Optimal squeezing for high-precision atom interferometers

We show that squeezing is a crucial resource for interferometers based on the spatial separation of ultra-cold interacting matter. Atomic interactions lead to a general limitation for the precision of these atom interferometers, which can neither be surpassed by larger atom numbers nor by conventional phase or number squeezing. However, tailored squeezed states allow to overcome this sensitivity bound by anticipating the major detrimental effect that arises from the interactions. We envisage applications in future high-precision differential matter-wave interferometers, in particular gradiometers, e.g., for gravitational-wave detection.