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 Phys. Rev. Lett. {\bf 100}, 250406 (2008), with optimal initial number-variance ${\sigma }_o\propto N^{1/3}$ and optimal signal-to-noise ratio $s_o\propto N^{2/3}$ for 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 {\it phase}-squeezing with ${\sigma }_o\propto \sqrt{uN}$ and $s_o\propto \sqrt{N/u}$ 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 $\sqrt{u}$.

8 pages, 6 figures

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• Nonlinear quantum interferometry with Bose condensed atoms
• Optical interferometry in the presence of large phase diffusion
• Effect of phase noise on useful quantum correlations in Bose Josephson junctions
• Mach-Zehnder interferometry with interacting trapped Bose-Einstein condensates
• Effect of one-, two-, and three-body atom loss processes on superpositions of phase states in Bose-Josephson junctions
• Information and backaction due to phase contrast imaging measurements of cold atomic gases: beyond Gaussian states
• Squeezing as a resource to counteract phase diffusion in optical phase estimation
• Quantum-limited measurement of magnetic-field gradient with entangled atoms
• Phase noise mitigation by a realistic optical parametric oscillator
• Simple atom interferometer in a double-well potential
• Many-body quantum metrology with scalar bosons in a single potential well
• Robust sub-shot-noise measurement via Rabi-Josephson oscillations in bimodal Bose-Einstein condensates