Squeezing on Momentum States for Atom Interferometry.

We propose and analyze a method that allows for the production of squeezed states of the atomic center-of-mass motion that can be injected into an atom interferometer. Our scheme employs dispersive probing in a ring resonator on a narrow transition in order to provide a collective measurement of the relative population of two momentum states. We show that this method is applicable to a Bragg diffraction-based strontium atom interferometer with large diffraction orders. This technique can be extended also to small diffraction orders and large atom numbers N by inducing atomic transparency at the frequency of the probe field, reaching an interferometer phase resolution scaling Δϕ∼N^{-3/4}. We show that for realistic parameters it is possible to obtain a 20 dB gain in interferometer phase estimation compared to the standard quantum limit. Our method is applicable to other atomic species where a narrow transition is available or can be synthesized.