Entanglement signature of the superradiant quantum phase transition

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.

Graphical abstract

Keywords

entanglement / superradiant quantum phase transition

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Declarations

The authors declare that they have no competing interests and there are no conflicts.

Acknowledgements

We acknowledge the support from the RESEARCH SUPPORT PLAN 2022 − Call for applications for funding allocation to research projects curiosity driven (F CUR) − Project “Entanglement Protection of Qubits’ Dynamics in a Cavity”– EPQDC and the support by the Italian National Group of Mathematical Physics (GNFM-INdAM). R. F. and A. V. would like to acknowledge INFN Pisa for the financial support to this activity.

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