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 obtain the optimal level of squeezing for a given phase-interval Δθ₀ and particle number N, with the resulting phase-estimation uncertainty smoothly approaching 3.5/N as Δθ₀ approaches 10/N, achieved with highly squeezed states near the Fock regime. We then analyze an adaptive measurement scheme which allows any phase on (-π/2,π/2) to be measured with a precision of 3.5/N requiring only a few measurements, even for very large N. We obtain an asymptotic scaling law of Δθapprox \(2.1+3.2ln(ln(N_tottanΔθ₀\)))/N_tot, resulting in a final precision of approx 10/N_tot. This scheme can be readily implemented in a double-well Bose-Einstein condensate system, as the optimal input states can be obtained by adiabatic manipulation of the double-well ground state.