Critical exponent of quantum phase transitions driven by colored noise

TL;DR

This paper investigates how the spectral properties of a reservoir influence critical behavior in a driven-dissipative quantum system, revealing the importance of the colored bath's spectral density on phase transition characteristics.

Contribution

It introduces a detailed analysis of the critical exponent in a quantum phase transition driven by colored noise, highlighting the role of the reservoir's spectral density.

Findings

Critical exponent depends on the low-frequency spectral density of the colored bath.

The soft mode does not fully capture the criticality in the presence of colored noise.

Finite temperature of the reservoir does not qualitatively change the spectral density's influence.

Abstract

We demonstrate that criticality in a driven-dissipative system is strongly influenced by the spectral properties of the reservoir. We study the open-system realization of the Dicke model, where a bosonic cavity mode couples to a large spin formed by two motional modes of an atomic Bose-Einstein condensate. The cavity mode is driven by a high frequency laser and it decays to a Markovian bath, while the atomic mode interacts with a colored reservoir. We reveal that the soft mode fails to describe the characteristics of the criticality. We calculate the critical exponent of the superradiant phase transition and identify an inherent relation to the low-frequency spectral density function of the colored bath. We show that a finite temperature of the colored reservoir does not modify qualitatively this dependence on the spectral density function.