Spin squeezing of a Bose-Einstein condensate via a quantum nondemolition measurement for quantum-enhanced atom interferometry

We theoretically investigate the use of quantum non-demolition measurement to enhance the sensitivity of atom interferometry with Bose-condensed atoms. In particular, we are concerned with enhancing existing high-precision atom interferometry apparatuses, so restrict ourselves to dilute atomic samples, and the use of free-propagating light, or optical cavities in the weak-coupling regime. We find the optimum parameter regime that balances between spin squeezing and atomic loss, and find that significant improvements in sensitivity are possible. Finally, we consider the use of squeezed light, and show that this can provide further boosts to sensitivity.