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. \nWe 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. \nWe 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. \nWe 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. \nWe 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. \nWe 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.
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. \nWe 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. \nWe 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. \nWe 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. \nWe 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. \nWe 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.
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 explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the relaxation dynamics that arise in comparison to systems evolving via classical rate equations. In particular, we focus on a scenario where both quantum and classical dissipative evolution lead to a stationary state with the same values of diagonal or "classical" observables. As a basis for illustrating our ideas we use spin systems whose dynamics becomes correlated and complex due to dynamical constraints, inspired by kinetically constrained models (KCMs) of classical glasses. We show that in the quantum case the relaxation can be orders of magnitude slower than the classical one due to the presence of quantum coherences. Aspects of these idealized quantum KCMs become manifest in a strongly interacting Rydberg gas under electromagnetically induced transparency (EIT) conditions in an appropriate limit. Beyond revealing a link between this Rydberg gas and the rather abstract dissipative KCMs of quantum glassy systems, our study sheds light on the limitations of the use of classical rate equations for capturing the non-equilibrium behavior of this many-body system.
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.
In the presence of strong dephasing noise the dynamics of Rydberg gases becomes effectively classical, due to the rapid decay of quantum superpositions between atomic levels. Recently a great deal of attention has been devoted to the stochastic dynamics that emerges in that limit, revealing several interesting features, including kinetically-constrained glassy behaviour, self-similarity and aggregation effects. However, the non-equilibrium physics of these systems, in particular in the regime where coherent and dissipative processes contribute on equal footing, is yet far from being understood. To explore this we study the dynamics of a small one-dimensional Rydberg lattice gas subject to dephasing noise by numerically integrating the quantum Master equation. We find indications that the main features observed in the strongly dissipative limit persist when the dissipation is not strong enough to annihilate quantum coherences at the dynamically relevant time scales. These features include a power law growth of the density of excitations and the existence of a time-dependent Rydberg blockade radius. Our results indicate that the power-law growth of density of excitations is characterised by an exponent which decreases as the dissipation becomes weaker.
Abstract In the presence of strong dephasing noise the dynamics of Rydberg gases becomes effectively classical, due to the rapid decay of quantum superpositions between atomic levels. Recently a great deal of attention has been devoted to the stochastic dynamics that emerges in that limit, revealing several interesting features, including kinetically constrained glassy behaviour, self-similarity and aggregation effects. However, the non-equilibrium physics of these systems, in particular in the regime where coherent and dissipative processes contribute on equal footing, is yet far from being understood. To explore this we study the dynamics of a small one-dimensional Rydberg lattice gas subject to dephasing noise by numerically integrating the quantum master equation. We interpolate between the coherent and the strongly dephased regime by defining a generalised concept of a blockade length. We find indications that the main features observed in the strongly dissipative limit persist when the dissipation is not strong enough to annihilate quantum coherences at the dynamically relevant time scales. These features include the existence of a time-dependent Rydberg blockade radius, and a growth of the density of excitations which is compatible with the power-law behaviour expected in the classical limit.
Abstract We investigate the relaxation dynamics of a Rydberg gas in regimes where coherent processes and dissipation compete. In the strongly dissipative limit, the dynamics is known to be governed by an effective classical rate equation and to exhibit kinetically constrained, glassy relaxation towards a trivial stationary state. This behaviour originates from the Rydberg blockade, which prevents simultaneous excitations within a characteristic blockade radius. However, the fate of kinetic constraints in the weakly dissipative limit remains unexplored in large systems above one dimension. To access large system sizes and two-dimensional geometries, we employ the truncated Wigner approximation, a phase-space method that captures correlated many-body dynamics beyond classical rate equations. To probe the emergence of kinetic constraints on timescales where coherent and dissipative processes are comparable, we analyse the relaxation dynamics starting from two initial states: a fully polarised state and a Néel state, which belongs to a manifold of so-called quantum scars. In both cases, we observe a pronounced slowdown in the relaxation of the magnetisation towards the stationary state and identify transient signatures of quantum kinetically constrained dynamics in one and two dimensions.