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arXiv:1810.07872 · Physical Review A

Enhancing the sensitivity of rotation in a multiatom Sagnac interferometer

Fei Yao, Yanming Che, Yuguo Su, Hongbin Liang, Jiancheng Pei, Xiaoguang Wang

Published May 30, 2019• 7 citations
arXivHTMLPDF

Abstract

We investigate quantum sensing of rotation with a multiatom Sagnac interferometer and present multipartite 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 the Heisenberg limit. We further find that the QFI may be of biquadratic dependence on the radius of the ring which confines the 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.

DOI
10.1103/physreva.99.052128

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We investigate quantum sensing of rotation with a multiatom Sagnac interferometer and present multipartite 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 zzz 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 the Heisenberg limit. We further find that the QFI may be of biquadratic dependence on the radius of the ring which confines the 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.
The Sagnac interferometry has widely been used to measure rotation frequency. Beyond the conventional single-particle scheme, we propose a multiparticle scheme via Bose condensed atoms. In our scheme, an ensemble of entangled two-state Bose atoms are moved in a ring via a state-dependent rotating potential, and then the atoms are recombined for interference via Ramsey pulses. The phase accumulation time is determined by the state-dependent rotating potential. The ultimate rotation sensitivity can be improved to the Heisenberg limit if the initial internal degrees of freedom are entangled. By implementing parity measurement, the ultimate measurement precision can be saturated, and the achieved measurement precisions approach the Heisenberg limit. Our results provide a promising way to exploit many-body quantum entanglement in precision rotation sensing.
We describe a Sagnac interferometer suitable for rotation sensing, implemented using an atomic Bose-Einstein condensate confined in a harmonic magnetic trap. The atom wave packets are split and recombined by standing-wave Bragg lasers, and the trapping potential steers the packets along circular trajectories with a radius of 0.2 mm. Two conjugate interferometers are implemented simultaneously to provide common-mode rejection of noise and to isolate the rotation signal. With interference visibilities of about 50%, we achieve a rotation sensitivity comparable to Earth's rate in about 10 min of operation. Gyroscope operation was demonstrated by rotating the optical table on which the experiment was performed.
Sagnac interferometers with massive particles promise unique advantages in achieving high-precision measurements of rotation rates over their optical counterparts. Recent proposals and experiments are exploring nonballistic Sagnac interferometers where trapped atoms are transported along a closed path. This is achieved by using superpositions of internal quantum states and their control with state-dependent potentials. We address emergent questions regarding the dynamical behavior of Bose-Einstein condensates in such an interferometer and its impact on rotation sensitivity. We investigate complex dependencies on atomic interactions as well as trap geometries, rotation rates, and speed of operation. We find that temporal transport profiles obtained from a simple optimization strategy for noninteracting particles remain surprisingly robust also in the presence of interactions over a large range of realistic parameters. High sensitivities can be achieved for short interrogation times far from the adiabatic regime. This highlights a route to building fast and robust guided-ring Sagnac interferometers with fully trapped atoms.
Quantum sensing with high precision and sensitivity plays an important role in quantum technologies and quantum information processing. Here, we propose a nonreciprocal quantum metrological scheme for estimating rotational angular velocity in a hybrid light-matter platform, where the setup consists of a spinning ring cavity coupled to a two-level system and an auxiliary bosonic mode. Through the Sagnac effect, the angular velocity is converted into a direction-dependent detuning, which modifies the effective light-matter dressing of the hybrid system. As a result, the angular velocity is encoded not only into the renormalized hybrid-mode spectrum, but also into the virtual excitations generated by ultrastrong coupling. These virtual excitations modify the polaritonic frequency response to rotation and enhance the quantum Fisher information (QFI) associated with angular velocity estimation, without requiring direct extraction of virtual excitations. Moreover, since the Sagnac-Fizeau shift enters the virtual-transition energy denominators, the metrological response becomes intrinsically different for opposite driving directions, leading to a tunable nonreciprocal sensitivity contrast. In addition, we also discuss a readout scheme and show that bundle emission coincidence counting can serve as an auxiliary direction-dependent readout channel. Our results provide a route toward exploiting nonreciprocal light-matter dressing and virtual excitations as resources for quantum rotation sensing.
Quantum information processing with geometric features of quantum states may provide promising noise-resilient 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 Cram\'er-Rao bound.
We propose a motional dynamical decoupling technique by utilizing a sequence of πππ-phase shifts, instead of the conventional πππ-pulses for spin flipping, to implement the quantum enhanced rotation sensing with a 1+2 dimensional hybrid atomic Sagnic interferometor. By fully disentangling the spin from the two-dimensional vibrational modes of the particle under rotation, the spin coherence time and thus the phase accumulation can be significantly increased. Consequently, both the achievable sensitivity and dynamic range of the rotation sensing can be significantly enhanced and extended simultaneously, compared to the previous schemes where the spin and motions of the particle were not completely decoupled. The experimental feasibility for the unambiguous estimation of the rotation parameters is also discussed. Hopefully, this technique holds promise for overcoming certain challenges existing in the usual matter-wave Sagnac interferometers with trapped particles, particularly for the practical inertial navigation that demands both high sensitivity and large dynamic range.