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Acta Physica Sinica

Dependence of sensitivity of atom interferometer gravimeters on the Raman laser pulse sequences

Ren Li-Chun, Zhou Lin, Runbing Li, Min Liu, Wang Jin, Mingsheng Zhan, (1)中国科学院武汉物理与数学研究所波谱与原子分子物理国家重点实验室,武汉 430071；中国科学院冷原子物理中心，武汉 430071; (2)中国科学院武汉物理与数学研究所波谱与原子分子物理国家重点实验室,武汉 430071；中国科学院冷原子物理中心，武汉 430071；中国科学院研究生院，北京 100049

Published Jan 1, 2009• 4 citations
Publisher

Abstract

We investigate the dependence of the sensitivity of atom interferometer gravimeter on the Raman laser pulse sequence. The sensitivity of atom gravimeter can be adjusted by changing the pulse duration. Under the standard pulse configuration condition, the atom interferometer with four pulses is insensitive to the gravity if only gravity and its first order gradient are taken into account. The three-pulse Raman atom interferometer gravimeter displays best sensitivity. Atom interferometers with more than four Raman pulses show poorer sensitivity.

DOI
10.7498/aps.58.8230

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We investigate the dependence of the sensitivity of atom interferometer gravimeter on the Raman laser pulse sequence. The sensitivity of atom gravimeter can be adjusted by changing the pulse duration. Under the standard pulse configuration condition, the atom interferometer with four pulses is insensitive to the gravity if only gravity and its first order gradient are taken into account. The three-pulse Raman atom interferometer gravimeter displays best sensitivity. Atom interferometers with more than four Raman pulses show poorer sensitivity.
For high-precision atom interferometry gravimeters, the effect of the Raman pulse duration will become an appreciable fraction and need to be taken into account. Its influence has been reported considering a homogeneous Earth’s gravitational field in some previous works. In this paper, by decomposing the time evolution operator into two parts, the free evolution part and the interaction part, we develop an approach to study this effect in a realistic situation where the Earth’s gravitational field is inhomogeneous. A mathematic expression for the interferometer phase shift because of the Raman pulse duration effect is obtained, which shows that the Raman pulse duration should be taken into account when the gravimeter reaches an accuracy of 10−10 g.
Owing to the use of a symmetrization $\ensuremath{\pi}$ pulse at the middle of their laser sequences, Mach-Zehnder-type atom interferometers are insensitive to clocks shifts and Doppler shifts, if constant, but to changes in these quantities, which makes them accurate and sensitive inertial-force sensors. However, variations of the Raman laser coupling between laser pulses restore a parasitic sensitivity to the Doppler shift. This effect, which sets a limit to the symmetry of the interferometer, is quantitatively evaluated here as a function of the experimental parameters, in the case of an atom gravimeter experiment, and compared to expectations. We show in particular that velocity-distribution asymmetries lead to parasitic phase shifts that can compromise the accuracy and long-term stability of the gravity measurement in the low ${10}^{\ensuremath{-}9}g$ range.
We investigated the Raman-pulse-duration effect in a gravity gradiometer with two atom interferometers. Since the two atom clouds in the gradiometer experience different gravitational fields, it is hard to compensate for the Doppler shifts of the two clouds simultaneously by chirping the frequency of a common Raman laser. This leads to an appreciable phase shift. The magnitude of the phase shift relative to the differential phase shift of the two interferometers is in an order of $\ensuremath{\tau}/T$, and cannot be neglected in the precision measurements such as measuring the gravity gradient and the Newtonian gravitational constant.
The sensitive axis of an atom gravimeter is defined by the direction of the Raman lasers. Any tilt of the Raman lasers with respect to the vertical direction introduces systematic errors in gravity measurements. In this work, we report a determination of the tilt of Raman lasers, where the fringe of the atom interferometer is scanned by varying the tilt, rather than the phase, of the Raman lasers. Unlike the periodic cosine fringes typically used in atom interferometers, the fringe obtained by changing the tilt, referred to as the tilt-scanned fringe, is aperiodic in tilt and exhibits a shift due to the presence of a nonzero tilt. The tilt-scanned fringe is highly sensitive to the tilt-caused shift, enabling convenient and precise determination of the Raman laser tilt in atom gravimeters. We demonstrate that one tilt-scanned fringe, corresponding to a tilt measurement sampling time of 13 s, can determine the tilt with a typical precision of about $30\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{rad}$ in our developed atom gravimeter. The short-term sensitivity and measurement accuracy of the tilt-scanned fringe method were evaluated, demonstrating performance comparable to conventional tilt determination techniques. We expect this method to offer a convenient solution for Raman laser alignment in atom gravimeters and enhance the efficiency of absolute gravity surveys.
Abstract Since the double-loop atom interferometer consisting of Raman π 2 − π − π − π 2 four-pulse sequences can eliminate the dependence of the interferometric phase shift on the atomic initial velocity, it is widely used for rotation measurements. However, our research shows that by coupling itself with both the atomic initial velocity and the laser detuning, the short pulse duration can contribute to unknown systematic errors within the current instrument sensitivity. The coupling of the pulse duration with the laser detuning inside the device is verified experimentally and presented in this work. An improved pulse sequence design is developed to eliminate these systematic errors and improve the precision of the rotation measurements.
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.