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arXiv:1611.00120 · Physical Review A

Heisenberg-limited Sagnac interferometer with multiparticle states

Chengyi Luo, Jiahao Huang, Xiangdong Zhang, Chaohong Lee

Published Feb 10, 2017• 28 citations
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Abstract

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.

DOI
10.1103/physreva.95.023608

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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 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.
Matter-wave interferometry with atoms propagating in a guiding potential is expected to provide compact, scalable and precise inertial sensing. However, a rotation sensing device based on the Sagnac effect with atoms guided in a ring has not yet been implemented despite continuous efforts during the last two decades. Here we discuss some intrinsic effects that limit the coherence in such a device and propose a scheme that overcomes these limitations and enables a multi-pass guiding Sagnac interferometer with a Bose-Einstein condensate (BEC) on a chip in a ring potential. We analyze crucial dephasing effects: potential roughness, phase diffusion due to atom-atom interactions and number uncertainty, and phase fluctuations. Owing to the recent progress in achieving high momentum beam splitting, creating smooth guides, and manipulating the matter-wavepacket propagation, guided interferometry can be implemented within the coherence time allowed by phase diffusion. Despite the lower particle flux in a guided Sagnac ring and the miniaturization of the interferometer, the estimated sensitivity, for reasonable and practical realizations of an atom chip-based gyroscope, is comparable to that of free-space interferometers, reaching 45 nrads^{-1}Hz^{-1/2}. A significant improvement over state-of-the-art free-space gyrocope sensitivities can be envisioned by using thermal atoms instead of a BEC, whereby the interferometer can be operated in a continuous fashion with the coherence limited by the scattering rate of the atoms with the background gas. Taking into account the sensitivity times length of the interferometer as the figure of merit which takes into account compactness, our configuration is expected to deliver a potential improvement of 2-4 orders of magnitude over state-of-the-art free-space gyroscopes for a BEC, and 4-6 orders of magnitude for thermal atoms.
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 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.
The Sagnac effect enables interferometric measurements of rotation with high precision. Using matter waves instead of light promises resolution enhancement by orders of magnitude that scales with particle mass. So far, the paradigm for matter wave Sagnac interferometry relies on de Broglie waves and thus on free propagation of atoms either in free fall or within waveguides. However, the Sagnac effect can be expressed as a proper time difference experienced by two observers moving in opposite directions along closed paths and has indeed been measured with atomic clocks flown around Earth. Inspired by this, we investigate an interferometer comprised of a single atomic clock. The Sagnac effect manifests as a phase shift between trapped atoms in different internal states after transportation along closed paths in opposite directions, without any free propagation. With analytic models, we quantify limitations of the scheme arising from atomic dynamics and finite temperature. Furthermore, we suggest an implementation with previously demonstrated technology.
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.