Multilevel atomic Ramsey interferometry for precise parameter estimations

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Multi-path (or multi-mode) entanglement has been proved to be a useful resource for sub-shot-noise sensitivity of phase estimation,which has aroused much research interest in quantum metrology recently.Various schemes of multi-path interferometers based on optical systems have been put forward.Here,we study a multi-state interferometer with multi-level atoms by projective measurements.Specifically,we investigate its ultimate sensitivity described by quantum Fisher information theory and find that the Cramer-Rao bound can be achieved.In particular,we investigate a specific scheme to improve the sensitivity of magnetometery with a three-state interferometry delivered by a single nitrogen-vacancy (NV)center of diamond with tailor pulses.The impacts of imperfections of the atomic beam-splitter,described by the three-level quantum Fourier transform,on the sensitivity of phase estimation is also discussed.
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