Probing the BCS-BEC crossover with photons in a nonlinear optical fiber

TL;DR

This paper proposes a method to simulate the BCS-BEC crossover using strongly correlated photons in a hollow-core fiber filled with cold atoms, enabling optical control and observation of quantum phases.

Contribution

It introduces a scheme to realize tunable Bose-Hubbard and Fermi-Hubbard models with photons, facilitating experimental study of correlated quantum phases.

Findings

Realization of an optically tunable two-component Bose-Hubbard model.

Analysis of conditions for effective Fermi-Hubbard model with photon pairing.

Potential for in situ observation of correlated photon phases.

Abstract

We propose a scheme where strongly correlated photons generated inside a hollow-core one-dimensional fiber filled with two cold atomic species can be used to simulate the BCS-BEC crossover. We first show how stationary light-matter excitations (polaritons) in the system can realize an optically tunable two component Bose-Hubbard model, and then analyze the optical parameters regime necessary to generate an effective Fermi-Hubbard model of photons exhibiting Cooper pairing. The characteristic correlated phases of the system can be efficiently observed due to the {\it in situ} accessibility of the photon correlations with standard optical technology.