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arXiv:0907.1138 · Journal of Modern Optics

Ultra-stable matter–wave gyroscopy with counter-rotating vortex superpositions in Bose–Einstein condensates

Sulakshana Thanvanthri, Kishore T. Kapale, Jonathan P. Dowling

Published Jul 11, 2012• 26 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1080/09500340.2012.702228

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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.
With high precision and sensitivity, quantum gyroscope has become a research hotspot of inertial technology in recent years. Because the Bose-Einstein Condensate (BEC) in atomic gas has more condensate atoms, atomic gas is pure and thin, and there is no friction in atoms, the matter–wave gyroscopy with counter-rotating vortex superpositions has great potential of higher sensitivity, higher precision, and miniaturization. The basic mechanism and sensitivity of the matter– wave gyroscopy with counter-rotating vortex superpositions were analyzed, and the interaction between superposition of vortex beams and BEC atomic gases were studied, it is Stimulated Raman Adiabatic Passage (STIRAP). In the study, the outstanding issue that the gyroscopy is difficult to obtain stable vortices with high order orbital angular momentum was clarified by theoretical derivation on the base of Gross-Pitaevskii equation which is the basic equation in BEC. For solving the above problems, the scheme which is easy to achieve based on Sombrero potential trap was proposed.
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.
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.
Abstract Matter-wave interferometer of ultracold atoms with different linear momenta has been extensively studied in theory and experiment. The vortex matter-wave interferometer with different angular momenta is applicable as a quantum sensor for measuring the magnetic field, rotation, geometric phase, etc. Here we report the experimental realization of a vortex matter-wave interferometer by coherently transferring the optical angular momentum to an ultracold Bose condensate. We use the angular interference technique to measure the relative phase of two vortex states. For a lossless interferometer with atoms only populating two spin states, the difference between the relative phases in the two spin states is locked to π. We also prove the robustness of this out-of-phase relation, not sensitive to the angular-momentum difference between two vortex states, constituent of Raman optical fields and expansion of the condensate. The experimental results agree well with the calculation from the unitary evolution of wave packet in quantum mechanics. This work opens a new way to build a quantum sensor based on the vortex matter-wave interference.
A gyroscope based on Sagnac interferometer measures the rotation rate relative to an inertial frame of reference. Sagnac effect originally has been derived and experimentally demonstrated with optical waves. Later, matter wave based Sagnac interferometers were developed due to inherent sensitivity over a photon based system. However in any interferometer whether it is photon or matter wave based the resultant phase shift due to counter-rotating waves is independent of the wave velocity. Here we show that one can have a larger phase shift with slower matter waves using Aharonov-Bohm effect: the phase difference of the counter propagating waves is proportional to the inverse square of the particle velocity.