First order dipolar phase transition in the Dicke model with infinitely coordinated frustrating interaction

TL;DR

This paper analytically demonstrates a first order quantum phase transition in a Josephson junction array coupled to a microwave cavity, modeled by an extended Dicke Hamiltonian with frustrating interactions, revealing a switch in the nature of the transition.

Contribution

It introduces a self-consistent Holstein-Primakoff approach to distinguish first and second order phase transitions in extended Dicke models with frustrating interactions.

Findings

Identified a first order quantum phase transition with a net dipole moment.

Showed the transition becomes second order when frustrating interactions are removed.

Proposed a Holstein-Primakoff method to analyze phase transition order.

Abstract

We found analytically a first order quantum phase transition in the Cooper pair box array of $N$ low-capacitance Josephson junctions capacitively coupled to a resonant photon in a microwave cavity. The Hamiltonian of the system maps on the extended Dicke Hamiltonian of $N$ spins one-half with infinitely coordinated antiferromagnetic (frustrating) interaction. This interaction arises from the gauge-invariant coupling of the Josephson junctions phases to the vector potential of the resonant photon field. In $N \gg 1$ semiclassical limit, we found a critical coupling at which ground state of the system switches to the one with a net collective electric dipole moment of the Cooper pair boxes coupled to superradiant equilibrium photonic condensate. This phase transition changes from the first to second order if the frustrating interaction is switched off. A self-consistently `rotating' Holstein-Primakoff representation for the Cartesian components of the total superspin is proposed, that enables to trace both the first and the second order quantum phase transitions in the extended and standard Dicke models respectively.