Entanglement Signature of the Superradiant Quantum Phase Transition

TL;DR

This paper investigates the entanglement and quantum correlations in the superradiant phase transition of the Tavis-Cummings model, revealing that entanglement acts as an order parameter and persists in the thermodynamic limit.

Contribution

It introduces a detailed analysis of entanglement as an order parameter in the superradiant phase transition within the Tavis-Cummings model, including new approximations and scaling laws.

Findings

Quantum correlations and entanglement crossover at the phase transition

Entanglement serves as an effective order parameter

Properties persist in the thermodynamic limit

Abstract

Entanglement and quantum correlations between atoms are not usually considered key ingredients of the superradiant phase transition. Here we consider the Tavis-Cummings model, a solvable system of two-levels atoms, coupled with a single-mode quantized electromagnetic field. This system undergoes a superradiant phase transition, even in a finite-size framework, accompanied by a spontaneous symmetry breaking, and an infinite sequence of energy level crossings. We find approximated expressions for the ground state, its energy, and the position of the level crossings, valid in the limit of a very large number of photons with respect to that of the atoms. In that same limit, we find that the number of photons scales quadratically with the coupling strength, and linearly with the system size, providing a new insight into the superradiance phenomenon. Resorting to novel multipartite measures, we then demonstrate that this quantum phase transition is accompanied by a crossover in the quantum correlations and entanglement between the atoms (qubits). The latters therefore represent suited order parameters for this transition. Finally, we show that these properties of the quantum phase transition persist in the thermodynamic limit.