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arXiv:2204.10550 · Physical review. B./Physical review. B

Signatures of a quantum stabilized fluctuating phase and critical dynamics in a kinetically constrained open many-body system with two absorbing states

Federico Carollo, Markus Gnann, Gabriele Perfetto, Igor Lesanovsky

Published Sep 29, 2022• 9 citations
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Abstract

We introduce and investigate an open many-body quantum system in which kinetically constrained coherent and dissipative processes compete. The form of the incoherent dissipative dynamics is inspired by that of epidemic spreading or cellular-automaton-based computation related to the density-classification problem. It features two nonfluctuating absorbing states as well as a ${\mathcal{Z}}_{2}$-symmetric point in parameter space. The coherent evolution is governed by a kinetically constrained ${\mathcal{Z}}_{2}$-symmetric many-body Hamiltonian which is related to the quantum XOR-Fredrickson-Andersen model. We show that the quantum coherent dynamics can stabilize a fluctuating state and we characterize the transition between this active phase and the absorbing states. We also identify a rather peculiar behavior at the ${\mathcal{Z}}_{2}$-symmetric point. Here the system approaches the absorbing-state manifold with a dynamics that follows a power law whose exponent continuously varies with the relative strength of the coherent dynamics. Our work shows how the interplay between coherent and dissipative processes as well as symmetry constraints may lead to a highly intricate nonequilibrium evolution and may stabilize phases that are absent in related classical problems.

DOI
10.1103/physrevb.106.094315

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We introduce and investigate an open many-body quantum system in which kinetically constrained coherent and dissipative processes compete. The form of the incoherent dissipative dynamics is inspired by that of epidemic spreading or cellular-automaton-based computation related to the density-classification problem. It features two nonfluctuating absorbing states as well as a Z2{\mathcal{Z}}_{2}Z2​-symmetric point in parameter space. The coherent evolution is governed by a kinetically constrained Z2{\mathcal{Z}}_{2}Z2​-symmetric many-body Hamiltonian which is related to the quantum XOR-Fredrickson-Andersen model. We show that the quantum coherent dynamics can stabilize a fluctuating state and we characterize the transition between this active phase and the absorbing states. We also identify a rather peculiar behavior at the Z2{\mathcal{Z}}_{2}Z2​-symmetric point. Here the system approaches the absorbing-state manifold with a dynamics that follows a power law whose exponent continuously varies with the relative strength of the coherent dynamics. Our work shows how the interplay between coherent and dissipative processes as well as symmetry constraints may lead to a highly intricate nonequilibrium evolution and may stabilize phases that are absent in related classical problems.
We introduce the concept of dark space phase transition, which may occur in open many-body quantum systems where irreversible decay, interactions, and quantum interference compete. Our study is based on a quantum many-body model that is inspired by classical nonequilibrium processes which feature phase transitions into an absorbing state, such as epidemic spreading. The possibility for different dynamical paths to interfere quantum mechanically results in collective dynamical behavior without classical counterpart. We identify two competing dark states, a trivial one corresponding to a classical absorbing state and an emergent one which is quantum coherent. We establish a nonequilibrium phase transition within this dark space that features a phenomenology which cannot be encountered in classical systems. Such emergent two-dimensional dark space may find technological applications, e.g., for the collective encoding of a quantum information.
We introduce the concept of dark space phase transition, which may occur in open many-body quantum systems where irreversible decay, interactions, and quantum interference compete. Our study is based on a quantum many-body model that is inspired by classical nonequilibrium processes which feature phase transitions into an absorbing state, such as epidemic spreading. The possibility for different dynamical paths to interfere quantum mechanically results in collective dynamical behavior without classical counterpart. We identify two competing dark states, a trivial one corresponding to a classical absorbing state and an emergent one which is quantum coherent. We establish a nonequilibrium phase transition within this dark space that features a phenomenology which cannot be encountered in classical systems. Such emergent two-dimensional dark space may find technological applications, e.g., for the collective encoding of a quantum information.
Collective non-equilibrium phenomena in many-body systems are strongly influenced by fluctuations, particularly in the vicinity of phase transitions, where the interplay between classical and quantum effects can alter cooperative behavior. Here, we investigate this classical-quantum competition in a kinetically constrained spin chain, the dissipative far-East model. In absence of fluctuations, the system exhibits emergent collective dynamics, resulting in phase coexistence. We find that this phenomenon is robust to quantum fluctuations, which further stabilize it, whereas classical fluctuations suppress phase coexistence at long times. We map out the steady-state phase diagram using a cluster mean-field approach and characterize the dynamics with stochastic tensor-network methods. Within the bistable phase we identify signatures of dynamical heterogeneity in both the local magnetization and the entanglement dynamics. This highlights how competing quantum fluctuations and classical kinetic constraints shape the relaxation dynamics and the phase structure of many-body systems.
Understanding and probing phase transitions in nonequilibrium systems is an ongoing challenge in physics. A particular instance are phase transitions that occur between a nonfluctuating absorbing phase, e.g., an extinct population, and one in which the relevant order parameter, such as the population density, assumes a finite value. Here, we report the observation of signatures of such a nonequilibrium phase transition in an open driven quantum system. In our experiment, rubidium atoms in a quasi-one-dimensional cold disordered gas are laser excited to Rydberg states under so-called facilitation conditions. This conditional excitation process competes with spontaneous decay and leads to a crossover between a stationary state with no excitations and one with a finite number of excitations. We relate the underlying physics to that of an absorbing-state phase transition in the presence of a field (i.e., off-resonant excitation processes) which slightly offsets the system from criticality. We observe a characteristic power-law scaling of the Rydberg excitation density as well as increased fluctuations close to the transition point. Furthermore, we argue that the observed transition relies on the presence of atomic motion which introduces annealed disorder into the system and enables the formation of long-ranged correlations. Our study paves the road for future investigations into the largely unexplored physics of nonequilibrium phase transitions in open many-body quantum systems.
Stochastic processes with absorbing states feature examples of nonequilibrium universal phenomena. While the classical regime has been thoroughly investigated in the past, relatively little is known about the behavior of these nonequilibrium systems in the presence of quantum fluctuations. Here, we theoretically address such a scenario in an open quantum spin model which, in its classical limit, undergoes a directed percolation phase transition. By mapping the problem to a nonequilibrium field theory, we show that the introduction of quantum fluctuations stemming from coherent, rather than statistical, spin flips alters the nature of the transition such that it becomes first order. In the intermediate regime, where classical and quantum dynamics compete on equal terms, we highlight the presence of a bicritical point with universal features different from the directed percolation class in a low dimension. We finally propose how this physics could be explored within gases of interacting atoms excited to Rydberg states.
Summary form only given. Understanding and probing phase transitions in non-equilibrium systems is an ongoing challenge in physics. A particular instance are phase transitions that occur between a non-fluctuating absorbing phase [1], e.g., an extinct population, and one in which the relevant order parameter, such as the population density, assumes a finite value. Here we report the observation of signatures of such a non-equilibrium phase transition in an open driven quantum system. In our experiment rubidium atoms in a quasi one-dimensional cold disordered gas are laser-excited to Rydberg states under so-called facilitation conditions [2]. This conditional excitation process competes with spontaneous decay (see Fig. 1a) and leads to a crossover between a stationary state with no excitations and one with a finite number of Rydberg excitations (see Fig. 1b, where the phase diagram is plotted as a function of the driving strength and detuning from resonance) [3]. We relate the underlying physics to that of an absorbing state phase transition in the presence of a field which slightly offsets the system from criticality. We observe a characteristic power-law scaling of the Rydberg excitation density as well as increased fluctuations close to the transition point. Furthermore, we argue that the observed transition relies on the presence of atomic motion which introduces annealed disorder into the system and enables the formation of long-ranged correlations. Our study paves the road for future investigations into the largely unexplored physics of non-equilibrium phase transitions in open many-body quantum systems.