a modified theory of quantum optics capable of capturing the influence of a thermal environment on the behaviour of QDs. Using this framework we demonstrate a striking departure of the emission spectra and photon measurement statistics of a classically driven QD when compared to an analogous atomic system. Furthermore, in contradiction to accepted notions of decoherence and dissipation, we show that the interaction between a QD and its thermal environment induces non-classical light-matter correlations in an otherwise semi-classical regime of cavity quantum electrodynamics. Away from QDs, we develop the reaction coordinate (RC) formalism to describe the dynamics of a system coupled to a low frequency environment - a regime important to EET systems. We do so by identifying and incorporating important environmental degrees of freedom into an enlarged system Hamiltonian. Uniquely, this approach gives insight directly into the dynamical evolution of the environment and correlations accumulated between the system and environment. Furthermore, it is demonstrated that these corre- lations persist into the steady state, generating non-canonical equilibrium states of the system and environment. We then apply the RC model to describe EET in a molecular dimer, highlighting the effect that under- and over-damped environments have on the excitation dynamics. In doing so, we show interactions between the dimer and a structured environment can significantly enhance the energy transfer rate.

Motivated by the continuous advancements in the miniaturization of devices down to reveal the quantum nature of matter, in this thesis we investigate the way a quantum system is affected by the presence of a thermal environment and propose methodologies to exploit this kind of sensitivity for quantum technologies. Since treating exactly the dynamics of the full system-environment compound is generally problematic for the diverging number of degrees of freedom involved in the calculation, effective master equations for the reduced system density matrix were developed in literature during the last century. Among them, the Redfield approach is an equation obtained under weakcoupling (or Born) and Markovian assumptions. Despite offering effective descriptions in a plethora of situations, it was criticized for not preserving the positivity (and hence the complete positivity) of the system density matrix. The latter property is in general a fundamental feature for assigning a probabilistic interpretation to the theory. We hence begin by facing the problem of the non-positivity character of the Redfield equation, curing it of the strict amount that is necessary via coarse-grain averaging performed on the Redfield equation in the interaction picture. In the analysis a central role is played by the coarse grain timescale. Once set it equal to a critical threshold value, the resulting equation (CP-Redfield) enables conserving the predictive power of the Redfield approach and preserving positivity at the same time. About it, we report both practical estimation and self-consistent methods to evaluate the critical timescale. Our strategy also allows to continuously map the Redfield equation into the secular master equation (diverging coarse-grain time interval) by appropriately tuning the coarse grain time, the latter being the equation usually adopted in the literature for ensuring thermodynamic consistency by enforcing a rotating-wave approximation. Starting from a minimal example concerning the dipole coupling between a qubit and a bosonic bath, we then apply this methodology to dissipative multipartite systems, for which the local vs global debate is of current interest. The local master equation is instead the equation that is obtained by assigning to each subsystem its proper thermal dissipator, preserving the local character of the microscopic interactions, while the global approach is the Redfield equation in the secular limit. In this context, we studied an asymmetric energy transfer model constituted by harmonic oscillators which, being exactly solvable, provides the appropriate benchmark for testing the efficiency of the different master equations.. Beyond finding useful the application of the CP-Redfield equation, we point out a sensible convex-mixture of the local and global solutions based on the timescale separation of the two strategies. The local approach is then applied in the context of quantum batteries, a field that was previously analyzed under closed (i.e. Hamiltonian) settings. We hence provide one of the first attempts of schematizing an open quantum battery, where, recalling in part the aforementioned asymmetric model, the charging process originates from external sources (coherent and/or noisy) and is mediated by a proper quantum charger. By studying different implementations, particular attention was devoted to find possible interplay between coherent and incoherent energy supply mechanisms in producing stored energy and ergotropy, the latter being defined in literature as the maximum extractable work. As a central result, increasing temperature is not always detrimental for the stored ergotropy. Going beyond the particular instance of bosonic bath, the sensitivity of a quantum system to its surrounding environment is finally exploited in the context of statistical tagging, where one aims to guess the quantum statistics (fermionic or bosonic) of a thermal bath of interest, introducing in this way a novel research line in the field of quantum metrology. We propose an indirect measurement protocol in which a quantum probe is let to interact with the unknown bath and relies on the consideration that, despite the final probe equilibrium configuration is not necessarily influenced by the bath nature, the latter generally leaves residual imprintings in the probe state before thermalization, i.e. out-of-equilibrium. Using figures of merit taken from quantum metrology such as the Holevo-Helstrom probability of error and the quantum Chernoff bound, we treated the cases of qubit and harmonic oscillator probes, finding that, generally, the presence of coherences in the input state of the probe is beneficial for the discrimination capability and noticing a bosonic advantage in reducing to zero the error probability.

This thesis probes the usefulness of non-classical correlations within imperfect continuous variable decoherent quantum systems. Although a consistent function and practical usefulness of these correlations is largely unknown, it is important to examine their characteristics in more realistic dissipative systems, to gain further insight into any possible advantageous behaviour. A bipartite separable discordant state under the action of controlled loss on one subsystem was considered. Under these conditions the Gaussian quantum discord not only proved to be robust against loss, but actually improves as loss is intensified. Harmful imperfections which reduce the achievable level of discord can be counteracted by this controlled loss. Through a purification an explanation of this effect was sought by considering system-environment correlations, and found that a flow of system-environment correlations increases the quantumness of the state. Entanglement recovery possibilities were discussed and revealed the importance of hidden quantum correlations along bi-partitions across the discordant state and a classically prepared "demodulating" system, acting in such a way as to partially cancel the entanglement preventing noise. Entanglement distribution by separable states was studied by a similar framework, in an attempt to explain the emergence of quantum entanglement by a specific flow of correlations in the globally pure system. Discord appears to play a less fundamental role compared to the qubit version of the protocol. The strengthening of non-classical correlations can be attributed to a flow of classical and quantum correlations. This work proves that discord can be created in unique ways and, in select circumstances, can act to counteract harmful imperfections in the apparatus. Due to this advantageous behaviour discord indeed may ultimately aid in more applicable "real world" applications, which are by definition decoherent.

Diese Dissertation untersucht Quantensysteme in kondensierter Phase, welche mit ihrer Umgebung wechselwirken und durch ultrakurze Laserpulse angeregt werden. Die Zeitskalen der verschiedenen beteiligten Prozessen lassen sich bei solchen Problemen nicht separieren, weshalb die Standardmethoden zur Behandlung offener Quantensysteme nicht angewandt werden können. Die Methode des Surrogate Hamiltonian stellt ein Beispiel neuer Herangehensweisen an dissipative Quantendynamik dar. Die Weiterentwicklung der Methode und ihre Anwendung auf Phänomene, die zur Zeit experimentell untersucht werden, stehen im Mittelpunkt dieser Arbeit. Im ersten Teil der Arbeit werden die einzelnen dissipativen Prozesse klassifiziert und diskutiert. Insbesondere wird ein Modell der Dephasierung in die Methode des Surrogate Hamiltonian eingeführt. Dies ist wichtig für zukünftige Anwendungen der Methode, z.b. auf kohärente Kontrolle oder Quantencomputing. Diesbezüglich hat der Surrogate Hamiltonian einen großen Vorteil gegenüber anderen zur Verfügung stehenden Methoden dadurch, daß er auf dem Spin-Bad, d.h. auf einer vollständig quantenmechanischen Beschreibung der Umgebung, beruht. Im nächsten Schritt wird der Surrogate Hamiltonian auf ein Standardproblem für Ladungstransfer in kondensierter Phase angewandt, zwei nichtadiabatisch gekoppelte harmonische Oszillatoren, die in ein Bad eingebettet sind. Dieses Modell stellt eine große Vereinfachung von z.B. einem Molekül in Lösung dar, es dient hier jedoch als Testbeispiel für die theoretische Beschreibung eines prototypischen Ladungstransferereignisses. Alle qualitativen Merkmale eines solchen Experimentes können wiedergegeben und Defizite früherer Behandlungen identifiziert werden. Ultraschnelle Experimente beobachten Reaktionsdynamik auf der Zeitskala von Femtosekunden. Dies kann besonders gut durch den Surrogate Hamiltonian als einer Methode, die auf einer zeitabhängigen Beschreibung beruht, erfaßt werden. Die Kombination der numerischen Lösung der zeitabhängigen Schrödingergleichung mit der Wignerfunktion, die die Visualisierung eines Quantenzustands im Phasenraum ermöglicht, gestattet es, dem Ladungstransferzyklus intuitiv Schritt für Schritt zu folgen. Der Nutzen des Surrogate Hamiltonian wird weiterhin durch die Verbindung mit der Methode der Filterdiagonalisierung erhöht. Dies gestattet es, aus mit dem Surrogate Hamiltonian nur für relative kurze Zeite konvergierte Erwartungswerten Ergebnisse in der Frequenzdomäne zu erhalten. Der zweite Teil der Arbeit beschäftigt sich mit der theoretischen Beschreibung der laserinduzierten Desorption kleiner Moleküle von Metalloxidoberflächen. Dieses Problem stellt ein Beispiel dar, in dem alle Aspekte mit derselben methodischen Genauigkeit beschrieben werden, d.h. ab initio Potentialflächen werden mit einem mikroskopischen Modell für die Anregungs- und Relaxationsprozesse verbunden. Das Modell für die Wechselwirkung zwischen angeregtem Adsorbat-Substrat-System und Elektron-Loch-Paaren des Substrats beruht auf einer vereinfachten Darstellung der Elektron-Loch-Paare als ein Bad aus Dipolen und auf einer Dipol-Dipol-Wechselwirkung zwischen System und Bad. Alle Parameter können aus Rechnungen zur elektronischen Struktur abgeschätzt werden. Desorptionswahrscheinlichkeiten und Desorptionsgeschwindigkeiten werden unabhängig voneinander im experimentell gefundenen Bereich erhalten. Damit erlaubt der Surrogate Hamiltonian erstmalig eine vollständige Beschreibung der Photodesorptionsdynamik auf ab initio-Basis.
This thesis investigates condensed phase quantum systems which interact with their environment and which are subject to ultrashort laser pulses. For such systems the timescales of the involved processes cannot be separated, and standard approaches to treat open quantum systems fail. The Surrogate Hamiltonian method represents one example of a number of new approaches to address quantum dissipative dynamics. Its further development and application to phenomena under current experimental investigation are presented. The single dissipative processes are classified and discussed in the first part of this thesis. In particular, a model of dephasing is introduced into the Surrogate Hamiltonian method. This is of importance for future work in fields such as coherent control and quantum computing. In regard to these subjects, it is a great advantage of the Surrogate Hamiltonian over other available methods that it relies on a spin, i.e. a fully quantum mechanical description of the bath. The Surrogate Hamiltonian method is applied to a standard model of charge transfer in condensed phase, two nonadiabatically coupled harmonic oscillators immersed in a bath. This model is still an oversimplification of, for example, a molecule in solution, but it serves as testing ground for the theoretical description of a prototypical ultrafast pump-probe experiment. All qualitative features of such an experiment are reproduced and shortcomings of previous treatments are identified. Ultrafast experiments attempt to monitor reaction dynamics on a femtosecond timescale. This can be captured particularly well by the Surrogate Hamiltonian as a method based on a time-dependent picture. The combination of the numerical solution of the time-dependent Schrödinger equation with the phase space visualization given by the Wigner function allows for a step by step following of the sequence of events in a charge transfer cycle in a very intuitive way. The utility of the Surrogate Hamiltonian is furthermore significantly enhanced by the incorporation of the Filter Diagonalization method. This allows to obtain frequency domain results from the dynamics which can be converged within the Surrogate Hamiltonian approach only for comparatively short times. The second part of this thesis is concerned with the theoretical treatment of laser induced desorption of small molecules from oxide surfaces. This is an example which allows for a description of all aspects of the problem with the same level of rigor, i.e. ab initio potential energy surfaces are combined with a microscopic model for the excitation and relaxation processes. This model of the interaction between the excited adsorbate-substrate complex and substrate electron-hole pairs relies on a simplified description of the electron-hole pairs as a bath of dipoles, and a dipole-dipole interaction between system and bath. All parameters are connected to results from electronic structure calculations. The obtained desorption probabilities and desorption velocities are simultaneously found to be in the right range as compared to the experimental results. The Surrogate Hamiltonian approach therefore allows for a complete description of the photodesorption dynamics on an ab initio basis for the first time.

Cette thèse est structurée autour de trois chapitres principaux. Dans le premier chapitre, je présente de nouveaux résultats obtenus pour la théorie S\phi^4S hors équilibre, dont la dynamique est décrite par une equation de Langevin en présence d'un bruit coloré. Les corrélations temporelles du bruit décroissent avec une loi de puissance déterminée par un certain exposant que j'appelerai SalphaS. Il s'avère qu'il y a un S\alpha_cS de transition qui dépend de la dimension SDS du système et qui sépare le plan S(\alpha, D)S en une région où la couleur du bruit modifie le comportement critique et une autre où cette couleur est non pertinente. Je discute également le comportement d'échelle des fonctions de corrélation hors équilibre. Dans le deuxième chapitre de ma thèse j'introduis un formalisme d'intégrale de chemin pour d'écrire le mouvement Brownien hors équilibre. Je présente de nouveaux résultats qui ont été obtenus pendant mon doctorat sur les fonctions de corrélation hors equilibre après une trempe quantique. La troisième partie de ma thèse est consacrée à la diffusion d'impuretés dans des liquides quantiques en une dimension, communément appelés des liquides de Luttinger. Après une introduction aux problèmes divers liés à un tel système composé d'une impureté et d'un liquide de Luttinger, je présente une nouvelle description de la dynamique de l'impureté en présence d'un piège harmonique. La densité du liquide de Luttinger non-homogène influence fortement la dynamique de l'impureté et mène à des comportements inédits. De tels systèmes physiques sont actuellement étudiés dans des expèriences d'atomes froids
This thesis is structured around three main chapters. In the first chapter I present new results which have been obtained for the out-of-equilibrium critical S\phi^4S-theory. Its dynamics are described by a Langevin equation driven by a colored noise. The temporal correlation of this noise features a power-law decrease which is governed by a certain exponent S\alphaS. It turns out that there exists a crossover S\alpha_cS which depends on the dimension SDS of the system and separates the S(\alpha, D)S-plane into a region where the color of the noise alters the critical behaviour and a region where the color is non relevant. I also discuss the scaling bahaviour of the non equilibrium correlation functions. In the second chapter I introduce a path integral formalism to describe non equilibrium quantum Brownian motion. I present the results which have been obtained during my PhD on the evolution of the non equilibrium correlation functions after a quantum quench. The third part of my thesis focuses on the impurity diffusion in one-dimensional quantum liquids which are commonly called Luttinger liquids. After an introductory part which covers the main issues related to such a system, I present a novel description of the impurity dynamics in the case where an external trapping potential is present. The non-homogeneous density profile of the Luttinger liquid then strongly influences on the impurity dynamics in a fascinating way. Such systems are currently being studied in cold atoms experiments

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

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

The outline of this work will be as follows: in chapter 1, after a brief overview of the systems studied and a preview of the results obtained, we will introduce the general models and methods we are going to use to tackle the systems considered, hopefully providing enough theory to understand our later extensive treatment, without entering in too much detail in the widely studied general theories of our models. In chapter 2 we will show our first application: the description of a spin-sensitive dissipation channel compatible with the experimental findings of an atomic force microscopy experiment. We will describe in some detail the experiment and the system under study and why some direct approaches are unable to account for the observed effect; we will then specialize the previously described path integral technique to obtain a numerical description of the system, highlighting our proposed dissipation mechanism. In chapter 3 we will consider electron current pumping in a threesite system and how it can be affected by the presence of an environment. We will first obtain and solve a simple equation for the isolated system, then couple a bath to this and specialize the master equation theory to obtain an analytical result for the system in presence of an environment, observing some interesting changes it its behavior. The experimental feasibility of the proposed setup will be explored. Finally, in chapter 4 we will briefly present another model for the description of dissipative systems which has been investigated but, for now, is not complete enough to produce interesting results: inspired from another atomic force microscopy experiment where frictional effects of hydrogen atoms on a surface are observed, we will try to investigate the possibility of inherently quantum effects in a similar system, where a light particle is coupled to other heavier atoms, treated classically. We will propose a model and a technique for its simulation, though this will prove too computationally demanding to be of practical use.

In this thesis, quantum dynamical simulations are performed in order to describe the vibrational motion of diatomic molecules in a highly quantum environment, so-called helium droplets. We aim to reproduce and explain experimental findings which were obtained from dimers on helium droplets. Nanometer-sized helium droplets contain several thousands of 4-He atoms. They serve as a host for embedded atoms or molecules and provide an ultracold “refrigerator” for them. Spectroscopy of molecules in or on these droplets reveals information on both the molecule and the helium environment. The droplets are known to be in the superfluid He II phase. Superfluidity in nanoscale systems is a steadily growing field of research. Spectra obtained from full quantum simulations for the unperturbed dimer show deviations from measurements with dimers on helium droplets. These deviations result from the influence of the helium environment on the dimer dynamics. In this work, a well-established quantum optical master equation is used in order to describe the dimer dynamics effectively. The master equation allows to describe damping fully quantum mechanically. By employing that equation in the quantum dynamical simulation, one can study the role of dissipation and decoherence in dimers on helium droplets. The effective description allows to explain experiments with Rb-2 dimers on helium droplets. Here, we identify vibrational damping and associated decoherence as the main explanation for the experimental results. The relation between decoherence and dissipation in Morse-like systems at zero temperature is studied in more detail. The dissipative model is also used to investigate experiments with K-2 dimers on helium droplets. However, by comparing numerical simulations with experimental data, one finds that further mechanisms are active. Here, a good agreement is obtained through accounting for rapid desorption of dimers. We find that decoherence occurs in the electronic manifold of the molecule. Finally, we are able to examine whether superfluidity of the host does play a role in these experiments
In dieser Dissertation werden quantendynamische Simulationen durchgeführt, um die Schwingungsbewegung zweiatomiger Moleküle in einer hochgradig quantenmechanischen Umgebung, sogenannten Heliumtröpfchen, zu beschreiben. Unser Ziel ist es, experimentelle Befunde zu reproduzieren und zu erklären, die von Dimeren auf Heliumtröpfchen erhalten wurden. Nanometergroße Heliumtröpfchen enthalten einige tausend 4-He Atome. Sie dienen als Wirt für eingebettete Atome oder Moleküle und stellen für dieseeinen ultrakalten „Kühlschrank“ bereit. Durch Spektroskopie mit Molekülen in oder auf diesen Tröpfchen erhält man Informationen sowohl über das Molekül selbst als auch über die Heliumumgebung. Man weiß, dass sich die Tröpfchen in der suprafluiden He II Phase befinden. Suprafluidität in Nanosystemen ist ein stetig wachsendes Forschungsgebiet. Spektren, die für das ungestörte Dimer durch voll quantenmechanische Simulationen erhalten werden, weichen von Messungen mit Dimeren auf Heliumtröpfchen ab. Diese Abweichungen lassen sich auf den Einfluss der Heliumumgebung auf die Dynamik des Dimers zurückführen. In dieser Arbeit wird eine etablierte quantenoptische Mastergleichung verwendet, um die Dynamik des Dimers effektiv zu beschreiben. Die Mastergleichung erlaubt es, Dämpfung voll quantenmechanisch zu beschreiben. Durch Verwendung dieser Gleichung in der Quantendynamik-Simulation lässt sich die Rolle von Dissipation und Dekohärenz in Dimeren auf Heliumtröpfchen untersuchen. Die effektive Beschreibung erlaubt es, Experimente mit Rb-2 Dimeren zu erklären. In diesen Untersuchungen wird Dissipation und die damit verbundene Dekohärenz im Schwingungsfreiheitsgrad als maßgebliche Erklärung für die experimentellen Resultate identifiziert. Die Beziehung zwischen Dekohärenz und Dissipation in Morse-artigen Systemen bei Temperatur Null wird genauer untersucht. Das Dissipationsmodell wird auch verwendet, um Experimente mit K-2 Dimeren auf Heliumtröpfchen zu untersuchen. Wie sich beim Vergleich von numerischen Simulationen mit experimentellen Daten allerdings herausstellt, treten weitere Mechanismen auf. Eine gute Übereinstimmung wird erzielt, wenn man eine schnelle Desorption der Dimere berücksichtigt. Wir stellen fest, dass ein Dekohärenzprozess im elektronischen Freiheitsgrad des Moleküls auftritt. Schlussendlich sind wir in der Lage herauszufinden, ob Suprafluidität des Wirts in diesen Experimenten eine Rolle spielt

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).

Exciton-polaritons are the fundamental excitations arising from the strong coupling of quantum well excitons and cavity photons in semiconductor microcavities. They are compound bosons for which stimulated scattering and macroscopic occupation of single quantum states can occur at sufficiently high densities. One way of creating such polariton condensates is with nonresonant optical pumping. Doing so creates a large density of free- carriers and excitons that strongly interact and blueshift the polariton energy levels. Using spatially patterned nonresonant fields, the polariton potential landscape can be tailored and optically trapped condensates can be created. This thesis shows that the spin properties of polariton condensates are strongly modified by such trapping. Under linearly polarised pumping, helicity can spontaneously develop at a critical occupation, breaking the parity symmetry. This formation of spin-up/spin-down condensates is explained within a Gross-Pitaevskii model which accurately reproduces the influence of electric fields and condensate density. Under elliptically polarised pumping, two phenomena are observed: the formation of condensates with the opposite handedness to the pump and hysteresis of both occupation and spin with respect to pump power. The spatial dependence of these effects highlights the limitations of commonly used models of polariton condensation. Finally, the suitability of patterned optical fields for the creation of polariton lattices is explored. For small chains of condensates, controllable coupling between adjacent spins is demonstrated, with the formation of antiferromagnetic and ferromagnetic domains. The extent of these domains is strongly affected by sample nonuniformity, fundamentally limiting the scalability of these lattices.

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.

Plus d'un siècle après sa découverte, la supraconductivité est aujourd'hui utilisée dans de nombreuses applications. Une de ces applications est l'électronique supraconductrice, et un des blocs de base de celle-ci est la jonction Josephson. Cet élément a permis la réalisation de circuits électroniques dans le régime quantique et il a aidé à redéfinir la valeur du Volt dans le Système International d'unité à partir d'effets quantiques. Ces dernières années, beaucoup de temps et d'efforts sont dépensés pour améliorer ce composant et les circuits l'intégrant dans l'objectif de réaliser de meilleurs circuits à bit quantique pour l'informatique quantique. Il est donc normal de se demander si l'existence de ces circuits de pointe contenant des jonctions Josephson et des supraconducteurs conventionnels indique une maîtrise parfaite de ceux-ci. Dans ce travail de thèse, nous montrons que cela n'est pas entièrement le cas via l'exploration de deux circuits quantiques supraconducteurs pour lesquels des études plus approfondies sont nécessaires. Le premier concerne la jonction Josephson elle-même et son comportement lorsqu'elle est mise en présence d'un environnement électromagnétique. En effet, il a été prédit il y a presque 40 ans qu'une jonction Josephson deviendrait isolante lorsqu'elle est connectée à une résistance plus grande que Rq=h/4e²≈6.45 kΩ. Nous ne trouvons aucunes traces de cet état isolant dans nos expériences qui mesurent l'admittance de jonctions Josephson connectées en parallèle de résistance de valeur R>Rq. Le deuxième circuit explore le composant supposé dual de la jonction Josephson, la jonction à sauts de phase quantique, qui consiste en un nanofil de supraconducteur fortement inductif. Dans ces nanofils, des sauts de 2π de la phase supraconductrice sont censés produire les effets duals des paires de Cooper passant par effet tunnel dans la jonction Josephson. La maîtrise de ces effets duals permettrait la réalisation d'une nouvelle classe de circuits supraconducteurs quantiques. Nous avons fabriqué des résonateurs micro-ondes à partir de couches minces de supraconducteur fortement inductif. Nous ne trouvons aucune signature de l'effet des sauts de phase quantiques dans nos dispositifs. Cependant, nous mesurons un fort bruit basse fréquence causé par des systèmes à deux niveaux, et nous explorons ses implications dans ce type de résonateur
More than a century after its discovery, superconductivity is used today in many applications. One of those is in superconducting electronics, of which the Josephson junction is a basic building block. This element has enabled the realisation of electronic circuits in the quantum regime, and it has helped redefining the Volt in the SI system around quantum effects. Nowadays, a lot of time and efforts are spent in order to improve Josephson junction based circuits to realise state of the art Quantum-bits for quantum computing. One may think that those highly sensitive experiments involving Josephson junctions and conventional superconductivity imply an exquisite understanding of the component and its behaviour. We show in this thesis work that this is not entirely the case, and we explore two types of superconducting quantum circuits that are in need of clarification. The first one concerns the Josephson junction itself, and a subtle issue regarding its interaction with its electromagnetic environment. Indeed, it has been predicted nearly 40 years ago that a Josephson junction would become insulating when connected to a resistance larger than Rq=h/4e²≈6.45 kΩ. We find no traces of such insulating state in our experiments which measure the admittance of a Josephson junction connected in parallel to a resistance R>Rq. The second circuit we explore is the supposedly dual circuit to the Josephson junction, the quantum phase slip junction, which consists of a nanowire made of a highly inductive superconductor. In those nanowires 2π phase slips of the superconducting phase should produce the dual effects of the Cooper-pair tunneling in Josephson junctions. The control of such an effect would then permit the realisation of a new class of superconducting quantum devices. We measured microwaves resonators patterned in a thin film of a highly inductive superconductor. We find no clear signal revealing the presence of quantum phase slips in our devices. However, we find a clear signature of two-level system low frequency noise, and we explore its implication in this kind of devices

Orientador: Amir Ordacgi Caldeira
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin
Made available in DSpace on 2018-08-06T02:34:45Z (GMT). No. of bitstreams: 1 Brito_FredericoBorgesde_D.pdf: 5789237 bytes, checksum: 6648aaced89bad6ff2fc57794c0ae747 (MD5) Previous issue date: 2006
Resumo: Esta tese teve como objetivo estudar processos de perda de coerência quântica, chamados de descoerência, em sistemas de matéria condensada eleitos pela literatura como possíveis implementações do bit quântico (qubit). Esta perda de coerência quântica ocorre devido ao inevitável acoplamento do sistema de interesse com o seu ambiente. Como os estados de superposição quântica são a chave para a realização de operações baseadas na lógica quântica, tem-se que tais processos limitam ou até mesmo impedem o uso de determinados sistemas na esperada realização física do computador quântico. Os sistemas de matéria condensada padecem de uma dificuldade maior para se isolar o qubit do seu ambiente, o que acarreta, em geral, na observação de tempos de coerência piores do que os encontrados em seus concorrentes. Por outro lado, a possibilidade de construção de vários qubits acoplados e de manipulação de cada um de modo individual, usando-se técnicas convencionais de engenharia, têm impulsionado esforços nestes tipos de dispositivos. Os sistemas abordados na tese foram: qubits supercondutores contendo junções Josephson; e qubits de pontos quânticos. Para a investigação completa do primeiro tipo tivemos que desenvolver o modelo Caldeira-Leggett para o caso de várias fontes de dissipação acopladas ao qubit. Com a prescrição apresentada aqui, pudemos determinar o número de banhos de osciladores necessários para a correta descrição das fontes, e verificar que as taxas totais de relaxação e de descoerência não são necessariamente as somas das taxas devido a cada fonte individualmente. Além disso, pudemos aplicar o formalismo desenvolvido no estudo de um qubit de uxo em investigação. Para o sistema de pontos quânticos seguimos a linha de determinação do banho efetivo visto pelo grau de liberdade de spin do elétron aprisionado no ponto quântico. Determinada a função espectral efetiva, pudemos encontrar soluções analíticas para a dinâmica do valor esperado para cada uma das componentes de spin s x,y,z. o que permitiu uma análise completa dos efeitos de cada parâmetro físico do sistema. Em ambos os casos, fomos capazes de indicar os melhores regimes de operação de cada qubit, e dar estimativas dos tempos de relaxação e de descoerência
Abstract: The purpose of this thesis was to study the process of loss of quantum coherence, named decoherence, in condensed matter systems cited in the literature as possible candidates for the implementation of a quantum bit (qubit). Decoherence occurs due to the inevitable coupling of the system of interest to its environment. Once the quantum superposition states are the key to perform operations based on quantum logic, these processes limit, or even hinder, the utilization of some of those systems in the physical realization of the quantum computer. Relatively to its competitors, condensed matter systems usually present a higher degree of difficulty as one tries to minimize the coupling between the qubit and its environment, which, generally, worsens its coherence time observations. On the other hand, these devices present advantages which stimulates its study, such as: the possibility of construction of several coupled qubits and the possibility of manipulating each one individually, using conventional engineering techniques. The systems studied in this thesis were: superconducting qubits with Josephson junctions; and electronic spins quantum dots. Aiming at a complete investigation of the first system, we developed the Caldeira-Leggett model for the case of several dissipation sources coupled to the qubit. With the prescription presented here, we determine the number of oscillator baths needed to the correct description of the noise sources, and verify that the total relaxation and decoherence rates are not necessarily the sum of the individual rates relative to each source. Moreover, we applied this formalism to the study of a ux qubit currently under investigation. For the quantum dot qubits, we employed the effective bath approach to treat the dynamics of the spin of the electron localized in the quantum dot. As a result, we found analytical solutions for the dynamics of the average value of each one of the spin components s x,y,z . In both cases, we indicated the best operational regime of each qubit and gave estimates of the relaxation and decoherence times
Doutorado
Física da Matéria Condensada
Doutor em Ciências

2007/2008
The experimental realization of Bose Einstein Condensates opened the path for a wide range of investigations in physics of ultracold atoms; the peculiar characteristics of these systems and the recent advances in optical confinement technology make them preferred candidates for the implementation of quantum communication and information protocols based on many-body coherent states. In this framework, the dissertation focuses on some consequences that the presence of a weakly coupled external environment has on a system of cold atoms in an optical trap. Typically, the presence of an environment leads to noise and dissipation; whereas the thesis investigates the capability of the environment of mediating an induced interaction between otherwise isolated atoms, making possible the rising of coherence between atoms localized in different sites of the confining potential. The effects of this coherence can be interpreted in terms of an atomic current flowing across the system. Standard open quantum systems methods, mainly related to the weak coupling limit, have been used in order to describe the dissipative dynamics by means of a memoryless master equation. Except for some special cases, this master equation cannot be analitically integrated; therefore, suitable techniques have been used to describe the coherence behaviour at small times, which are of the order of the characteristic times of the dissipative phenomena in the thesis. In detail, the weak coupling limit has been reviewed in the general formalism of open quantum systems; then, after a brief introduction about the physycs of ultracold atoms, the master equation ruling the dissipative dynamics in the presence of a weakly coupled environment, typically a heat bath or a stochastic classical field, has been derived. Two different kinds of coupling have been considered, mainly differing in the conservation of the total number of particles. Having obtained the master equation, which depends on typical phenomenological parameters relative to the environment, the cases in which a dissipative induced current arises as a consequence of the coupling with the environment, have been examined. The effects of this current have been shown to be, in principle, experimentally accessible by looking at absorption images of the freely expanding atomic cloud once the trapping potential has been switched off. From these images it is possible to extract a spatial density profile after the free expansion; the presence of interference fringes in this density profile denotes the presence of coherence in the trapped system. This experimental procedure has been described in the general framework of the quantum measurement theory: from actual experimental evidence, it has been shown that a consistent use of the wave packet reduction principle leads to theoretical predictions for the expected density profile, which are slightly different from the ones commonly used in the literature. These differences have been briefly discussed both theoretically and for their possible experimental relevance.
La realizzazione sperimentale di condensati di Bose-Einstein ha inaugurato un ampio settore di studi nell'ambito della fisica dei gas di atomi ultrafreddi anche dal punto di vista teorico; le loro particolari caratteristiche, unite allo sviluppo delle tecnologie di confinamento di molti atomi in reticoli ottici, ne fanno degli ottimi candidati per l'applicazione di alcuni protocolli di comunicazione ed informazione quantistica basati sulla costruzione di stati coerenti a molti corpi. Il lavoro di tesi parte da questo contesto e si concentra su alcune conseguenze della presenza di un ambiente esterno in interazione con un sistema di atomi freddi confinati in potenziali ottici. Tipicamente, la presenza di un ambiente da' luogo ad effetti di rumore e dissipazione; la tesi studia invece la possibilita' che esso medi un'interazione tra atomi altrimenti isolati, rendendo in alcuni casi possibile la generazione di coerenza tra atomi localizzati nei siti costituenti il potenziale confinante, coerenza che si manifesta in maniera sperimentalmente rilevabile per mezzo di una corrente di materia. Le tecniche utilizzate si rifanno alla teoria dei sistemi quantistici aperti, ed in particolare al limite di accoppiamento debole, grazie al quale e' possibile descrivere la dinamica dissipativa tramite un'equazione master priva di effetti di memoria. Tranne che in casi molto particolari, non e' possibile integrare analiticamente l'equazione master; sono percio' state utilizzate delle tecniche in grado di rivelare il comportamento della coerenza per tempi sufficientemente brevi, quali quelli tipici dei fenomeni dissipativi studiati in questa tesi. In dettaglio, nella tesi e' stata introdotta dapprima la teoria del limite di accoppiamento debole nell'opportuno formalismo dei sistemi quantistici aperti; quindi, dopo una breve introduzione della fisica degli atomi freddi confinati in potenziali ottici, e' stata ricavata l'equazione master che ne determina l'evoluzione dissipativa quando questi sono debolmente accoppiati ad un ambiente esterno, tipicamente un bagno termico oppure un campo stocastico classico. Sono stati considerati due possibili esempi di accoppiamento, i quali differiscono tra loro per la conservazione e non del numero totale di atomi. Una volta ricavata l'equazione master, caratterizzata da specifici parametri fenomenologici relativi all'ambiente, sono stati studiati i casi in cui a questi corrisponde una corrente quantistica tra i siti del potenziale ottico confinante. Gli effetti di tale corrente sono stati dimostrati essere in linea di principio sperimentalmente accessibili tramite immagini di assorbimento ottenute illuminando le nuvole atomiche liberate dal confinamento.Da queste si ottengono misure di densita' spaziale che evidenziano, tramite frange di interferenza, l'eventuale presenza di coerenza di fase. Queste procedure sperimentali sono state descritte per mezzo della teoria quantistica della misura: in base alle evidenze sperimentali finora acquisite, e' stato mostrato che un utilizzo consistente delle tecniche relative alla riduzione del pacchetto d'onda porta ad una predizione teorica per il profilo di densita' spaziale formalmente diversa da quella comunemente utilizzata in letteratura. Questa differenza e' stata brevemente discussa sia per quanto riguarda il suo aspetto teorico che per la sua possibile rilevanza sperimentale.
XXI Ciclo
1981

There are several reasons why exotic and artificial atoms attract the interest of different scientific communities.In exotic atoms, matter and antimatter can coexist for surprisingly long times. Thus, they present a unique natural laboratory for high precision antimatter studies. In artificial atoms, electrons can be confined in an externally controlled way. This aspect is crucial, as it opens new possibilities for high precision measurements and also makes artificial atoms promising potential candidates for qubits, i.e. the essential bricks for quantum computation.The first part of the thesis presents theoretical studies of resonant states in antiprotonic atoms and spherical two-electron quantum dots, where well established techniques, frequently used for conventional atomic systems, can be applied after moderate modifications. In the framework of Markovian master equations, it is then demonstrated that systems containing resonant states can be approached as open systems in which the resonance width determines the environmental coupling. The second part of the thesis focuses on possible quantum computational aspects of two kinds of artificial atoms, quantum dots and Penning traps. Environmentally induced decoherence, the main obstacle for a practical realization of a quantum computer based on these devices, is studied within a simple phenomenological model. As a result, the dependence of the decoherence timescales on the temperature of the heat bath and environmental scattering rates is obtained.

La première partie de cette thèse est consacrée à l'élaboration théorique de processus adiabatiques permettant le transfert de population entre un état initial et un état cible d'un système quantique. La stratégie du passage adiabatique parallèle pour laquelle les paramètres de couplage sont conçus de telle sorte que la différence des valeurs propres du système reste constante à chaque instant, permet de minimiser à zéro les transitions non-adiabatiques données par la formule DDP. Cette technique permet de combiner à la fois l'efficacité énergétique des méthodes impulsion-pi et la robustesse du passage adiabatique. La seconde partie de cette thèse concerne les effets de la dissipation sur le passage adiabatique. La formule de probabilité de transition d'un système à deux niveaux tenant compte des effets de la dissipation est établie. Cette formule permet de reformuler la solution générale d'un système dissipatif à deux niveaux dans la limite adiabatique qui est valable au-delà du régime de faible dissipation.

In this work the semiclassical hybrid dynamics is extended in order to be capable of treating open quantum systems considering finite baths. The corresponding phenomena, i.e. decoherence and dissipation, are investigated for various scenarios.

In the present thesis the dynamics of the correlations between an open quantum system and its environment is investigated. This becomes feasible by means of a very useful representation of the total system-environment state. General conditions for separability and entanglement of the latter are derived, and investigated in the framework of an open quantum two-level system, which is coupled to a dissipative and a dephasing environment.

This doctoral study consists of two parts. In the first part, the quantum statistical effects on the formation process of the heavy ion fusion reactions have been investigated by using the c-number quantum Langevin equation approach. It has been shown that the quantum effects enhance the over-passing probability at low temperatures. In the second part, we have developed a simulation technique for the quantum noises which can be approximated by two-term exponential colored noise.

2010 - 2011
In this dissertation we discuss several aspects of a two level system (qubit) in the context of quantum mechanics and quantum field theory. The presence of geometrical phases in the evolution of a qubit state is shown. We study geometric structures, which are correlated to an unitary time evolution and its interesting gauge structure. They can be very useful in quantum computational processes. We illustrate the quantum field theoretical formulation of boson mixed fields, and oscillation formulas for neutral and charged fields are found. We show that the space for the mixed fields is unitary inequivalent to the state space where the unmixed field are defined, and we also derive the structure of the currents and charges for the charged mixed fields. Phenomenological aspects of meson mixing in the presence of the decay are discussed. In particular, we show that the effective Hamiltonian is non-Hermitian and non-normal in the Wigner-Weisskopf approximation and we use the biorthonormal basis formalism to diagonalize such an Hamiltonian. Finally, the presence of CP and CPT violations in meson mixing is shown. [edited by author]
X n.s.

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.

In der vorliegenden Arbeit werden Untersuchungen vorgestellt, die sich mit drei verschiedenen Aspekten der Dynamik offener Quantensysteme beschäftigen. Zwei Themenkreise haben dabei mehr grundsätzliche Probleme der Theorie dissipativer Molekularsysteme zum Gegenstand. Dementsprechend müssen die Betrachtungen dazu auf einem allgemeineren Niveau verbleiben. In dem dritten Themenkreis jedoch, der sich mit Zwei-Teilchen-Effekten in der dissipativen Dynamik befaßt, können die Untersuchungen bis hin zu Berechnung von Meßgrößen geführt werden. Im ersten Teil der Arbeit gelingt eine Verallgemeinerung der vielbenutzten Standardform der Quanten-Master-Gleichung hin zur Nichtlinearen Quanten-Master-Gleichung. Mit der Anwendung der dazugehörigen zeitabhängigen Projektionsoperator-Technik kann ein Formalismus reaktiviert werden, der in der Literatur bisher eine nur sehr eingeschränkte Verbreitung findet. Der zweite Teil der Arbeit widmet sich Untersuchungen zur Monte-Carlo-Wellenfunktions-Methode mit dem Ergebnis, eine konsistente Verallgemeinerung auf ein Reservoir mit endlicher Temperatur anzugeben. Den Ausgangspunkt dazu bildet ein mikroskopisches Modell zur System-Reservoir-Kopplung, welches im Rahmen der Bewegungsgleichung für den reduzierten statistischen Operator in die sogenannte Lindblad-Form der Dissipation überführt wird. Nach der Betrachtung von Ein-Teilchen-Transferprozessen beschäftigt sich der dritte Teil der Arbeit mit der korrelierten Bewegung von zwei Quantenteilchen in einer dissipativen Umgebung mit der Hinwendung zum Zwei-Wasserstoff-System (Dihydrid-System) an Übergangsmetall-Verbindungen. Zunächst werden Modellrechnungen zur dissipationfreien Zwei-Teilchen-Dynamik in einem Potentialmodell durchzuführt. Der Einfluß, den die Teilchen-Teilchen-Korrelationen auf das Durchtunneln eines Potentialwalles besitzt, können durch verschiedene numerische Rechnungen aufgezeigt werden. Wie sich diese Effekte in Neutronenstreuexperimenten an dem Zwei-Teilchen-System der Übergangsmetall-Hydrid-Komplexe äußern, wird basierend auf Simulationsrechnungen untersucht. Kernstück dieser Betrachtungen bildet eine neuartige Formel für die Neutronenstreuung, die auf der dissipativen Dynamik des betrachteten Zwei-Teilchen-Systems aufbaut.
In the report at hand studies are presented dealing with three differentaspects of the dynamics of open quantum systems. Two topics are about the fundamental problems of the theory of dissipative molecular systems. Accordingly these investigations must remain on a more general level. In the third subject, however, which is about the two-particle effects in the dissipative dynamics the analyses can be extended to the computation of measurements. In the first part of the report a generalization of the well known standard quantum master equation to the nonlinear quantum master equation is developed. With the help of the projection operator technique belonging to it a formalism, that has not been popular in literature so far, can be reactivated. The second part of the report concentrates on examinations of the Monte-Carlo wave-function method, and results in the consistent generalization for a reservoir of finite temperature. The starting point for this is a microscopic model of the system-reservoir coupling, which is expanded to the so called Lindblad form of the dissipation in the line of the equation of motion for the reduced statistical operator. After the analysis of one-particle transfer processes the third part of the report is about the correlated motion of two quantum particles in a dissipative environment with main emphasis on the two-hydrogen system (dihydrid system) in transition metal complexes. First of all model computations for the dissipationless two-particle dynamics in a potential model are made. By different numerical computations the influence, which the particle-particle correlations exert on the tunneling through a potential barrier, can be shown.Based on simulations it is examined how these effects can be seen in neutron scattering experiments on two-particle systems of transition metal complexes. Main item of these investigations is a new formula for the neutron scattering which is based on the dissipative dynamics of the examined two-particle system.

Exploiter des effets dépendants du temps pour induire et contrôler des courants à travers des conducteurs mésoscopiques et nanoscopiques est un enjeu majeur dans le domaine du transport quantique. Dans cette thèse, nous considérons deux systèmes de taille nanométrique pour lesquels un courant est induit grâce au couplage entre champs extérieurs dépendants du temps et le transport d'électrons. Nous étudions d'abord un problème de pompage quantique au sein d'un système à trois sites en configuration d'anneau, en considérant la possibilité d'induire un courant continu par modulation temporelle des paramètres de contrôle. Nous nous intéressons en particulier à la transition entre régime adiabatique et antiadiabatique en présence d'un mécanisme de dissipation modélisé par un couplage entre le système et un bain extérieur.Nous montrons que le modèle dissipatif admet une solution analytique complète valable pour la composante DC du courant à fréquence arbitraire. Ceci nous permet de bien comprendre comment le courant induit dépend de la fréquence de pompage. Nous nous concentrons ensuite sur un autre système de contrôle du courant exploitant le phénomène des oscillations tunnel à un électron (SETOs). Contrairement au cas précédent, ici la circulation d'un courant continu à travers un circuit comportant une jonction tunnel produit, pour le régime approprié, un courant quasi-périodique d'électrons. On étudie le spectre de bruit à température nulle d'une jonction tunnel dans différents environnements résistifs dans le but de déterminer les limites du régime des SETOs et de quantifier leur degré de périodicité. Nous généralisons par la suite les résultats à température finie et discutons des effets des fluctuations quantiques
Exploiting time-dependent effects to induce and control currents through mesoscopic and nano\-scopic conductors is a major challenge in the field of quantum transport. In this dissertation we consider two nanoscale systems in which a current can be induced through intriguing mechanisms of coupling between excitations by external fields and electron transport.We first study a quantum pumping problem, analyzing the possibility to induce a DC response to an AC parametric driving through a three-site system in a ring configuration. We are interested in particular in the crossover between adiabatic and antiadiabatic driving regimes and in the presence of dissipation, which is accounted for by coupling with an external bath. We show that for a clever choice of this coupling the dissipative model admits a full analytical solution for the steady state current valid at arbitrary frequency, which allows us to fully understand the pumping-frequency dependence of the induced current. We then focus on a different current-controlling scheme exploiting the phenomenon of single-electron tunneling oscillations (SETOs). In this case, opposite to what happens for pumping, an AC effect, an almost periodic current of single electrons, arises through a tunnel junction circuit as a consequence of a DC bias. We study the zero-temperature noise spectrum of a tunnel junction in different resistive environments with the aim to determine the boundaries of the SETOs regime and quantify their quality in terms of periodicity. We then discuss the finite-temperature generalization and the possibility to account for the effects of quantum fluctuations