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arXiv:physics/0604082 · Physical Review A

Atom interferometer as a selective sensor of rotation or gravity

B. Dubetsky, Mark A. Kasevich

Published Aug 21, 2006• 110 citations
arXivHTMLPDF

Abstract

In the presence of Earth gravity and gravity-gradient forces, centrifugal and Coriolis forces caused by the Earth rotation, the phase of the time-domain atom interferometers is calculated with accuracy up to the terms proportional to the fourth degree of the time separation between pulses. We considered double-loop atom interferometers and found appropriate condition to eliminate their sensitivity to acceleration to get atomic gyroscope, or to eliminate the sensitivity to rotation to increase accuracy of the atomic gravimeter. Consequent use of these interferometers allows one to measure all components of the acceleration and rotation frequency projection on the plane perpendicular to gravity acceleration. Atom interference on the Raman transition driving by noncounterpropagating optical fields is proposed to exclude stimulated echo processes which can affect the accuracy of the atomic gyroscopes. Using noncounterpropagating optical fields allows one to get a new type of the Ramsey fringes arising in the unidirectional Raman pulses and therefore centered at the two-quantum line center. Density matrix in the Wigner representation is used to perform calculations. It is shown that in the time between pulses, in the noninertial frame, for atoms with fully quantized spatial degrees of freedom, this density matrix obeys classical Liouville equations.

DOI
10.1103/physreva.74.023615

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In the presence of Earth gravity and gravity-gradient forces, centrifugal and Coriolis forces caused by the Earth rotation, the phase of the time-domain atom interferometers is calculated with accuracy up to the terms proportional to the fourth degree of the time separation between pulses. We considered double-loop atom interferometers and found appropriate condition to eliminate their sensitivity to acceleration to get atomic gyroscope, or to eliminate the sensitivity to rotation to increase accuracy of the atomic gravimeter. Consequent use of these interferometers allows one to measure all components of the acceleration and rotation frequency projection on the plane perpendicular to gravity acceleration. Atom interference on the Raman transition driving by noncounterpropagating optical fields is proposed to exclude stimulated echo processes which can affect the accuracy of the atomic gyroscopes. Using noncounterpropagating optical fields allows one to get a new type of the Ramsey fringes arising in the unidirectional Raman pulses and therefore centered at the two-quantum line center. Density matrix in the Wigner representation is used to perform calculations. It is shown that in the time between pulses, in the noninertial frame, for atoms with fully quantized spatial degrees of freedom, this density matrix obeys classical Liouville equations.
Cold atom free-fall interferometers now realize state-of-the-art precision inertial sensors, opening perspectives towards embedded devices for applications and fundamental physics tests on earth and in space. The acceleration of gravity can be measured in a stimulated Raman transition interferometer where the acceleration under gravity of a cloud of freely falling atoms is sensed by three Raman pulses allowing to split, reflect and interfere atomic wave packets [1]. The gravimeter developped at SYRTE allows to measure the acceleration of gravity at state-of-the-art performances compared to the best classical absolute gravimeters, with a sensitivity of 2×10−8g over 1s and an exactitude of 5×10−9 g [2]. This exactitude is currently limited by wavefront aberrations of the lasers, sampled by residual transverse trajectories of the molasse-cooled cloud over the free fall. Unbalanced transverse trajectories will also bias the measurement due to Coriolis effect [3]. We will investigate the use of a colder atom source to reduce these systematic effects, by implementing Bose-Einstein condensation of the initial cloud, allowing both better position control and better focusing of our source.
We report on an original and simple formulation of the phase shift in N-light-pulse atom interferometers. We consider atomic interferometers based on two-photon transitions (Raman transitions or Bragg pulses). Starting from the exact analytical phase shift formula obtained from the atom optics ABCD formalism, we use a power series expansion in time of the position of the atomic wave packet with respect to the initial condition. The result of this expansion leads to a formulation of the interferometer phase shift where the leading coefficient in the phase terms up to T^k dependences (k >= 0) in the time separation T between pulses, can be simply expressed in terms of a product between a Vandermonde matrix, and a vector characterizing the two-photon pulse sequence of the interferometer. This simple coefficient dependence of the phase shift reflects very well the atom interferometer's sensitivity to a specific inertial field in the presence of multiple gravito-inertial effects. Consequently,we show that this formulation is well suited when looking for selective atomic sensors of accelerations, rotations, or photon recoil only, which can be obtained by simply zeroing some specific coefficients. We give a theoritical application of our formulation to the photon recoil measurement.
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.
Abstract In closed-loop dual-atom interferometers, the initial phase shift is a non-inertial phase induced by Raman pulses. This initial optical phase affects the measurements of both acceleration and rotation rate. In this study, we present a method to modulate the initial optical phase of light pulse atom interferometers (LPAIs). Employing this modulation method, we investigated the influence of the initial optical phase on a closed-loop dual-atom interferometer. The results reveal a better short-term sensitivity in the rotation rate measurement at an initial optical phase of 0. Our closed-loop dual-atom interferometer allows for decoupled measurements of rotation rate and acceleration. With a short interrogation time of 2T = 1.73 ms, the short-term sensitivities of the rotation rate and acceleration measurements are 2.73 × 10 − 5 ( rad / s ) / Hz and 272 μ g / Hz , respectively.
We demonstrate a closed-loop light-pulse atom-interferometer inertial sensor that can realize continuous decoupled measurements of acceleration and rotation rate. The sensor operates with double-loop atom interferometers, which share the same Raman light pulses in a spatially separated Mach-Zehnder configuration and use continuous cold atomic beams propagating in opposite directions from two 2D+{\text{2D}}^{+}2D+ magneto-optical trappings. Acceleration and the rotation rate are decoupled and simultaneously measured by the sum and difference of dual-atom-interferometer signals, respectively. The sensitivities of inertial measurements are also increased to be approximately 1.86 times higher than that of a single atom interferometer. The acceleration phase shift is compensated in real time by phase locking these interferometers via the Raman laser phases from the sum-interferometer signal, and the gyroscope performance is improved. We achieve long-term stabilities of $6.1\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\text{g}$ and 840 nrad/s for the acceleration and the rotation rate, respectively, using a short interrogation time of 0.87 ms (interference area A=0.097mm2A=0.097\phantom{\rule{0.2em}{0ex}}{\text{mm}}^{2}A=0.097mm2). This work provides a building block for an atomic interferometer-based inertial measurement unit for use in field applications that require a high data rate and high stability.
An exact expression for the phase of an atomic interferometer located in a non-inertial reference frame (platform) moving along an arbitrary trajectory and with an orientation that changes arbitrarily over time is obtained. This expression takes into account precisely gravitational, Coriolis, centrifugal, and gravity-gradient forces, which arise during the rotation of the gravity source at a permanent rate. To achieve this result, we utilized the equations for the atomic density matrix in the Wigner representation. Starting from the exact formula, we derived three new terms in the well-known limit of small rotation angles and short interrogation time, which are attributed to the rotation and translational motion of the platform.