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arXiv:0910.0182 · Physical Review A

Scalable Bose-Einstein-condensate Sagnac interferometer in a linear trap

John H. Burke, Charles A. Sackett

Published Dec 7, 2009• 44 citations
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Abstract

We demonstrate a two-dimensional atom interferometer in a harmonic magnetic waveguide using a Bose-Einstein condensate. Such an interferometer could measure rotation using the Sagnac effect. Compared to free space interferometers, larger interactions times and enclosed areas can in principle be achieved, since the atoms are not in free fall. In this implementation, we induce the atoms to oscillate along one direction by displacing the trap center. We then split and recombine the atoms along an orthogonal direction using an off-resonant optical standing wave. We enclose a maximum effective area of $0.1\text{ }{\text{mm}}^{2}$ limited by fluctuations in the initial velocity and by the coherence time of the interferometer. We argue that this arrangement is scalable to enclose larger areas by increasing the coherence time and then making repeated loops.

DOI
10.1103/physreva.80.061603

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We demonstrate a two-dimensional atom interferometer in a harmonic magnetic waveguide using a Bose-Einstein condensate. Such an interferometer could measure rotation using the Sagnac effect. Compared to free space interferometers, larger interactions times and enclosed areas can in principle be achieved, since the atoms are not in free fall. In this implementation, we induce the atoms to oscillate along one direction by displacing the trap center. We then split and recombine the atoms along an orthogonal direction using an off-resonant optical standing wave. We enclose a maximum effective area of 0.1 mm20.1\text{ }{\text{mm}}^{2}0.1 mm2 limited by fluctuations in the initial velocity and by the coherence time of the interferometer. We argue that this arrangement is scalable to enclose larger areas by increasing the coherence time and then making repeated loops.
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.
We report the experimental realization of a large-area and multiaxis atomtronic interferometer in an optical waveguide for rotation sensing. A large enclosed area is achieved through multiloop operation in a guided-atom interferometer using Bose-Einstein condensates. We demonstrate a three-loop interferometer with a total interrogation time of ∼ 0.4 s and an enclosed area of 8.7 mm 2 —the largest reported in a fully guided or one-dimensional setup. High-contrast interference fringes are observed for up to five Sagnac orbits in a smaller loop-area configuration. Our approach enables interleaved rotation measurements about multiple arbitrary axes within the same experimental setup. We present results for area-enclosing interferometers in both horizontal and vertical planes, demonstrating that the interferometer contrast remains comparable across orthogonal orientations of the enclosed area vectors.
We analyze a Bose-Einstein condensate (BEC)-based free oscillation atom Michelson interferometer in a weakly confining harmonic magnetic trap. A BEC at the center of the trap is split into two harmonics by a laser standing wave. The harmonics move in opposite directions with equal speeds and turn back under the influence of the trapping potential at their classical turning points. The harmonics are allowed to pass through each other and a recombination pulse is applied when they overlap at the end of a cycle after they return for the second time. We derive an expression for the contrast of the interferometric fringes and obtain the fundamental limit of performance of the interferometer in the parameter space.
Confining the propagating wave packets of an atom interferometer inside a waveguide can substantially reduce the size of the device while preserving high sensitivity. We have realized a two-dimensional Sagnac atom interferometer in which Bose-condensed 87Rb^{87}\mathrm{Rb}87Rb atoms propagate within a tight waveguide formed by a collimated laser beam, a matter wave analog of the fiber optic gyro. The condensate is split, reflected, and recombined with a series of Bragg pulses while the waveguide moves transversely so that the wave-packet trajectories enclose an area. Delta-kick cooling is used to prepare low-density atomic wave packets with a temperature of 3nK3\phantom{\rule{0.16em}{0ex}}\mathrm{n}\mathrm{K}3nK. The low density reduces the impact of interatomic interactions, while the low temperature limits the expansion of the wave packet during the interferometer cycle. The effective enclosed area is 0.8mm20.8\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{m}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}0.8mm2 with an average fringe contrast of 20% and underlying contrast up to 60%. The main source of the reduced average contrast is phase noise caused by mechanical vibrations of the optical components. We present a measurement of Allan deviation for such an atom rotation sensor, showing that the interferometer phase noise falls with averaging time $\ensuremath{\tau}$ as ${\ensuremath{\tau}}^{\ensuremath{-}1/2}$ for $\ensuremath{\tau}$ up to 10 000 seconds. The statistical noise falls below the Earth rotation rate after 30 minutes of averaging.
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.