Quantum Phase Transition and Berry Phase in an Extended Dicke Model

TL;DR

This paper explores quantum phase transitions and Berry phase in an extended Dicke model involving atoms and a non-linear optical medium, revealing controllable quantum criticality via optical parameters.

Contribution

It introduces a modified Dicke model with non-linear optical effects and demonstrates how quantum criticality can be controlled experimentally using low intensity lasers.

Findings

Quantum phase transition characterized by observables and Berry phase.

Control of quantum criticality through optical medium parameters.

Potential experimental access to superradiant phase with low intensity lasers.

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.