Photon Counting as a Probe of Superfluidity in a Two-Band Bose Hubbard System Coupled to a Cavity Field

TL;DR

This paper demonstrates that photon counting can effectively distinguish superfluid from Mott-insulating phases in a two-band Bose-Hubbard system coupled to a cavity, offering a new method to probe superfluidity and measure the order parameter.

Contribution

It introduces a novel approach using photon number measurements to detect superfluidity and quantify the order parameter in a cavity-coupled two-band Bose-Hubbard model.

Findings

Photon number differs between superfluid and Mott-insulating phases.

Photon field dynamics correlate with the initial superfluid order parameter.

Photon counting provides a practical method to detect superfluidity.

Abstract

We show that photon number measurement can be used to detect superfluidity for a two-band Bose-Hubbard model coupled to a cavity field. The atom-photon coupling induces transitions between the two internal atomic levels and results in entangled polaritonic states. In the presence of a cavity field, we find different photon numbers in the Mott-insulating versus superfluid phases, providing a method of distinguishing the atomic phases by photon counting. Furthermore, we examine the dynamics of the photon field after a rapid quench to zero atomic hopping by increasing the well depth. We find a robust correlation between the field's quench dynamics and the initial superfluid order parameter, thereby providing a novel and accurate method of determining the order parameter.