Optimal Gaussian squeezed states for atom interferometry in the presence of phase diffusion

Abstract

We optimize the signal-to-noise ratio of a Mach-Zehnder atom interferometer with Gaussian squeezed input states in the presence interactions. For weak interactions, our results coincide with those of Huang and Moore [Y. P. Huang and M. G. Moore, Phys. Rev. Lett. 100, 250406 (2008)], with an optimal initial number variance ${\ensuremath{\sigma}}_{o}\ensuremath{\propto}{N}^{1/3}$ and an optimal signal-to-noise ratio ${s}_{o}\ensuremath{\propto}{N}^{2/3}$ for the total atom number $N$. As the interaction strength $u$ increases past unity, phase diffusion becomes dominant, leading to a transition in the optimal squeezing from initial number squeezing to initial phase squeezing with ${\ensuremath{\sigma}}_{o}\ensuremath{\propto}\sqrt{\mathit{uN}}$ and ${s}_{o}\ensuremath{\propto}\sqrt{N/u}$ shot-noise scaling. The initial phase squeezing translates into hold-time number squeezing, which is less sensitive to interactions than coherent states and improves ${s}_{o}$ by a factor of $\sqrt{u}$.