This thesis investigates the physics of strongly interacting driven–dissipative bosonic systems in one dimension, combining field-theoretical approaches with various numerical simulation techniques. While weakly interacting condensates are accurately described by a generalized Gross–Pitaevskii equation, the strongly correlated regime of the same microscopic models remains far less understood, particularly out of equilibrium. This thesis aims to bridge this gap by developing controlled quantum-many-body simulations for open systems governed by Lindblad dynamics, as well as investigating the corresponding action under the functional renormalization group.In the first part, we formulate a field-theoretical description of driven–dissipative one-dimen-sional bosons using the Schwinger–Keldysh formalism and the functional renormalization group (fRG).Two models are analyzed: (i) a driven-dissipative condensate whose phase dynamics is expected to exhibit emergent Kardar–Parisi–Zhang (KPZ) behavior, for which we search the emergent KPZ fixed point starting from the bosonic field theory; and (ii) a two-photon–driven system with two-body losses realizing dissipative cat qubits. For the latter, we determine the phase diagram and identify a continuous phase transition between symmetry-broken and symmetric phases, which motivates the construction of an fRG Ansatz capturing this critical behavior.The second part of the thesis focuses on the open system dynamics using exact diagonalization and tensor-network methods. For the Bose–Hubbard model with incoherent pump and loss, we characterize the steady state, and study spectral functions across the full parameter space. We show that key ground-state features are absent under dissipation, while the high-temperature unitary spectrum captures aspects of the open-system dynamics. In an extended model with additional two-body and non-local losses, we establish the semi-classical emergence of KPZ scaling and extract the KPZ dynamical exponent from the spectral function. A finite-size analysis exposes the current limitations of the tensor-network methods for reaching the high occupancy regime in the full quantum evolution.Finally, a last project develops a two-loop perturbative RG analysis of a spin-1 chain at its continuous symmetry breaking quantum critical point, revealing critical exponents distinct from the Ising universality class.Together, these results advance the understanding of strongly interacting open quantum systems, elucidating their symmetries, effective field theories, and dynamical properties, and outlining key directions for future theoretical and numerical work.
This thesis investigates the physics of strongly interacting driven–dissipative bosonic systems in one dimension, combining field-theoretical approaches with various numerical simulation techniques. While weakly interacting condensates are accurately described by a generalized Gross–Pitaevskii equation, the strongly correlated regime of the same microscopic models remains far less understood, particularly out of equilibrium. This thesis aims to bridge this gap by developing controlled quantum-many-body simulations for open systems governed by Lindblad dynamics, as well as investigating the corresponding action under the functional renormalization group.In the first part, we formulate a field-theoretical description of driven–dissipative one-dimen-sional bosons using the Schwinger–Keldysh formalism and the functional renormalization group (fRG).Two models are analyzed: (i) a driven-dissipative condensate whose phase dynamics is expected to exhibit emergent Kardar–Parisi–Zhang (KPZ) behavior, for which we search the emergent KPZ fixed point starting from the bosonic field theory; and (ii) a two-photon–driven system with two-body losses realizing dissipative cat qubits. For the latter, we determine the phase diagram and identify a continuous phase transition between symmetry-broken and symmetric phases, which motivates the construction of an fRG Ansatz capturing this critical behavior.The second part of the thesis focuses on the open system dynamics using exact diagonalization and tensor-network methods. For the Bose–Hubbard model with incoherent pump and loss, we characterize the steady state, and study spectral functions across the full parameter space. We show that key ground-state features are absent under dissipation, while the high-temperature unitary spectrum captures aspects of the open-system dynamics. In an extended model with additional two-body and non-local losses, we establish the semi-classical emergence of KPZ scaling and extract the KPZ dynamical exponent from the spectral function. A finite-size analysis exposes the current limitations of the tensor-network methods for reaching the high occupancy regime in the full quantum evolution.Finally, a last project develops a two-loop perturbative RG analysis of a spin-1 chain at its continuous symmetry breaking quantum critical point, revealing critical exponents distinct from the Ising universality class.Together, these results advance the understanding of strongly interacting open quantum systems, elucidating their symmetries, effective field theories, and dynamical properties, and outlining key directions for future theoretical and numerical work.
We consider a one-dimensional driven-dissipative Bose-Hubbard model subjected to incoherent pump and one- and two-body losses, and analyze it by studying its two-point space-time correlations. By employing a combination of numerical methods, such as stochastic semi-classical simulations and tensor network methods, as well as perturbation theory within the Keldysh formalism, we characterize the system at varying filling and interaction strength. We present results for two complementary regimes: i) at large filling and weak interactions, where we show that Kardar-Parisi-Zhang scaling is visible in the linewidth of the spectral function and ii) at weak filling and strong interactions, where we analyze what remains of the mean field transition and identify a change of nature of the excitations. Our study covers two important regions of the phase diagram of such a system.
This thesis is about the theory of open quantum many-body physics with a particular focus on driven-dissipative photonic and spin lattices. After a review of the main physical platforms and theoretical concepts, we describe our original results. In Chapter 2, we present a theory of the single-mode Kerr model with a time-dependent pump. This model describes a single-mode optical cavity with a third-order optical nonlinearity. In the regime of parameters where the semiclassical analysis shows bistability, we find that a dynamic hysteresis loop appears in the exact solution. The hysteresis area as a function of the sweep time shows a double power-law decay where the second exponent is independent of the system parameters. We show how these effects are related to the emergence of a dissipative phase transition. We also describe concisely the experimental results which have recently confirmed such theoretical predictions. In Chapter 3, we present the corner-space renormalization method. In order to obtain the steady-state density matrix of the lattice, we solve the Lindblad master equation in a subspace of the Hilbert space (the "corner"). The states spanning the corner space are selected iteratively using eigenvectors of the density matrix of smaller lattice systems, merging in real space two lattices at each iteration and selecting M pairs of states by maximizing their joint probability. The accuracy of the results is then improved by increasing the dimension M of the corner space until convergence is reached. The method has been benchmarked on a two-dimensional Bose-Hubbard model with coherent driving. The strength and limitations of the method are critically discussed.In Chapter 4, we investigate a dissipative phase transition in the two-dimensional anisotropic Heisenberg XYZ model. Using the corner-space renormalization method we present a finite-size analysis of steady-state observables. In particular, we show the critical behaviour of the magnetic susceptibility, the entropy growth and the entanglement witnesses, providing a first evaluation of the critical exponents characterizing the transition. A study of the dynamics of finite-size systems is also consistent with a critical slowing down. For comparison, we present the corresponding analysis for one-dimensional arrays, showing the absence of criticality due to the reduced dimension.In Chapter 5, we explore the non-equilibrium photonic phases of a dissipative Bose-Hubbard model with incoherent pumping of coupled two-level systems. Within a Gutzwiller mean-field approach, we determine the steady-state phase diagram of the system. We predict a second-order phase transition between an incompressible Mott-like phase and a coherent delocalized phase.
Bosons unidimensionnels avec pompe et dissipation — du quantique au classique Cette thèse étudie la physique des systèmes bosoniques unidimensionnels avec pompe et dissipation et fortement corrélés, en combinant des approches de théorie des champs avec diverses techniques de simulation numérique. Alors que les condensats à faible interaction sont décrits avec précision par une équation de Gross–Pitaevskii généralisée, le régime fortement corrélé du même modèle microscopique demeure bien moins compris, en particulier hors de l'équilibre. Notre objectif est de combler cette lacune en développant des simulations quantiques à N corps contrôlées pour des systèmes ouverts régis par une dynamique de Lindblad, ainsi qu’en étudiant l’action correspondante en utilisant le groupe de renormalisation fonctionnelle.Dans la première partie, nous formulons une description de théorie des champs pour les bosons unidimensionnels avec pompe et dissipation à l’aide du formalisme de Schwinger–Keldysh et du groupe de renormalisation fonctionnelle (fRG). Nous examinons deux modèles :(i) motivés par l’apparition de la physique de Kardar–Parisi–Zhang (KPZ) dans les quasi-condensats sous pompe et dissipation, nous recherchons le point fixe KPZ émergent dans la théorie de champ bosonique ;(ii) un pompage cohérent à deux photons combiné à des pertes incohérentes à deux particules décrit des qubits «chat» dissipatifs. Nous étudions le diagramme de phases et mettons en évidence une transition de phase du second ordre entre un état brisé et un état symétrique, que nous analysons à l’aide d’un Ansatz fRG.La seconde partie de la thèse porte sur la dynamique des systèmes ouverts au moyen de la diagonalisation exacte et des méthodes de réseaux de tenseurs. Pour le modèle de Bose–Hubbard avec pompage et perte incohérents, nous caractérisons l’état stationnaire et étudions les fonctions spectrales sur l’ensemble de l’espace des paramètres. Nous montrons que les propriétés clés de l’état fondamental disparaissent sous dissipation, tandis que le spectre unitaire à haute température reproduit certains aspects de la dynamique du système ouvert. Dans un modèle étendu avec pertes additionnelles à deux corps et pertes non locales à un corps, nous établissons l’émergence semi-classique du régime KPZ et extrayons l’exposant dynamique KPZ à partir de la fonction spectrale. Une analyse en taille finie révèle les limitations actuelles des méthodes de réseaux de tenseurs pour atteindre le régime de forte occupation dans l’évolution quantique complète.Enfin, un dernier projet développe une analyse RG perturbative à deux boucles d’une chaîne de spins 1 au point critique quantique associé à une brisure continue de symétrie, révélant des exposants critiques distincts de ceux de la classe d’universalité d’Ising.Dans l’ensemble, ces résultats approfondissent la compréhension des systèmes quantiques ouverts fortement corrélés, en mettant en lumière leurs symétries, leurs théories effectives et leurs propriétés dynamiques, tout en identifiant des axes prometteurs pour de futurs travaux théoriques et numériques.
This thesis presents several experiments investigating the regimes of behaviour of a proto-typical open quantum many-body system far away from equilibrium. The experimental platform is based on ultracold atoms laser-excited to Rydberg states, which we engineer to emulate a strongly interacting, driven-dissipative quantum spin system. The high degree of control over the relevant microscopic processes and their parameters, as well as the ability to widely tune interaction and driving strengths provides the means to address fundamental questions on how different regimes of dynamical behaviour emerge in complex open quantum systems and how they can be characterised. \n \nIn the first part, we discuss how control over the relevant properties of Rydberg spin systems, like temperature, density, long evolution times, strong interactions, tunable driving, and dissipation can be achieved. We introduce the new experimental apparatus developed during this thesis, which combines both single-photon and two-photon Rydberg excitation schemes with high atom densities and long excitation times using an optical dipole trap. Additionally, we investigate theoretically how long coherence times exceeding motional timescales combined with strong many-body interactions can be achieved in such a system. We identify an optimal parameter regime for two-photon excitation where such conditions can be generated with coherence times and interaction strengths comparable to what is achievable for single-photon excitation. \n \nIn the second part we explore the macroscopic non-equilibrium behaviour of our system and devise suitable observables for characterising different regimes of behaviour. We discover that the slow atom loss inherent to our system provides a convenient observable for the many-body state of the system. Focussing on evolution times where the effect of the atom loss on the evolution is small, we discover that the rate of atom loss exhibits powerlaw scaling with the driving strength over several orders of magnitude. The measured scaling exponents reveal the non-equilibrium phase structure of the many-body system and allow us to distinguish dissipation-dominated, paramagnetic and critical regimes, as well as an instability. In the observed critical regime, collectively enhanced driving dominates over dissipation, leading to scaling associated to the critical point of the non-dissipative equilibrium Rydberg spin system. Based on the known microscopic processes of our system, we perform classical many-body rate equation simulations, which agree well with the observed phase structure as well as the position and associated scaling exponents of the individual regimes. These findings open up new means to study and classify out of equilibrium systems based on slow particle loss and powerlaw scaling. \n \nIn the last part of this thesis we reveal a second type of criticality in our system, which is genuinely non-equilibrium in character and arises from an absorbing state phase transition. The critical state of this phase transition dominates the system evolution at late times where particle loss is no longer negligible. We identify self-organisation as the mechanism driving the system to this critical state, which we observe through powerlaw scaling of the non-equilibrium steady-state. These experiments establish Rydberg atoms as a well controlled platform for implementing and exploring models of absorbing state phase transitions and self-organised criticality with unprecedented access to the underlying microscopic properties of the system.
Quantum many-body systems coupling photonic and matter degrees of freedom are ideal for the realization of driven open quantum dynamics at the intersection of quantum optics and condensed matter. They offer the possibility to address unresolved issues regarding a variety of non-equilibrium phenomena. In such open systems, the substructure of the reservoir then introduces further timescales that may enter into competition with rapid system processes, raising long-standing questions about the influence of non-Markovian effects on dynamics and equilibration out of equilibrium. \n \nThe central result of this thesis is a general pseudo-particle technique that can be applied to a large class of models of interacting light and matter and allows for realistic and efficient simulations of the full non-equilibrium dynamics of these systems. Since organic molecules, as used in experiments with photon condensates, which provide the main area of application for this thesis, possess an electronic transition coupled to vibrational phonon modes, we construct a representation where an auxiliary boson is assigned to each vibrational state of the molecule. An operator constraint then enforces single occupation across all of these states. We emphasize that we implement the operator constraint exactly and that we are the first to apply a faithful auxiliary-boson representation to open quantum systems. \n \nAs a contribution to bridging the gap between well-understood equilibrium and less explored non-equilibrium phenomena, we investigate photon condensates as they are driven away from equilibrium. The earliest signs of the non-equilibrium character of the driven-dissipative photon gas do not manifest in the spectrally resolved intensity distribution but in the time dependence of the intensity fluctuations. The energy flow through the system renders it {non-Hermitian} and induces a novel driven-dissipative transition in the second-order correlations characterized by the appearance of exceptional points. If only the static intensity spectrum is monitored, this transition remains unnoticed, as does the fact that the system is not truly in equilibrium. Non-Markovian effects due to the non-separability of system and reservoir timescales are shown to become important far away from equilibrium. Furthermore, we derive a novel photon-condensate Gross-Pitaevskii equation, which is capable of describing photo-molecular coherence. Such effects cannot be captured by existing theories and hence serve as a validation of our auxiliary-boson method. These results provide a building block to understanding the properties of the photon condensates in stationary operation where they act as fluctuating light sources. In the future, lattice systems of coupled photon condensates may lead to the appearance of novel driven-dissipative phases of light.
In this thesis we explore different phenomena occurring in open quantum many-body systems. This is a research field which is becoming increasingly more important due to the experimental progress towards realization of quantum-simulators and quantum computers using a variety of platforms, from ultracold atoms to superconducting qubit arrays. These systems are inherently driven and open, and it is an ongoing effort to develop theoretical tools and approaches to study their non-equilibrium physics. In the first part of this thesis we explore the different non-equilibrium condensate phases of resonantly interacting bosons in the presence of coherent pump and incoherent losses. This study might be of relevance to existing Rydberg-polariton setups. We derive an effective non-equilibrium field-theory of this model and study its resulting phase diagram. We find a rich phase diagram in- cluding a phase where particles form a condensate of tightly bound molecules. By changing the detuning from the scattering resonance it is possible to drive an Ising phase transition from the molecule condensate phase to a more standard atom condensate phase. In the second part of this thesis we explore the many-body localization (MBL) transition in an open-driven system. Typically, coupling to a bath is expected to destroy localization and transform the sharp MBL transition to a crossover. Here we show how one can use the couplings to non- equilibrium baths in order to detect sharp signatures of the transition, including the divergence of the dynamical exponent in the Griffith regime of the ergodic phase. This is done by solving for the steady-state of the Lindblad quantum-master equation using matrix-product operator tech- niques. Our work here suggests a new scalable numerical approach to study the MBL transition. In the third part of this thesis we study the entanglement properties of measurement trajectories in a free-fermion system subject to dephasing noise. These trajectories describe the evolution of an open system when photons exiting the system are continuously monitored. We are inspired by recent works which studied the entanglement dynamics in hybrid quantum circuits consisting of random-unitary gates and projective measurements. There it was found that a phase transition between a phase with volume-law scaling of entanglement and an area-law phase occurs at a critical value of the measurement rate. In our case we find a new regime, where at weak noise rate the system exhibits logarithmic entanglement scaling, similar to that of (1 + 1)d conformal field- theories. For some measurement protocols, we find a transition to an area-law phase at a critical noise strength.