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arXiv:2006.14354

Velocity-dependent phase shift in a light-pulse atom interferometer

Léo Morel, Zhibin Yao, Pierre Cladé, Saïda Guellati-Khélifa

Published Jun 25, 2020• 4 citations
arXivHTMLPDF

Abstract

Atom interferometry relies on the separation and recombination of atom wavepackets. When the two paths overlap perfectly at the end of the interferometer, the phase is insensitive to the atomic velocity distribution. Here, we show that, when the separation and recombination is performed using a Raman transition there is a displacement of the atomic wavepacket due to a phase shift during light pulses. Because of the variation of the laser intensity seen by the atoms, there is an imperfect cancellation of these displacements. The observation of a velocity-dependent phase shift on the interferometer is the signature of this effect, which has been modeled. Thanks to the signature we have identified, we are able to compensate for this effect by applying laser power ramps during the interferometer to mitigate intensity variations.

DOI
10.48550/arxiv.2006.14354

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Atom interferometry relies on the separation and recombination of atom wavepackets. When the two paths overlap perfectly at the end of the interferometer, the phase is insensitive to the atomic velocity distribution. Here, we show that, when the separation and recombination is performed using a Raman transition there is a displacement of the atomic wavepacket due to a phase shift during light pulses. Because of the variation of the laser intensity seen by the atoms, there is an imperfect cancellation of these displacements. The observation of a velocity-dependent phase shift on the interferometer is the signature of this effect, which has been modeled. Thanks to the signature we have identified, we are able to compensate for this effect by applying laser power ramps during the interferometer to mitigate intensity variations.
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Gravity gradients represent a major obstacle in high-precision measurements by atom interferometry. Controlling their effects to the required stability and accuracy imposes very stringent requirements on the relative positioning of freely falling atomic clouds, as in the case of precise tests of Einstein's equivalence principle. We demonstrate a new method to exactly compensate the effects introduced by gravity gradients in a Raman-pulse atom interferometer. By shifting the frequency of the Raman lasers during the central π pulse, it is possible to cancel the initial position- and velocity-dependent phase shift produced by gravity gradients. We apply this technique to simultaneous interferometers positioned along the vertical direction and demonstrate a new method for measuring local gravity gradients that does not require precise knowledge of the relative position between the atomic clouds. Based on this method, we also propose an improved scheme to determine the Newtonian gravitational constant G towards the 10 ppm relative uncertainty.
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.
The sensitivity of atom interferometers depends on the fidelity of the light pulses used as beamsplitters and mirrors. Atom interferometers typically employ pulses that affect π/2 and π fractional Rabi oscillations, the fidelities of which are reduced when there are variations in atomic velocity and laser intensity. We have previously demonstrated the application of optimal control theory to design pulses more robust to such errors; however, if these variations exhibit a time dependence over periods on the order of the interferometer duration then phase shifts can be introduced in the final fringe that potentially reduce the sensitivity. In this paper, we explain why care must be taken when optimising interferometer pulse sequences to ensure that phase shifts arising from inter-pulse variations are not significantly increased. We show that these phase shifts can in fact be minimised by choosing an appropriate measure of individual pulse fidelity.
Light Pulse Atom lnterferometryLight Pulse Atom Interferometers (LPAI) utilize Raman or Bragg transitions to coherently split, redirect, and recombine atomic wave packets.1In free space LPAIs, light pulses impart momentum kicks to freely expanding cold atomic clouds released from rest.During the atom-light interaction, the laser phase is imprinted onto the atom's wave function.Atoms experience different phase shifts along each interferometer arm which gives us information about their spatial trajectories and thus their local acceleration.The quadratic dependence of the phase shift on the interrogation time, T, have prompted researchers to increase the system's size.For field use, however, smaller compact devices are desired.Guided atom interferometers confine atoms spatially, increasing the interrogation time while minimizing the laser power needed to drive these systems. Beam 4litterIg,p) Mirror