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Journal of the Optical Society of America B

Raman pulse duration effect in high-precision atom interferometry gravimeters

Li Xia, Cheng-Gang Shao, Zhong-Kun Hu

Published Jan 12, 2015• 19 citations
Publisher

Abstract

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.

DOI
10.1364/josab.32.000248

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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.
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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.
High-precision inertial sensing demonstrations with light pulse atom interferometry have typically used Raman pulses having durations orders of magnitude shorter than the dwell time between interferometer pulses. Environmentally robust sensors operating at high-bandwidth will be required to operate at short (millisecond scale) dwell times between Raman pulses. In such an operational mode, the Raman pulse duration becomes an appreciable fraction of the dwell time between pulses. In addition, high-precision inertial sensing applications have typically been demonstrated in mildly dynamic or nondynamic environments having low rate of change of inertial input, ensuring that applied Raman pulses satisfy the Raman resonance condition. Application of nonresonant pulses will be inevitable in sensors registering time-varying inertial input. We present a diagrammatic technique for calculation of atomic output state populations for multipulse atom optics manipulations that explicitly account for the effects of finite pulse duration and finite Raman detuning effects on the laser-induced atomic phase. We analyze several atom interferometer sequences. We report accelerometer and gyroscope phase evolution for fixed Raman laser frequency difference incorporating corrections in powers of the ratio of pulse duration to time interval between interferometer pulses. Our accelerometer result agrees with other published results.
Abstract With the rapid development of atom interference technology, multi-loop atom interferometers are widely used in the high-precision measurement of various physical constants and testing of various gravity-related effects. However, in ground-based multi-loop atom interference experiments, the systematic error contribution by classical effects is an important factor that affects the experimental measurement accuracy and gravitational effect detection. Based on this, we used the atomic wave-function evolution-phase accumulation method to provide a high-order interference phase of multi-loop atom interferometers in an inhomogeneous gravitational field containing Earth’s rotation. Furthermore, we propose a new scheme that combines optimised frequency-shift compensation technology with an improved pulse sequence to eliminate systematic errors due to the gravity gradient, Earth’s rotation, and their coupling effect with the pulse duration, as well as the coupling effect of laser detuning with the pulse duration. This study lays a theoretical foundation for experiments on multi-loop atom interferometers with higher precision.
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.
Although frequency-shift gravity-gradient compensation is currently the technique with the most potential to test the weak equivalence principle with atom interferometry at high precision, it faces an unavoidable obstacle on how to cancel the coupling between the Raman-pulse-duration effect and the gravity gradient related to the atomic initial kinematics. According to the Einstein equivalence principle, we develop a method to calculate this coupling effect in a space-stretching free-falling frame, based on which an improved frequency-shift gravity-gradient compensation technique is put forward to make high-accuracy weak-equivalence-principle tests with the microscopic particles, such as at the level of ${10}^{\ensuremath{-}14}$, more possible.