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 Deltatheta{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 (-Deltatheta{0},Deltatheta{0}) can be measured with a precision of 3.5/N, requiring only 2-4 measurements, provided only that Ntan(Deltatheta{0})<10{40}. In a double-well Bose-Einstein condensate, the optimized input states can be created by adiabatic manipulation of the ground state.