Phase transitions with finite atom number in the Dicke Model

TL;DR

This paper investigates quantum phase transitions in the Dicke Model with finite atoms using symmetry-adapted coherent states, revealing how finite-size effects influence critical behavior and order parameters.

Contribution

It introduces a symmetry-adapted SU(2) coherent state approach to describe phase transitions with finite atom numbers, extending mean field analysis beyond the thermodynamic limit.

Findings

Finite atom number phase transition linked to order parameter discontinuity

Discontinuous behavior arises from competition between local minima in energy surface

Method provides a finite-size perspective on quantum critical phenomena

Abstract

Two-level atoms interacting with a one mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom-cavity coupling strength. Two popular examples are the number of photons inside the cavity and the number of excited atoms. Coherent states provide a mean field description, which becomes exact in the thermodynamic limit. Employing symmetry adapted (SA) SU(2) coherent states (SACS) the critical behavior can be described for a finite number of atoms. A variation after projection treatment, involving a numerical minimization of the SA energy surface, associates the finite number phase transition with a discontinuity in the order parameters, which originates from a competition between two local minima in the SA energy surface.