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arXiv:1912.04793 · Physical Review A

Accurate trajectory alignment in cold-atom interferometers with separated laser beams

Matteo Altorio, Leonid A. Sidorenkov, Romain Gautier, Denis Savoie, Arnaud Landragin, Rémi Geiger

Published Mar 10, 2020• 22 citations
arXivHTMLPDF

Abstract

Cold-atom interferometers commonly face systematic effects originating from the coupling between the trajectory of the atomic wave packet and the wavefront of the laser beams driving the interferometer. Detrimental for the accuracy and the stability of such inertial sensors, these systematics are particularly enhanced in architectures based on spatially separated laser beams. Here we analyze the effect of a coupling between the relative alignment of two separated laser beams and the trajectory of the atomic wave packet in a four-light-pulse cold-atom gyroscope operated in fountain configuration. We present a method to align the two laser beams at the $0.2\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{rad}$ level and to determine the optimal mean velocity of the atomic wave packet with an accuracy of $0.2\phantom{\rule{4pt}{0ex}}\mathrm{mm}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Such fine tuning constrains the associated gyroscope bias to a level of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{3.33333pt}{0ex}}\mathrm{rad}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. In addition, we reveal this coupling using the point-source interferometry technique by analyzing single-shot time-of-flight fluorescence traces, which allows us to measure large angular misalignments between the interrogation beams. The alignment method which we present here can be employed in other sensor configurations and is particularly relevant to emerging gravitational wave detector concepts based on cold-atom interferometry.

DOI
10.1103/physreva.101.033606

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Cold-atom interferometers commonly face systematic effects originating from the coupling between the trajectory of the atomic wave packet and the wavefront of the laser beams driving the interferometer. Detrimental for the accuracy and the stability of such inertial sensors, these systematics are particularly enhanced in architectures based on spatially separated laser beams. Here we analyze the effect of a coupling between the relative alignment of two separated laser beams and the trajectory of the atomic wave packet in a four-light-pulse cold-atom gyroscope operated in fountain configuration. We present a method to align the two laser beams at the 0.2\ensuremathμrad0.2\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{rad}0.2\ensuremathμrad level and to determine the optimal mean velocity of the atomic wave packet with an accuracy of 0.2mms\ensuremath−10.2\phantom{\rule{4pt}{0ex}}\mathrm{mm}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}0.2mms\ensuremath−1. Such fine tuning constrains the associated gyroscope bias to a level of 1\ifmmode×\else\texttimes\fi10\ensuremath−10rads\ensuremath−11\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{3.33333pt}{0ex}}\mathrm{rad}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}1\ifmmode×\else\texttimes\fi10\ensuremath−10rads\ensuremath−1. In addition, we reveal this coupling using the point-source interferometry technique by analyzing single-shot time-of-flight fluorescence traces, which allows us to measure large angular misalignments between the interrogation beams. The alignment method which we present here can be employed in other sensor configurations and is particularly relevant to emerging gravitational wave detector concepts based on cold-atom interferometry.
We present a precision atom interferometry gyroscope with a Sagnac area of 6.0 cm 2 . To drive the cold atom interferometry gyroscope, we utilize two sets of Raman beams with a pulse sequence of π /2- π - π - π /2. We present a procedure for aligning the two sets of Raman beams at the microradian level by making use of the atom interferometer itself in different configurations. Additionally, we measured the atomic cloud trajectory and implemented a spatial symmetry alignment for the atom interferometer. With these improvements, we construct a sensitive atom gyroscope with a stability of 1 nrad/s at an integration time of 10000 s. We analyzed the influence of Raman beams and the limitations of the system, and present the technical limits to the sensitivity and long-term stability. Finally, we point out the primary sources of noise in the atom interferometry gyroscope, clearing the way for the construction of further large-area atom gyroscopes.
Summary form only given. Atom interferometry based on cold atoms and light beamsplitters is a mature technique, which allows for the realization of highly sensitive inertial sensors. In the most advanced inertial sensors based on atom interferometry, atomic wavepackets are manipulated by light beamsplitters using two-photon Raman transitions. The interferometer phase shift, which depends on the acceleration and the rotation of the experimental setup with respect to the inertial reference frame defined by the atoms in free fall, is derived from the relative displacement of the atoms with respect to the beamsplitter laser's equiphases. Wavefront aberrations thus induce parasitic phase shifts, which bias the measurement, and which are linked to the residual ballistic motion of the atoms across the laser beam profile during their free fall and cancels out at zero atomic temperature. The wavefront distortions of the lasers beamsplitters is an important limit in the accuracy of atom interferometers and in particular, the dominating contribution in best cold atom gravimeters (CAG) uncertainty budget. This work clears the way towards unprecedented accuracies for absolute gravimetry, below the 1 μGal level. The method proposed can be applied to any atomic sensor based on light beamsplitters, which are inevitably affected by distortions of the lasers wavefronts. The improved control of systematics it provides will have significant impact in high precision measurements with atom interferometry, with important applications to geodesy, fundamental physics tests and to the development of highest grade inertial sensors.
One of the main residual limitations of inertial sensors based on atom interferometry stems from laser beam distortions, which cause parasitic phase shifts and non-homogeneous matter-light couplings. Here we present numerical simulations, accompanied by analytical calculations, which quantify the impact of these effects in a cold atom gradiometer. We demonstrate that the propagation of interferometric laser beam aberrations, combined with initial asymmetry and significant time-of-flight expansion of the the two atomic sources, limit the common-mode rejection of phase noise in a differential configuration. The resulting deviations in gravitational acceleration and its gradient are within reach of current experimental devices. Our study allows us to evaluate the surface quality requirements for retroreflective optics in cold-atom gradiometers of various baselines, and can be extended to other sensors based on different interferometer geometries.
The angular alignment of the effective wave vectors of spatially separated Raman beams is crucial for the closed interferometric paths in atom-interferometer gyroscopes. A sensitive and reliable method based on the optical interference is proposed for the preliminary alignment of Raman beams in a four-pulse atom interferometer. The distribution of the optical interference fringe is perpendicular to the angular deviation, while the fringe width reveals the size of the misaligned angle. The alignment method can also be extended in the atom-interferometer gyroscopes with three pairs of separated Raman beams.
Matter-wave interferometry has enabled high precision measurements of inertial forces such as gravity and the Coriolis force. This is facilitated by the long-term stability of the physical properties of atoms and lasers. Recent experiments have demonstrated the operation of portable, robust sensors using atom interferometry. This has potential uses in the context of inertial navigation, where conventional devices suffer from long-term drifts due to bias instability. Furthermore, determining position via dead reckoning requires minimisation of dead time between measurements. This thesis presents the development of an atom interferometer for measuring horizontal accelerations. In this configuration, gravity induces motion across the laser wavefront, which constrains the tolerable level of wavefront distortions. Effective control of the experiment allows the interferometer to be operated at a rate of 4 Hz. A cold ensemble of 10^6 atoms in the same internal state is prepared in 150 ms. The interferometer operates using a sequence of three laser pulses separated by T= 25 ms to achieve sensitivity to horizontal accelerations. Combining this with a classical accelerometer provides a method of correcting for vibration-induced noise, as well as determining the interferometer fringe order. After an integration time of 40 s, the sensitivity to horizontal accelerations is better than 3^-6 m s^-2. Effects which limit this sensitivity are discussed.
We report a Mach-Zehnder-type dual-atom-interferometer gyroscope with an interrogation arm of 40-cm length and the interference area up to 1.2cm21.2\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}1.2cm2. The precise angular alignment of the large-scale separated Raman lasers is demonstrated by seeking the phase intersection of Ramsey-$\mathrm{Bord}\stackrel{\ifmmode \acute{}\else \'{}\fi{}}{\mathrm{e}}$ interferometers after the gravity effect is compensated and by decoupling the velocity dependent cross-talk phase shifts, and applied to build the Mach-Zehnder atom interferometer. Then a compact inertial rotation sensor is realized based on dual large-area Mach-Zehnder atom interferometers by precisely aligning the large-scale separated Raman lasers, in which the coherence is well preserved and the common noise is differentially suppressed. The sensor presents a sensitivity of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ rad/s/Hz1/2\mathrm{rad}/\mathrm{s}/{\mathrm{Hz}}^{1/2}rad/s/Hz1/2, and a stability of $9.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.16em}{0ex}}\mathrm{rad}/\mathrm{s}$ at 23000 s. The absolute rotation measurement is carried out by adjusting the atomic velocity which corresponds to modulating the scale factor.