Excitations of optically driven atomic condensate in a cavity: theory of photodetection measurements

TL;DR

This paper analyzes the excitations and photodetection measurements of an optically driven Bose-Einstein condensate in a cavity, revealing critical behavior and excitation softening near the Dicke quantum phase transition.

Contribution

It provides a theoretical framework for understanding photodetection signals and excitation dynamics in a cavity QED system undergoing a Dicke phase transition.

Findings

Photon flux scaling near criticality differs from mean field predictions.

Second order photon correlations reveal quantum critical behavior.

Modulation techniques can directly observe polaritonic excitation softening.

Abstract

Recent experiments have demonstrated an open system realization of the Dicke quantum phase transition in the motional degrees of freedom of an optically driven Bose-Einstein condensate in a cavity. Relevant collective excitations of this light-matter system are polaritonic in nature, allowing access to the quantum critical behavior of the Dicke model through light leaking out of the cavity. This opens the path to using photodetection based quantum optical techniques to study the dynamics and excitations of this elementary quantum critical system. We first discuss the photon flux observed at the cavity face and find that it displays a different scaling law near criticality than that obtained from the mean field theory for the equivalent closed system. Next, we study the second order correlation measurements of photons leaking out of the cavity. Finally, we discuss a modulation technique that directly captures the softening of polaritonic excitations. Our analysis takes into account the effect of the finite size of the system which may result in an effective symmetry breaking term.