Impact of quantum noise on phase transitions in an atom-cavity system with limit cycles

TL;DR

This paper investigates how quantum noise influences phase transitions and the emergence of limit cycles in an atom-cavity system, revealing noise-induced temporal ordering and fluctuations in oscillation frequencies.

Contribution

It demonstrates that quantum noise can induce limit cycles at lower interaction strengths and explores the impact on time crystal behavior in atom-cavity systems.

Findings

Quantum noise smoothens phase transitions.

Limit cycles can emerge below critical interaction strength due to noise.

Oscillation frequencies exhibit larger fluctuations in 1D regimes.

Abstract

Quantum fluctuations are inherent in open quantum systems and they affect not only the statistical properties of the initial state but also the time evolution of the system. Using a generic minimal model, we show that quantum noise smoothens the transition between a stationary and a dynamical phase corresponding to a limit cycle (LC) in the semiclassical mean-field approximation of a generic open quantum system. Employing truncated Wigner approximation, we show that the inherent quantum noise pushes the system to exhibit signatures of LCs for interaction strengths lower than the critical value predicted by the standard mean-field theory, suggesting a noise-induced emergence of temporal ordering. Our work demonstrates that the apparent crossover-like behavior between stationary phases brought by finite-size effects from quantum fluctuations also apply to transitions involving dynamical phases. To demonstrate this on a specific physical system, we consider a transversely pumped atom-cavity setup, wherein LCs have been observed and identified as continuous time crystals. We compare the oscillation frequencies of the LCs in the one-dimensional (1D) and two-dimensional regimes, and find that the frequencies have larger shot-to-shot fluctuations in 1D. This has an important consequence in the effectiveness of entrainment of LCs for a periodically driven pump intensity or light-matter coupling strength.