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

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.

17 pages, 7 figures, 1 table. Substantial revisions made, the title changed. The version accepted in Phys. Rev. A

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Cited by in corpus (10)

• Entangled time-crystal phase in an open quantum light-matter system
• Observation of the Magnonic Dicke Superradiant Phase Transition
• Phase transitions of the anisotropic Dicke model
• Perfect Intrinsic Squeezing at the Superradiant Phase Transition Critical Point
• Cavity-QED of a quantum metamaterial with tunable disorder
• Genuine Quantum effects in Dicke-type Models at large atom numbers
• Multipartite quantum correlations in a two-mode Dicke model
• Magnonic Superradiant Phase Transition
• Digital-Analog Simulations of Schrödinger Cat States in the Dicke-Ising Model
• Transport of pseudothermal photons through an anharmonic cavity