Functional Methods in the Generalized Dicke Model

TL;DR

This paper analyzes the generalized fermion Dicke model using path integral methods, revealing phase transitions, superradiance, and quantum critical behavior, including cases with virtual processes and the rotating-wave approximation.

Contribution

It introduces a generalized fermion Dicke model with multiple coupling constants and analyzes its phase transitions and excitation spectrum using functional path integral methods.

Findings

Identifies a second order phase transition from normal to superradiant phase.

Derives the spectrum of collective bosonic excitations.

Shows superradiance can occur with virtual processes alone.

Abstract

The Dicke model describes an ensemble of N identical two-level atoms (qubits) coupled to a single mode of a bosonic field. The fermion Dicke model should be obtained by changing the atomic pseudo-spin operators by a linear combination of Fermi operators. The generalized fermion Dicke model is defined introducing different coupling constants between the single mode of the bosonic field and the reservoir. In the thermodynamic limit, the fermion Dicke model can be analized using the path integral approach with functional method. The system exhibits a second order phase transition from normal to superrandiance at some critical temperature with the presence of a condensate. We evaluate the critical transition temperature and present the spectrum of the collective bosonic excitations. There is quantum phantum critical behavior when the coupling constants satisfy an especific condition. Two particular situations are analyzed. First, we present the spectrum of the collective bosonic excitations in the case using the rotating-wave approximation, recovering the well know results. Second, the case only considering virtual processes. In the last case, it is possible to have a superradiance phase when only virtual processes are introduced in the interaction Hamiltonian. Here also appears a quantum phase transition at some critical coupling, and for larger values for the critical coupling, the system enter in this superradiant phase with a Goldstone mode.