This thesis deals with the study of dynamical properties of out-of-equilibrium quantum systems. We introduce in particular a general class of Spin-Boson models, which describe for example light-matter interaction or dissipative phenomena. We contribute to the development of a stochastic approach to describe the spin dynamics in these models. In this context, the effect of the bosonic environment is encapsulated into additional stochastic degrees of freedom whose time-correlations are determined by spectral properties of the bosonic environment. We use this approach to study many-body phenomena such as the dissipative quantum phase transition induced by an ohmic bosonic environment. Synchronization phenomena as well as dissipative topological transitions are identified. We also progress in the study of arrays of interacting light-matter systems. These theoretical developments follow recent experimental achievements, which could ensure a quantitative study of these phenomena. This notably includes ultra-cold atoms, trapped ions and cavity and circuit electrodynamics setups. We finally investigate hybrid systems comprising electronic quantum dots coupled to electromagnetic resonators, which enable us to provide a spectroscopic analysis of many-body phenomena linked to the Kondo effect. We also introduce thermoelectric applications in these devices.
This thesis deals with the study of dynamical properties of out-of-equilibrium quantum systems. We introduce in particular a general class of Spin-Boson models, which describe for example light-matter interaction or dissipative phenomena. We contribute to the development of a stochastic approach to describe the spin dynamics in these models. In this context, the effect of the bosonic environment is encapsulated into additional stochastic degrees of freedom whose time-correlations are determined by spectral properties of the bosonic environment. We use this approach to study many-body phenomena such as the dissipative quantum phase transition induced by an ohmic bosonic environment. Synchronization phenomena as well as dissipative topological transitions are identified. We also progress in the study of arrays of interacting light-matter systems. These theoretical developments follow recent experimental achievements, which could ensure a quantitative study of these phenomena. This notably includes ultra-cold atoms, trapped ions and cavity and circuit electrodynamics setups. We finally investigate hybrid systems comprising electronic quantum dots coupled to electromagnetic resonators, which enable us to provide a spectroscopic analysis of many-body phenomena linked to the Kondo effect. We also introduce thermoelectric applications in these devices.
Recent advances in theoretical physics have increasingly focused on the dynamics of quantum systems with many interacting degrees of freedom, while ultracold atom platforms now enable the realization of diverse theoretical models with precise control over system parameters and advanced monitoring techniques. A prominent example is cavity quantum electrodynamics (CQED), where large atomic or molecular ensembles are coupled to high-finesse optical cavities, enabling strong interaction with confined electromagnetic modes and leading to phenomena such as the superradiant phase transition, in which atoms and photons form a coherent state. Most theoretical studies of CQED have concentrated on regimes of spatially uniform atom–cavity coupling, where collective behavior allows a description in terms of the classical dynamics of a few macroscopic variables. However, experimental capabilities now permit exploration beyond this limit, though theoretical progress is hindered by the exponential computational complexity of simulating large quantum systems, particularly when environmental coupling is included. This thesis addresses such challenges by developing efficient approaches, within the Keldysh formalism of non-equilibrium quantum field theory, to study systems with strongly disordered interactions coupled to external reservoirs. Two representative models are considered: a disordered spin–boson model describing light–matter interactions with quenched disorder, relevant to recent CQED experiments in confocal cavities, and a fermion–phonon system governed by the Yukawa–Sachdev–Ye–Kitaev (Yukawa-SYK) model. Both systems are quantum critical, exhibiting a continuum of low-energy modes above their stationary states, yet disorder produces qualitatively distinct dynamical behaviors: in the spin–boson system it induces slow, glassy relaxation, whereas in the Yukawa-SYK model it leads to rapid thermalization. These contrasting outcomes reveal the non-trivial role of disorder in quantum many-body systems and motivate further investigation into its effects on non-equilibrium quantum dynamics.
The study of many-body quantum physics has been recently challenged by the appearance of an increasing number of experimental platforms where genuine quantum phenomena take place notwithstanding the presence of an environment and of dissipation. Exciton-polaritons, lossy atomic and molecular gases, cavity QED arrays, arrays of trapped ions and Rydberg atoms, are only few prominent examples of a long list. The present work is ideally divided into two parts, the former is devoted to methodological results; the latter to the theoretical characterization of experimental data. Whereas the notion of equilibrium has been a fruitful guide to the development of standard many-body physics, these setups are inherently out of equilibrium and their modelisation requires the introduction of new theoretical tools. Several methods for addressing this dissipative out-of-equilibrium dynamics have been proposed, based for instance on quantum trajectories, truncated Wigner expansions, tensor networks, machine learning, but the solution of many-body physics for open quantum systems remains a formidable task. Clearly, techniques developed in the framework of Hamiltonian closed systems are a continuous source of inspiration for novel developments, and in this work we present the generalization of one such technique, the so-called flow equations, to the dissipative framework where the generator of the dynamics is a linear non-Hermitian operator; notable examples include non-Hermitian Hamiltonians and Lindblad master equations. In the second part of this work we focus on two-body lossy dynamics in strongly-correlated cold atomic gases. In particular, we derive an effective description for the long-time dynamics of a spin ½ fermionic system by extending a pre-existing theory for the bosonic case.
Remarkable experimental progress and theoretical advancements in the study of strongly corre- lated systems have opened up new doors towards a better understanding of interesting states of matter. Such states could possibly be used to develop novel technological applications based on the principles of quantum mechanics. In recent years, the investigation of both complex solid state and ultracold atom systems has lead to a number of fascinating discoveries with regards to their non-equilibrium properties. One route to probe non-equilibrium physics is to consider the evolution of open systems defined by the coupling to an external environment introducing dissipation. Engineering the environment according to predefined requirements can then be used to dynamically prepare states which are difficult to access otherwise. This thesis explores the dynamics of many-body open quantum systems aiming at under- standing the effects resulting from the interplay of kinetic motion, interactions and dissipation in different physical settings. First, we build upon recent developments concerning the coupling of ultracold atoms to optical resonators which are subject to photon losses. We show how the dissipation can trigger an attractor dynamics towards a topologically non-trivial steady state that is robust against perturbations. The numerically obtained full open system evolution en- ables us to not only characterize in detail the steady state but also to analyze the features of the approaching dynamics. Second, we study the propagation of two-time correlation functions in interacting quantum spin-1/2 chains in contact with an environment causing dephasing. Pro- vided with the numerically exact full time-evolution, we identify an algebraic scaling regime where time-translation invariance breaks down and uncover the emergence of aging dynam- ics. Finally, we study a system of interacting fermionic atoms in a one-dimensional lattice with particle loss at the central site. There we report on the dissipation-induced deceleration of the non-equilibrium dynamics known as the quantum Zeno effect. As in the majority of cases quantum many-body systems are not solvable analytically, another central aspect of this thesis deals with adapting numerical methods based on matrix product state algorithms to investigate open quantum systems dynamics.
We review recent developments regarding the quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues, by analogy with atomic physics. We start with quantum impurity models addressing dissipative and driven systems. Both theorists and experimentalists are making efforts towards the characterization of these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect can be characterized by a renormalized light frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled with an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing one to engineer the Jaynes–Cummings lattice and Rabi lattice models through the presence of superconducting qubits in the cavities. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott–superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin–orbit couplings have been successfully implemented in quantum materials and with ultra-cold atoms in optical lattices — using time-dependent Floquet perturbations periodic in time, for example — as well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose–Hubbard models in ladder and two-dimensional geometries, producing phase coherence and Meissner currents. The Bose–Hubbard model is related to the Jaynes–Cummings lattice model in the large detuning limit between light and matter (the superconducting qubits). In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase.
We study the dynamics in low dimensional correlated quantum systems. Advances in this thesis are three-fold. First, as a methodical point we extend the real-time formulation of the functional renormalization group approach introduced in [1]. Describing the transient time dependence of a given microscopic model prepared in an initial non-equilibrium state poses a formidable challenge in the presence of interaction. We successfully extend the functional renormalization group approach of [1] to finite temperature as well as extended interacting geometries. Furthermore, for both extensions we test the validity of the perturbatively motivated treatment by explicitly benchmarking to complementary methods and find that for not too large interactions the functional renormalization group proves to be quantitatively accurate. Second, we examine the non-equilibrium dynamics of open as well as closed quantum systems in the presence of correlations. We study a prominent prototype model for coherence in small quantum systems coupled to dissipative environments, namely the spin-boson model. We reveal that prevailing literature does not cover the full complexity of the dynamics encountered. The relaxation dynamics formerly classified as coherent and incoherent should be refined according to the results presented in this thesis: we propose a subdivision of the coherent regime into partially and asymptotically coherent. For the former the coherence signature of the dynamics is restricted only to intermediate times, while in the latter it extends in the asymptotic regime. Interestingly, we explicitly show that elevating temperature might be conducive to coherence, which is opposite to the expected behavior. For those closed quantum systems known to fall into the so called Luttinger Liquid universality class in equilibrium, we provide evidence that the equilibrium concept of universality seemingly carries over to the non-equilibrium steady-state. This is rather counter-intuitive, as universality is usually attributed to the low energy degrees of freedom only. Third, we study the thermoelectric transport properties of quantum dots. Quantum dots are promising candidates for highly efficient thermoelectric devices as they are not bounded by the Wiedemann-Franz law which strongly limits the efficiency of ordinary bulk systems. For this we study a charge fluctuating model and a model which additionally allows for spin fluctuations and phononic degrees of freedom. We find that in certain regimes quantum dots show very high efficiency when operated as power engines. [1] D. M. Kennes, ‘A Renormalization Group Approach to the Time Evolution of Correlated Quantum Dots’ Master’s thesis, RWTH Aachen (2011).
This thesis explores non-equilibrium phenomena in quantum many-body systems, with a focus on correlated electron systems and photon Bose-Einstein condensates. The first part develops the theoretical foundation, beginning with the Lindblad master equation and the construction of non-equilibrium quantum field theory. The two-particle irreducible effective action formalism is introduced, from which the Kadanoff-Baym equations for real-time evolution and the Dyson equation for steady-states are derived. The theoretical groundwork continues with a treatment of strongly correlated electron systems, where non-equilibrium dynamical mean-field theory (DMFT), auxiliary particles, and the non-crossing approximation (NCA) are introduced. These techniques, together with the Lindblad and Kadanoff-Baym approaches, are used throughout the subsequent chapters. The second part presents the main research projects of this thesis. The first two projects are concerned with the fate of the heavy fermion state under irradiation of light. To accurately incorporate light-matter interactions in this case, dipole transitions must be included. In the first project a periodically driven system is considered, where the light can be treated semiclassically. A Floquet DMFT+NCA framework is developed, revealing the mechanisms and conditions under which the heavy fermion state is most strongly suppressed. The second project analyzes a THz spectroscopy experiment performed on CeCu6. In this case a semi-classical treatment of the light field is no longer sufficient, and a full two-time evolution of all the non-equilibrium Green functions is necessary. This approach reveals the microscopic mechanisms underlying the collapse and revival of the Kondo state observed in the experiment. The next project investigates a recent experiment regarding an observation of a non-Hermitian phase transition in EuO. The equilibrium properties of EuO are first analyzed, and then an exciton model is constructed that gives rise to the non-Hermitian phase transition, in good agreement with experimental observations. In the final project, a photon Bose-Einstein condensate in a dye-filled microcavity is studied. A stabilization mechanism, distinct from thermalization, is revealed which admits a condensate phase for orders of magnitude longer than the experimentally relevant timescales.