Quantum quenches in the Dicke model: statistics of the work done and of other observables

TL;DR

This paper investigates the statistical behavior of work and other observables during quantum quenches in the Dicke model, revealing critical phenomena and singularities near phase transition points.

Contribution

It provides a detailed analysis of work statistics and observable dynamics in the Dicke model near criticality, highlighting singular behaviors and phase transition effects.

Findings

Work distribution shows singular behavior near critical coupling.

Average work diverges as initial coupling approaches criticality.

Edge singularities appear in work distribution for quenches ending near criticality.

Abstract

We study the statistics of the work done in a zero temperature quench of the coupling constant in the Dicke model describing the interaction between a gas of two level atoms and a single electromagnetic cavity mode. When either the final or the initial coupling constants approach the critical coupling $\lambda_c$ that separates the normal and superradiant phases of the system, the probability distribution of the work done displays singular behavior. The average work tends to diverge as the initial coupling parameter is brought closer to the critical value $\lambda_c$. In contrast, for quenches ending close to criticality, the distribution of work has finite moments but displays a sequence of edge singularities. This contrasting behavior is related to the difference between the processes of compression and expansion of a particle subject to a sudden change of its confining potential. We confirm this by studying in detail the time dependent statistics of other observables, such as the quadratures of the photons and the total occupation of the bosonic modes.