Finite-size scaling in the quantum phase transition of the open-system Dicke-model

TL;DR

This paper investigates the finite-size effects in the quantum phase transition of an open-system Dicke-model realized with a laser-driven Bose-Einstein condensate in an optical resonator, highlighting differences from equilibrium criticality.

Contribution

It introduces a Hartree-Fock-Bogoliubov method tailored for open, driven-damped systems to analyze finite-size scaling in the Dicke-model transition.

Findings

Finite-size scaling exponents are determined.

A clear distinction between non-equilibrium and equilibrium quantum criticality is identified.

The method provides insights into critical behavior in open quantum systems.

Abstract

Laser-driven Bose-Einstein condensate of ultracold atoms loaded into a lossy high-finesse optical resonator exhibits critical behavior and, in the thermodynamic limit, a phase transition between stationary states of different symmetries. The system realizes an open-system variant of the celebrated Dicke-model. We study the transition for a finite number of atoms by means of a Hartree-Fock-Bogoliubov method adapted to a damped-driven open system. The finite-size scaling exponents are determined and a clear distinction between the non-equilibrium and the equilibrium quantum criticality is found.