Optimized Double-Well Quantum Interferometry with Gaussian Squeezed States

Previous Hiesenberg-limited interferometry schemes using NOON, Twin-Fock and similar states perform worse than shot-noise when measuring a nonzero phase. We have found that a Mach-Zehnder interferometer with a Gaussian number-difference squeezed input state can exhibit sub-shot-noise phase resolution over a large phase interval, accomplished by optimizing the level of squeezing based on the phase interval $\Delta \theta_0$ and particle number $N$ [1]. This can be combined with an adaptive measurement sequence in which the amount of squeezing is increased with each measurement, with the result that 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 interaction to tunneling ratio, and is robust against imprecise control of squeezing and inaccurate knowledge of $N$. [1] Y. P. Huang and M. G. Moore, Phys. Rev. Lett. 100, 250406 (2008).