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arXiv:1304.6169

Boosting the Rotational Sensitivity of Matter-wave Interferometry with Nonlinearity

Michal Kolář, Tomáš Opatrný, Kunal K. Das

Published Apr 23, 2013• 0 citations
arXivHTMLPDF

Abstract

We propose a mechanism to use nonlinearity arising from inter-particle interactions to significantly enhance rotation sensitivity of matter-wave interferometers. The method relies on modifying Sagnac interferometers by introducing a weak circular lattice potential that couples modes with opposite orbital angular momenta (OAM). The primary observable comprises of the modal population distributions measured at particular times. This provides an alternate mechanism for rotation sensing that requires substantially smaller ring size, even in the linear non-interacting regime. Nonlinearity can improve the sensitivity, as well as operation timescales, by several orders of magnitude.

DOI
10.48550/arxiv.1304.6169

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We propose a mechanism to use nonlinearity arising from inter-particle interactions to significantly enhance rotation sensitivity of matter-wave interferometers. The method relies on modifying Sagnac interferometers by introducing a weak circular lattice potential that couples modes with opposite orbital angular momenta (OAM). The primary observable comprises of the modal population distributions measured at particular times. This provides an alternate mechanism for rotation sensing that requires substantially smaller ring size, even in the linear non-interacting regime. Nonlinearity can improve the sensitivity, as well as operation timescales, by several orders of magnitude.
We theoretically analyze the operating principles of a proposed matter-wave Sagnac interferometer utilizing Bose-Einstein-condensate (BEC) phonon modes as an interference medium. Previous work found that the orbital angular momentum phonon modes of a ring-trapped BEC are split in frequency by rotations, leading to a measurable rotation signal. We develop an alternate description in which an imbalance in the counterpropagating modes' amplitudes (populations) is induced by the rotation of the system during condensation. This description gives analytic forms for the interferometic phase shift in one dimension and is readily generalized to include mean-field interactions. To validate our findings, we simulate a ring-trapped BEC Sagnac interferometer in one dimension and demonstrate that measurement of an unknown rotation rate can be performed using a modified analysis. Our simulation data show strong agreement with our analytic results, and we further employ simulations to explore and clarify the role of superfluidity in this matter-wave Sagnac interferometer.
Lights carrying orbital angular momentum (OAM) have potential applications in precise rotation measurement, especially in remote sensing. Interferometers, especially nonlinear quantum interferometers, have also been proven to greatly improve the measurement accuracy in quantum metrology. By combining these two techniques, we theoretically propose a new atom-light hybrid Sagnac interferometer with OAM lights to advance the precision of the rotation measurement. A rotation sensitivity below standard quantum limit is achieved due to the enhancement of the quantum correlation of the interferometer even with 96% photon losses. This makes our protocol robustness to the photon loss. Furthermore, combining the slow light effect brings us at least four orders of magnitude of sensitivity better than the earth rotation rate. This new type interferometer has potential applications in high precision rotation sensing.
Lights carrying orbital angular momentum (OAM) have potential applications in precise rotation measurement, especially in remote sensing. Interferometers, especially nonlinear quantum interferometers, have also been proven to greatly improve the measurement accuracy in quantum metrology. By combining these two techniques, we theoretically propose a new atom-light hybrid Sagnac interferometer with OAM lights to advance the precision of the rotation measurement. A rotation sensitivity below standard quantum limit is achieved due to the enhancement of the quantum correlation of the interferometer even with 96% photon losses. This makes our protocol robustness to the photon loss. Furthermore, combining the slow light effect brings us at least four orders of magnitude of sensitivity better than the earth rotation rate. This new type interferometer has potential applications in high 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 interferometers are, in principle, orders of magnitude more sensitive than their optical counterparts. Nevertheless, creation of matter–wave currents to achieve such a sensitivity is a continuing challenge. Here, we propose the use of Optical-Angular-Momentum (OAM) induced vortex superpositions in Bose–Einstein condensates (BECs) as an alternative to other atom interferometers for gyroscopy. The coherent superposition of two counter-rotating vortex states of a trapped condensate leads to an interference pattern that rotates by an angle proportional to the angular velocity of the rotating trap – in accordance with the Sagnac effect. We show that the rotation rate can be easily read out, and that the device is highly stable. The signal-to-noise ratio and sensitivity of the scheme are also estimated.
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.