Photon Recoil Momentum in Dispersive Media

We have measured a systematic shift of the photon recoil momentum due to the index of refraction of a dilute gas of atoms. The recoil frequency was measured with a two pulse light grating interferometer using near resonant laser light. By measuring the resulting frequency as a function of the laser detuning, we found a distinctive dispersive shape for $\omega_{rec}$ that fit the recoil momentum as $n\hbar k$, where $n$ is the index of refraction of the gas. For high atomic densities, this shift can have a significant effect on atom interferometers, and is of particular importance for precision measurements of $h/m$ with cold atoms.