Optimized double-well quantum interferometry with Gaussian squeezed states

A Mach-Zender interferometer with a Gaussian number-difference squeezed input state can exhibit sub-shot-noise phase resolution over a large phase interval. We derive the optimal level of squeezing for a given phase interval Delta theta(0) and particle number N. We then propose an adaptive measurement sequence in which the amount of squeezing is increased with each measurement. With this scheme, any phase on (-Delta theta(0),Delta theta(0)) can be measured with a precision of 3.5/N, requiring only 2-4 measurements, provided only that N tan(Delta theta(0))<10(40). In a double-well Bose-Einstein condensate, the optimized input states can be created by adiabatic manipulation of the ground state.