Effective dynamics of strongly dissipative Rydberg gases

Abstract

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.

arXiv comment31 pages, 5 figures

References in corpus (40)

• Quantum information with Rydberg atoms
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Preparation of Entangled States by Quantum Markov Processes
• Glassy dynamics of kinetically constrained models
• Topology by Dissipation in Atomic Quantum Wires
• Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
• Cooperative optical non-linearity due to dipolar interactions in an ultra-cold Rydberg ensemble
• Cooperative atom-light interaction in a blockaded Rydberg ensemble
• Dynamic first-order phase transition in kinetically constrained models of glasses
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Stochastic wave function method for non-Markovian quantum master equations
• Storage and control of optical photons using Rydberg polaritons
• Dynamical crystallization in a low-dimensional Rydberg gas
• Dynamical Crystallization in the Dipole Blockade of Ultracold Atoms
• Quantum simulation of open-system dynamical maps with trapped ions
• Quantum critical behavior in strongly interacting Rydberg gases
• Strongly correlated growth of Rydberg aggregates in a vapor cell
• Full counting statistics of laser excited Rydberg aggregates in a one-dimensional geometry
• Kinetic constraints, hierarchical relaxation and onset of glassiness in strongly interacting and dissipative Rydberg gases
• Out-of-equilibrium structures in strongly interacting Rydberg gases with dissipation
• Many-body theory of excitation dynamics in an ultracold Rydberg gas
• Two-Stage Melting in Systems of Strongly Interacting Rydberg Atoms
• Coherent Population Trapping with Controlled Interparticle Interactions
• Steady-state crystallization of Rydberg excitations in an optically driven lattice gas
• Majorana Modes in Driven-Dissipative Atomic Superfluids With Zero Chern Number
• Universal scaling in a strongly interacting Rydberg gas
• Antiferromagnetic long-range order in dissipative Rydberg lattices
• Spatial correlations of Rydberg excitations in optically driven atomic ensembles
• Two-dimensional Rydberg gases and the quantum hard squares model
• Investigation of dephasing rates in an interacting Rydberg gas
• Self-Consistent Projection Operator Theory for Quantum Many-Body Systems
• Exciton dynamics in emergent Rydberg lattices
• Entropic enhancement of spatial correlations in a laser-driven Rydberg gas
• Coherent versus incoherent excitation dynamics in dissipative many-body Rydberg systems
• Out-of-equilibrium evolution of kinetically constrained many-body quantum systems under purely dissipative dynamics
• A hybrid model for Rydberg gases including exact two-body correlations
• Collective excitation of Rydberg-atom ensembles beyond the $\sqrt{N}$ enhancement
• Two-dimensional crystals of Rydberg excitations in a resonantly driven lattice gas
• Non-linear absorption and density dependent dephasing in Rydberg EIT-media
• Non-classical correlations in a class of spin chains with long-range interactions and exactly solvable ground states

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• Experimental observation of controllable kinetic constraints in a cold atomic gas
• Two-time Correlations Probing the Dynamics of Dissipative Many-Body Quantum Systems: Aging and Fast Relaxation
• Experimental signatures of an absorbing-state phase transition in an open driven many-body quantum system
• Role of interactions in a dissipative many-body localized system
• Universality in driven open quantum matter
• Classical Stochastic Discrete Time Crystals
• Non-equilibrium effective field theory for absorbing state phase transitions in driven open quantum spin systems
• Non-equilibrium universality in the dynamics of dissipative cold atomic gases
• Dynamic nuclear polarization as kinetically constrained diffusion
• Signatures of associative memory behavior in a multi-mode spin-boson model
• Uncovering the non-equilibrium phase structure of an open quantum spin system
• Adiabatic Elimination and Sub-space Evolution of Open Quantum Systems
• Full spectrum of the Liouvillian of open dissipative quantum systems in the Zeno limit
• Epidemic dynamics in open quantum spin systems
• Arrested relaxation in an isolated molecular ultracold plasma
• Emergent kinetic constraints in open quantum systems
• Projection based adiabatic elimination of bipartite open quantum systems
• Many-body radiative decay in strongly interacting Rydberg ensembles
• Self-similar non-equilibrium dynamics of a many-body system with power-law interactions
• Quantum accelerated approach to the thermal state of classical spin systems with applications to pattern-retrieval in the Hopfield neural network
• Rydberg atomtronic devices
• Atomic loss and gain as a resource for non-equilibrium phase transitions in optical lattices
• Unfolding quantum master equation into a system of real-valued equations: computationally effective expansion over the basis of $SU(N)$ generators
• Radiation trapping in a dense cold Rydberg gas
• Quench dynamics of a dissipative Rydberg gas in the classical and quantum regime
• Dynamics of strongly coupled disordered dissipative spin-boson systems
• Non-equilibrium physics of Rydberg lattices in the presence of noise and dissipative processes
• Diffusion and entanglement in open quantum systems
• Physical swap dynamics, shortcuts to relaxation and entropy production in dissipative Rydberg gases