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.
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.
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.
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.
We show that the dynamics of a laser driven Rydberg gas in the limit of strong dephasing is described by a master equation with manifest kinetic constraints. The equilibrium state of the system is uncorrelated but the constraints in the dynamics lead to spatially correlated collective relaxation reminiscent of glasses. We study and quantify the evolution towards equilibrium in one and two dimensions, and analyze how the degree of glassiness and the relaxation time are controlled by the interaction strength between Rydberg atoms. We also find that spontaneous decay of Rydberg excitations leads to an interruption of glassy relaxation that takes the system to a highly correlated nonequilibrium stationary state. The results presented here, which are in principle also applicable to other systems such as polar molecules and atoms with large magnetic dipole moments, show that the collective behavior of cold atomic and molecular ensembles can be similar to that found in soft condensed-matter systems.
We investigate the evolution of interacting Rydberg gases in the limit of strong noise and dissipation. Starting from a description in terms of a Markovian quantum master equation we derive effective equations of motion that govern the dynamics on a 'coarse-grained' timescale where fast dissipative degrees of freedom have been adiabatically eliminated. Specifically, we consider two scenarios which are of relevance for current theoretical and experimental studies—Rydberg atoms in a two-level (spin) approximation subject to strong dephasing noise as well as Rydberg atoms under so-called electromagnetically induced transparency (EIT) conditions and fast radiative decay. In the former case we find that the effective dynamics is described by classical rate equations up to second order in an appropriate perturbative expansion. This drastically reduces the computational complexity of numerical simulations in comparison to the full quantum master equation. When accounting for the fourth order correction in this expansion, however, we find that the resulting equation breaks the preservation of positivity and thus cannot be interpreted as a proper classical master rate equation. In the EIT system we find that the expansion up to second order retains information not only on the 'classical' observables, but also on some quantum coherences. Nevertheless, this perturbative treatment still achieves a non-trivial reduction of complexity with respect to the original problem.
The glass phase and its quantum analog are prominent challenges of current non-equilibrium statistical mechanics and condensed matter physics. As a model system to study the transition from classical to quantum glassy dynamics, we propose a setup of laser driven three-level atoms trapped in an optical lattice. Tuning the strength of the laser driving to the intermediate level allows one to study the transition from a classical kinetically constrained model to the coherent regime. For strong driving, Rydberg excitations evolve analogously to defects in the one-spin facilitated model, a minimal model known to exhibit glassy dynamics. In our setup, the constraints result from the interplay between Rydberg interactions and the laser detuning from the Rydberg state. The emerging heterogeneous relaxation timescales are tuneable over several orders of magnitudes. In the opposite limit of weak driving of the intermediate level, we find an effective cluster model which describes the dynamics in a reduced subspace of the allowed number and positions of Rydberg excitations. This subspace is uniquely determined by the initial state and is characterized by a fixed number of clusters of Rydberg excitations. In addition, we investigate the influence of random fields on the classical relaxation. We find that the glassy dynamics can relax faster in the presence of weak random fields.
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.