Regular Article

Quantum phase transition and Berry phase in an extended Dicke model

¹ Universidad de Antioquia, Instituto de Fsica, Facultad de Ciencias Exactas y Naturales, Calle 70 No. 52-21, Medelln, Colombia
² Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 CDMX, Mexico

^a e-mail: alberto.estrada@udea.edu.co

Received: 10 June 2020
Received in final form: 27 August 2020
Accepted: 1 September 2020
Published online: 1 October 2020

Abstract

We investigate quantum phase transitions, quantum criticality, and Berry phase for the ground state of an ensemble of non-interacting two-level atoms embedded in a non-linear optical medium, coupled to a single-mode quantized electromagnetic field. The optical medium is pumped externally through a classical electric field, so that there is a degenerate parametric amplification effect, which strongly modifies the field dynamics without affecting the atomic sector. Through a semiclassical description the different phases of this extended Dicke model are described. The quantum phase transition is characterized with the expectation values of some observables of the system as well as the Berry phase and its first derivative, where such quantities serve as order parameters. It is remarkable that the model allows the control of the quantum criticality through a suitable choice of the parameters of the non-linear optical medium, which could make possible the use of a low intensity laser to access the superradiant region experimentally.