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arXiv:2201.12461 · Physical Review A

Matter-wave analog of a fiber-optic gyroscope

Katarzyna A. Krzyzanowska, Jorge Ferreras, Changhyun Ryu, E. Carlo Samson, M. G. Boshier

Published Oct 10, 2023• 40 citations
arXivHTMLPDF

Abstract

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 $^{87}\mathrm{Rb}$ 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 $3\phantom{\rule{0.16em}{0ex}}\mathrm{n}\mathrm{K}$. 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 $0.8\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{m}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}$ 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.

DOI
10.1103/physreva.108.043305

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Matter-wave interferometers show great a potential for improving inertial sensing. The absence of drifts recommends them for a variety of applications in geodesy, navigation, or fundamental physics. Here, ultracold atomic ensembles, featuring a velocity distribution well below the photon recoil velocity, open up new perspectives. In contrast to standard laser cooling methods, they allow to reach better beam-splitting efficiencies and, hence, a higher contrast as well as to reduce systematic uncertainties and biases. Presently, Bose-Einstein condensates (BECs) provide the means to achieve the lowest expansion energies of few picokelvin. Indeed, the momentum distribution of a BEC can be further narrowed after reaching the regime of ballistic expansion, where all mean field energy is converted to kinetic energy, by the application of the delta-kick collimation technique. With such ensembles, Bragg processes can be driven with an efficiency of above 95% as well as Bloch oscillations performed without large atomic losses or dephasing. Both enable efficient large momentum transfer in interferometers to enhance their sensitivity for inertial effects. In a so-called twin-lattice atom interferometers more than thousand photon recoils are used to form compact but sensitive atom interferometers. These methods not only bring in reach extremely accurate gravimeters and accelerometers but also gyroscopes. Like the Sagnac effect in ring laser or fiber gyroscopes, the sensitivity of atom interferometers to rotations increases with the space-time area enclosed by the interferometer. In the case of light interferometers, the latter can be enlarged by forming multiple fiber loops. However, the equivalent for matter-wave interferometers remains an experimental challenge. An atom interferometer with scalable area may be formed in a twin lattice combined with a relaunch mechanism to obtain multi loops as well. Due to this scalability, it offers the perspective of reaching unprecedented sensitivities for rotations in comparably compact sensor head setups. Moreover, atom-chip technologies offer the possibility to generate a BEC and perform delta-kick collimation in a fast and reliable away, paving the way for field-deployable miniaturized atomic devices. Last but not least, the extremely low expansion energies of BECs open up to extend the time atoms spend in the interferometer to tens of seconds. This brings in reach unprecedented sensitivities in space-borne applications such as satellite geodesy.
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 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 propose a novel implementation of a trapped- atom Sagnac gyroscope based on the interference between matter- wave solitons confined around an optical microring resonator. Our integrated nanophotonic approach to trapped atom interferometry combines the long-term stability and quantum-limited sensitivity of ultracold matter-wave interferometers with the robustness, scalability and low power operation of nanophotonic architectures. The use of optical microresonators for atomic confinement ensures disorder-free symmetric waveguides for the confined atoms, a high degree of vibration insensitivity owing to the reciprocal structure of the waveguide, and enhanced bias and scale-factor stability via concurrent feedback stabilization of the microresonator. We have performed detailed quantum simulations based on demonstrated experimental parameters to confirm stable dispersion-free propagation of matter-wave solitons around the microresonator and the appearance of high contrast interference fringes due to the accrued Sagnac phase shift. We estimate the shot-noise limited rotation sensitivity of this gyroscope to be 0.8 μrad/s/Hz1/2for single-loop propagation of the solitons around a microring of radius 1 mm, with the possibility of substantial improvements via multiloop propagation of the solitons, fabrication of microring resonators of larger diameter, and the use of quantum-correlated states such as spin- squeezed quantum states. The proposed device illustrates the benefits of harnessing quantum many-body states such as matter- wave solitons for quantum-enhanced inertial sensing applications.
Atom interferometers and gyroscopes are highly sensitive atom-optical devices which are capable to measure inertial, gravitational, electric, and magnetic fields and to sense rotations. Theoretically, the signal-to-noise ratio of atomic gyroscopes is about a hundred billion times more than that of their optical counterparts for the same particle flux and the enclosed area. Ultra cold atoms from a Bose-Einstein condensate (BEC) can easily be controlled and coherently manipulated on small chips by laser pulses. Atom-optical devices will therefore play a significant role in fundamental research, precision measurements, and navigation systems. In BEC-based atom interferometers, a BEC in a trap is split by using laser pulses, the split clouds are allowed to evolve, they are reflected, and then recombined by laser pulses to observe interference. The split clouds accumulate spatial phase because of the trap and the nonlinearity caused by atom-atom interactions. A velocity mismatch due to reflection laser pulses also introduces a phase gradient across each cloud. These factors contribute to spatial relative phase between the clouds at recombination, causing the loss of contrast of the interference fringes. The main objective of this dissertation is to study the dynamics of a split condensate in atom Michelson interferometers, investigate the effect of trap frequencies, nonlinearity, and the velocity mismatch on the contrast, and to obtain the best theoretical limit of performance in terms of the experimental parameters: trap frequencies, number of atoms, and the velocity imparted to the clouds by the splitting laser pulses.
We propose to develop a new generation of compact high sensitivity gyroscopes using guided matter-waves on atom chips, able to fulfill the requirements of metrological applications. They will be designed to overcome the main limitations of free falling atoms interferometers: interrogation time and quantum projection noise. A cloud of cold 87Rb atoms will be coherently split and constrained to propagate along a circular guide of a few millimeters radius. At the output of the guide an interference signal sensitive to rotation via the Sagnac effect will be measured.