Sine-Gordon and Bose-Hubbard dynamics with photons in a hollow-core fiber

Abstract

We show that sine-Gordon and Bose-Hubbard dynamics with stationary polaritons could be observed in a hollow-core one-dimensional fiber loaded with a cold atomic gas. Utilizing the strong light confinement in the fiber, a range of different strongly correlated polaritonic and photonic states corresponding to both strong and weak interactions can be created and probed. The key ingredient is the creation of a tunable effective lattice potential acting on the interacting polaritonic gas, which is possible by slightly modulating the atomic density. We analyze the relevant phase diagram corresponding to the realizable Bose-Hubbard (weak) and sine-Gordon (strong) interacting regimes and conclude by describing the measurement process. The latter consists of mapping the stationary excitations to propagating light pulses whose correlations can be efficiently probed once they exit the fiber using available optical technologies. © 2012 American Physical Society.