Abstract
We study the transmission spectra of a Bose Einstein condensate (BEC) confined in an optical lattice interacting with two modes of a cavity via nonlinear two-photon transition. In particular, we show that the one-photon and two-photon cavity transmission spectra of a BEC are different. We found that when the BEC is in the Mott state, the usual normal mode splitting present in the one-photon transition is missing in the two-photon interaction. When the BEC is in the superfluid state, the transmission spectrum shows the usual multiple lorentzian structure. However the separation between the lorentzians for the two-photon case is much larger than that for the one-photon case. This study could form the basis for nondestructive high resolution Rydberg spectroscopy of ultracold atoms or two-photon spectroscopy of a gas of ultracold atomic hydrogen.
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