We investigate quantum sensing of rotation with a multi-atom Sagnac interferometer and present multi-partite entangled states to enhance the sensitivity of rotation frequency. For studying the sensitivity, we first present a Hermitian generator with respect to the rotation frequency. The generator, which contains the Sagnac phase, is a linear superposition of a z component of the collective spin and a quadrature operator of collective bosons depicting the trapping modes, which enables us to conveniently study the quantum Fisher information (QFI) for any initial states. With the generator, we derive the general QFI which can be of square dependence on the particle number, leading to Heisenberg limit. And we further find that the QFI may be of biquadratic dependence on the radius of the ring which confines atoms, indicating that larger QFI is achieved by enlarging the radius. In order to obtain the square and biquadratic dependence, we propose to use partially and globally entangled states as inputs to enhance the sensitivity of rotation.
Quantum information processing with geometric features of quantum states may provide promising noiseresilient schemes for quantum metrology. In this work, we theoretically explore phase-space geometric Sagnac interferometers with trapped atomic clocks for rotation sensing, which could be intrinsically robust to certain decoherence noises and reach high precision. With the wave guide provided by sweeping ring-traps, we give criteria under which the well-known Sagnac phase is a pure or unconventional geometric phase with respect to the phase space. Furthermore, corresponding schemes for geometric Sagnac interferometers with designed sweeping angular velocity and interrogation time are presented, and the experimental feasibility is also discussed. Such geometric Sagnac interferometers are capable of saturating the ultimate precision limit given by the quantum Cramér-Rao bound.
We derive a general phase-matching condition (PMC) for enhancement of sensitivity in SU(1,1) interferometers. Under this condition, the quantum Fisher information (QFI) of two-mode SU(1,1) interferometry becomes maximal with respect to the relative phase of two modes, for the case of an arbitrary state in one input port and an even (odd) state in the other port, and the phase sensitivity is enhanced. We also find that optimal parameters can let the QFI in some areas achieve the Heisenberg limit for both pure and mixed initial states. As examples, we consider several input states: coherent and even coherent states, squeezed vacuum and even coherent states, squeezed thermal and even coherent states. Furthermore, in the realistic scenario of the photon loss channel, we investigate the effect of photon losses on QFI with numerical studies. We find the PMC remains unchanged and is not affected by the transmission coefficients for the above input states. Our results suggest that the PMC can exist in various kinds of interferometers and the phase-matching is robust to even strong photon losses.
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