Nonlinear interferometry with Bose-Einstein condensates

Abstract

We analyze a proposed experiment [Boixo et al., Phys. Rev. Lett. 101, 040403 (2008)] for achieving sensitivity scaling better than $1/N$ in a nonlinear Ramsey interferometer that uses a two-mode Bose-Einstein condensate (BEC) of $N$ atoms. We present numerical simulations that confirm the analytical predictions for the effect of the spreading of the BEC ground-state wave function on the ideal $1/N^{3/2}$ scaling. Numerical integration of the coupled, time-dependent, two-mode Gross-Pitaevskii equations allows us to study the several simplifying assumptions made in the initial analytic study of the proposal and to explore when they can be justified. In particular, we find that the two modes share the same spatial wave function for a length of time that is sufficient to run the metrology scheme.

16 pages, 7 figures. Added references and minor changes to match published version

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• Generalized Limits for Single-Parameter Quantum Estimation
• Quantum Metrology: Dynamics vs. Entanglement
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• A nonlinear Ramsey interferometer operating beyond the Heisenberg limit
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