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Physical Review A

State independence in atom interferometry and insensitivity to acceleration and rotation

Karl-Peter Marzlin, Jürgen Audretsch

Published Jan 1, 1996• 44 citations
Publisher

Abstract

We demonstrate that for atom interferometers with lasers serving as beam splitters state independence (including freedom from Doppler effects) of the phase shift is obtained if the paths of the two interfering beams are closed and have obtained the same momentum transfer. This is also the case when the center-of-mass motion of the atoms is subject to a constant force field (acceleration). Among these interferometers the one with the simplest geometry is deduced for which the phase shift does not depend on acceleration. Its remaining sensitivity to rotation is discussed. Finally the geometry of a state-independent interferometer that is practically insensitive to both acceleration and rotation is worked out. As an application its relevance for the detection of the influence of space-time curvature on the atomic motion is studied. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.312

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We demonstrate that for atom interferometers with lasers serving as beam splitters state independence (including freedom from Doppler effects) of the phase shift is obtained if the paths of the two interfering beams are closed and have obtained the same momentum transfer. This is also the case when the center-of-mass motion of the atoms is subject to a constant force field (acceleration). Among these interferometers the one with the simplest geometry is deduced for which the phase shift does not depend on acceleration. Its remaining sensitivity to rotation is discussed. Finally the geometry of a state-independent interferometer that is practically insensitive to both acceleration and rotation is worked out. As an application its relevance for the detection of the influence of space-time curvature on the atomic motion is studied. \textcopyright{} 1996 The American Physical Society.
We study in a general treatment the influence of a class of perturbations acting on the atoms of an atomic interferometer. An exact expression for the resulting shift of the interference pattern is given for an arbitrary number of laser zones with travelling or standing waves. The assumption made is that the two-level model is appropriate for the description of atoms and that the perturbations can be neglected in the laser zones. As an important application we calculate the influence acceleration, rotation, and space-time curvature on the Ramsey interferometer and the atomic fountain. The measurability of the respective phase shifts is discussed.
A rotation-rate sensor was developed using atom interferometry and the Sagnac effect for matter waves. This device has a short-term sensitivity of 6× 10−10 rad/sec for a 1 second integration time, which is the best publicly reported value to date. It has high intrinsic accuracy because it relies on interactions between atoms and laser light that is stabilized to an atomic transition. Long-term stability is promising and characterization is currently underway. Potential applications include inertial navigation, geophysical studies, and general relativity tests such as verification of the Lense-Thirring and geodetic effects. The principle of operation is as follows: A thermal cesium atomic beam crosses three laser interaction regions where two-photon stimulated Raman transitions between cesium ground states transfer momentum to atoms and divide, deflect, and recombine the atomic wavepackets. Rotation induces a phase shift between the two possible trajectories and causes a change in the detected number of atoms with a particular internal state. Counterpropagating atomic beams form two interferometers using shared lasers for common-mode rejection, and the rotation phase shifts have opposite sign since the phase shift is proportional to the vector velocity of the atoms. Therefore, subtracting or adding the interferometer signals discriminates between rotation and transverse acceleration summed with laser arbitrary phase. Furthermore, in the inertial reference frame of the atoms, rotations Doppler-shift the Raman lasers. Adding Raman frequency shifts to cancel these Doppler-shifts allows operation at an effective zero rotation rate, improving sensitivity and bandwidth. Modulating these frequency shifts facilitates sensitive lock-in detection readout techniques.
We have observed momentum transfer in cesium atoms using the process of adiabatic transfer between dark states. We have investigated the sensitivity of this process to Zeeman shifts and to the differences between the translational energies of the states involved. We have shown that, for a chosen velocity class, the resultant phase shifts of the magnetic substates can be canceled so a dark state is maintained. Two different laser polarization configurations were used to perform the experiments: two circularly polarized beams or a linearly and a circularly polarized beam. Results for each are presented. Finally we discuss the relevance of our results to atomic interferometry and consider methods to minimize the possible phase shifts introduced in an atomic interferometer based upon adiabatic transfer. \textcopyright{} 1996 The American Physical Society.
The exquisite precision of atom interferometers has sparked the interest of a large community for uses ranging from fundamental physics to geodesy and inertial navigation. However, their implementation for onboard applications is still limited, not least because rotation and acceleration are intertwined in a single phase shift, which makes the extraction of a useful signal more challenging. Moreover, the spatial separation of the wave packets due to rotations leads to a loss of signal. We present an atom interferometer operating over a large range of random angles, rotation rates and accelerations. A model of the expected phase shift allows us to untangle the rotation and acceleration signals. We also implement a real-time compensation system using fiber-optic gyroscopes and a rotating reference mirror to maintain the full contrast of the interferometer. We demonstrate a single-shot sensitivity to acceleration of 24 μg for rotation rates reaching 14° s−1. Cold atoms inertial sensors offer great precision and sensitivity, yet their use in mobile applications has been hindered by the effects of rotations on their measurements. Here, authors demonstrate an atom interferometer operating over a wide range of orientations and rotation rates, thanks to hybridisation with accelerometers and gyroscopes.
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.