Two-photon nonlinear spectroscopy of periodically trapped ultracold atoms in a cavity

TL;DR

This paper investigates the transmission spectra of a Bose-Einstein condensate in an optical lattice interacting with a cavity via nonlinear two-photon transitions, revealing distinct spectral features for different quantum phases.

Contribution

It demonstrates how two-photon interactions produce qualitatively different spectra compared to one-photon interactions in ultracold atomic systems.

Findings

Normal mode splitting is absent in the Mott state during two-photon interaction.

Superfluid state shows multiple Lorentzian peaks with larger separation in two-photon case.

Spectral differences can enable non-destructive high-resolution spectroscopy.

Abstract

We study the transmission spectra of a Bose Einstein condensate confined in an optical lattice interacting with two modes of a cavity via nonlinear two-photon transition. In particular we show that a nonlinear two-photon interaction between the superfluid (SF) phase and the Mott insulating (MI) phase of a Bose-Einstein condensate (BEC) and the cavity field show qualitatively different transmission spectra compared to the one-photon interaction. 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 spectra 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 non-destructive high resolution Rydberg spectroscopy of ultracold atoms or two-photon spectroscopy of a gas of ultracold atomic hydrogen.