  We investigate the prospect of enhancing the phase sensitivity of atom
interferometers in the Mach-Zehnder configuration with squeezed light.
Ultimately, this enhancement is achieved by transferring the quantum state of
squeezed light to one or more of the atomic input beams, thereby allowing
operation below the standard quantum limit. We analyze in detail three specific
schemes that utilize (1) single-mode squeezed optical vacuum (i.e. low
frequency squeezing), (2) two-mode squeezed optical vacuum (i.e. high frequency
squeezing) transferred to both atomic inputs, and (3) two-mode squeezed optical
vacuum transferred to a single atomic input. Crucially, our analysis considers
incomplete quantum state transfer (QST) between the optical and atomic modes,
and the effects of depleting the initially-prepared atomic source.
Unsurprisingly, incomplete QST degrades the sensitivity in all three schemes.
We show that by measuring the transmitted photons and using information
recycling [Phys. Rev. Lett. 110, 053002 (2013)], the degrading effects of
incomplete QST on the sensitivity can be substantially reduced. In particular,
information recycling allows scheme (2) to operate at the Heisenberg limit
irrespective of the QST efficiency, even when depletion is significant.
Although we concentrate on Bose-condensed atomic systems, our scheme is equally
applicable to ultracold thermal vapors.
