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 $Δθ_0$ and particle number $N$, with the resulting phase-estimation uncertainty smoothly approaching $3.5/N$ as $Δθ_0$ 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 $Δθ\approx (2.1+3.2\ln(\ln(N_{tot}\tanΔθ_0)))/N_{tot}$, 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.