Bridging the classical and quantum regimes in a dissipative Ising chain

TL;DR

This paper explores the transition from classical to quantum behavior in a dissipative Ising chain, revealing how classical limit cycles fade and quantum ferromagnetic states emerge, with implications for Rydberg gases.

Contribution

It introduces a unified framework describing the crossover between classical and quantum regimes in a dissipative Ising chain using a Lindblad master equation.

Findings

Classical limit exhibits nonlinear equations with limit cycles.

Quantum limit approaches a ferromagnetic steady state.

Spontaneous breaking of translation symmetry leads to antiferromagnetic states.

Abstract

We study the long-time dynamics of a dissipative Ising chain with varying quantum correlation. Invoking an ensemble-average formalism, and assuming spatial translation symmetry, we show that the dynamics can be described by a Lindblad master equation with an interpolated coherent Hamiltonian. In the classical limit, the interpolation Hamiltonian leads to a set of nonlinear equations of motion, where limit cycles can emerge in the long-time dynamics. In the quantum limit, by contrast, the system approaches a ferromagnetic steady state at long times. In between the two extremes, the discrete spatial translation symmetry can be spontaneously broken, as an antiferromagnetic steady state emerges, bridging the classical and quantum regimes. In particular, we illustrate how the classical limit-cycle behavior gradually disappears with the increase of quantum correlation. Since our model in the two extremes respectively applies to a dissipative Rydberg gas in the high- and zero-temperature limits, we expect it to provide a qualitatively correct description of dissipative Rydberg gases at interim temperatures, and shed light on the fate of limit cycles in a quantum open system.