Abstract
A concept of hybrid atom-optical quantum gyroscope based on ring-shaped Bose–Einstein condensate (BEC) of atoms is developed. Optical probe field grants the systems sensitivity to rotation and detects the condensate response to rotation via optical interferometry. Measurement of rotation angular velocity may ideally be fulfilled without loss of atoms, but inevitably leads to degradation of BEC spatial coherence. We construct a mathematical model of this crucial phenomenon. A quantum master equation for BEC state is derived and solved analytically in the slow decoherence limit.
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Notes
We assume that L ≫ l, i.e. the finite coherence length does not obscure interference observation, despite the lengthening of the path in one of MZI arms due to cavity.
There is no contradiction in appearance of two modes a and b instead of a single mode Ψ. It follows from the fact that apart from \(\hat {\Psi }\) = \(\sqrt p \hat {a}\) + \(\sqrt q \hat {b}\) there exists an orthogonal combination \({{\hat {\Psi }}_{ \bot }}\) = \(\sqrt q \hat {a}\) – \(\sqrt p \hat {b}\), such that [\({{\hat {\Psi }}_{ \bot }}\), \({{\hat {\Psi }}^{\dag }}\)] = 0. For this reason, if a condensate is in the state |BEC〉 ∝ (\({{\hat {\Psi }}^{\dag }}\))N|0〉at, then 〈\(\hat {\Psi }_{ \bot }^{\dag }{{\hat {\Psi }}_{ \bot }}\)〉 = 0. During gyroscope operation, the latter equality is violated because of decoherence. The description indeed becomes two-mode.
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Funding
This work is supported by the State order (project AAAA-A21-121021800168-4) at the Institute of Automation and Electrometry SB RAS. Participation of L.V. Il’ichov is supported by RSCF (grant 20-12-00081).
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Tomilin, V.A., Il’ichov, L.V. BEC Decoherence in Hybrid Atom-Optical Quantum Gyroscope. J. Exp. Theor. Phys. 135, 285–290 (2022). https://doi.org/10.1134/S1063776122090114
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DOI: https://doi.org/10.1134/S1063776122090114