Virtual Processes and Superradiance in Spin-Boson Models

TL;DR

This paper explores phase transitions in spin-boson models with virtual and real processes, revealing superradiant phases and entropy anomalies across three different models at thermal equilibrium.

Contribution

It introduces and analyzes three spin-boson models, including a modified Dicke model with intensity-dependent coupling, highlighting the role of virtual processes in phase transitions.

Findings

Phase transitions occur even with virtual process-only Hamiltonian terms.

The zero mode causes negative entropy at low temperatures in the first model.

Superradiant phases are identified in the generalized Dicke models.

Abstract

We consider spin-boson models composed by a single bosonic mode and an ensemble of $N$ identical two-level atoms. The situation where the coupling between the bosonic mode and the atoms generates real and virtual processes is studied, where the whole system is in thermal equilibrium with a reservoir at temperature $\beta^{-1}$. Phase transitions from ordinary fluorescence to superradiant phase in three different models is investigated. First a model where the coupling between the bosonic mode and the $j-th$ atom is via the pseudo-spin operator $\sigma^{,z}_{(j)}$ is studied. Second, we investigate the generalized Dicke model, introducing different coupling constants between the single mode bosonic field and the environment, $g_{1}$ and $g_{2}$ for rotating and counter-rotating terms, respectively. Finally it is considered a modified version of the generalized Dicke model with intensity-dependent coupling in the rotating terms. In the first model the zero mode contributes to render the canonical entropy a negative quantity for low temperatures. The last two models presents phase transitions, even when only Hamiltonian terms which generates virtual processes are considered.