Universal fluctuations and squeezing in generalized Dicke model near the superradiant phase transition

TL;DR

This paper investigates photon fluctuations and squeezing near the superradiant phase transition in a generalized Dicke model with unequal coupling strengths, revealing universal fluctuation behaviors and distinct temperature scalings.

Contribution

It introduces an effective theory for the generalized Dicke model, analyzing critical fluctuations, squeezing, and universal photon number fluctuations across different regimes.

Findings

Photon fluctuations exhibit universal values near the transition.

Distinct temperature scalings of squeezing parameters are identified.

A temperature scale for quantum fluctuation dominance is established.

Abstract

In a view of recent proposals for the realization of anisotropic light-matter interaction in such platforms as (i) non-stationary or inductively and capacitively coupled superconducting qubits, (ii) atoms in crossed fields and (iii) semiconductor heterostructures with spin-orbital interaction, the concept of generalized Dicke model, where coupling strengths of rotating wave and counter-rotating wave terms are unequal, has attracted great interest. For this model, we study photon fluctuations in the critical region of normal-to-superradiant phase transition when both the temperatures and numbers of two-level systems are finite. In this case, the superradiant quantum phase transition is changed to a fluctuational region in the phase diagram that reveals two types of critical behaviors. These are regimes of Dicke model (with discrete $\mathbb{Z}_2$ symmetry), and that of (anti-) and Tavis-Cummings $U(1)$ models. We show that squeezing parameters of photon condensate in these regimes show distinct temperature scalings. Besides, relative fluctuations of photon number take universal values. We also find a temperature scales below which one approaches zero-temperature quantum phase transition where quantum fluctuations dominate. Our effective theory is provided by a non-Goldstone functional for condensate mode and by Majorana representation of Pauli operators. We also discuss Bethe ansatz solution for integrable $U(1)$ limits.