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Physical Review A

Phase shifts in precision atom interferometry due to the localization of atoms and optical fields

Andreas Wicht, Edina Sarajlic, Joel M. Hensley, Steven Chu

Published Aug 1, 2005• 30 citations
Publisher

Abstract

We discuss details of momentum transfer in the interaction between localized atoms and localized optical fields which are relevant to precision atom interferometry. Specifically, we consider a $\ensuremath{\Lambda}$-type atom coherently driven between its ground states by a bichromatic optical field. We assume that the excited state can be eliminated adiabatically from the time evolution. It is shown that the average recoil momentum is given by the phase gradient of the two-photon field at the ``position'' of the atom, provided that the optical field can be described by a function which is separable in position and time and that the atomic wave function is symmetric and well localized within the optical field envelope. The result does not require the optical fields to have a Gaussian spatial dependence. Our discussion provides the basis for the analysis of systematic errors in precision atom interferometry arising from optical wave-front curvature, wave-front distortion, and the Gouy phase shift of Gaussian beams. We apply our result to the atom interferometer experiment of Chu and co-workers which measures the fine-structure constant.

DOI
10.1103/physreva.72.023602

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We discuss details of momentum transfer in the interaction between localized atoms and localized optical fields which are relevant to precision atom interferometry. Specifically, we consider a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type atom coherently driven between its ground states by a bichromatic optical field. We assume that the excited state can be eliminated adiabatically from the time evolution. It is shown that the average recoil momentum is given by the phase gradient of the two-photon field at the ``position'' of the atom, provided that the optical field can be described by a function which is separable in position and time and that the atomic wave function is symmetric and well localized within the optical field envelope. The result does not require the optical fields to have a Gaussian spatial dependence. Our discussion provides the basis for the analysis of systematic errors in precision atom interferometry arising from optical wave-front curvature, wave-front distortion, and the Gouy phase shift of Gaussian beams. We apply our result to the atom interferometer experiment of Chu and co-workers which measures the fine-structure constant.
In an atom interferometry experiment, the output phase shift depends on the wave vector of photons and the recoil momentum in optical transitions. This Letter puts forward a hypothesis that in light-atom interaction, the atom wave function could provide a transverse confinement to photons and thus could affect the mean recoil momentum. We propose a model to analyze the photon effective wave vector in a monochromatic optical field and calculate the relative shift of |k[over →]_{eff}| to k when an atom with a 3D Gaussian wave function absorbs one photon in a Gaussian beam. This shift could lead to a systematic effect related to the spatial distribution of atoms and the transverse beam profile in high-precision experiments based on atom interferometry.
The basic physical principles behind atom interferometers based on optical pulses of light are summarized. This method of atom interferometry is based on measurements in the time and frequency domain and is an inherently precise measurement technique. After a brief discussion of some of the important technical requirements for good fringe accuracy and visibility, we describe an interferometer that has measured the acceleration of an atom due to gravity with a resolution better than one part in 1010. We project that the absolute accuracy of our measurement will be of the order of a few parts in 109. We also describe an interferometer experiment that measures the recoil energy shift of an atom when it absorbs a photon. When combined with the value of the Rydberg constant and the mass ratios MCs/mp and mp/me, one can obtain a value for α, the fine structure constant. Currently, we have an experimental resolution Δα/α ∼ 10-8 after two hours of integration time and are studying the systematic effects that affect the measurement.
Time-resolved atom interferometry, as employed in applications such as gravitational-wave detection and searches for ultralight dark matter, requires precise control over systematic effects. In this work, we investigate phase noise arising from shot-to-shot fluctuations in the atoms’ transverse motion in the presence of the wavefront curvature of the interferometer beam, and analyze its dependence on the laser-beam geometry in long-baseline, large-momentum-transfer atom interferometers. We use a semiclassical framework to derive analytical expressions for the effective phase perturbation in position-averaged measurements and validate them using Monte Carlo simulations. Applied to 100 m and 1 km atom gradiometers representative of next-generation experiments, the model shows that configurations maximizing pulse efficiency also amplify curvature-induced phase noise, requiring micron-level control of the atom cloud's center-of-mass position and submicron-per-second control of its center-of-mass velocity to achieve sub- 10 − 5 rad phase stability. Alternative beam geometries can suppress this noise by up to 2 orders of magnitude, but at the cost of reduced pulse efficiency. To address this limitation, we propose a mitigation strategy based on position-resolved phase-shift readout, which empirically learns and corrects the wavefront-induced bias from measurable quantities such as the phase-shift gradient and final cloud position. This approach restores high-sensitivity operation in the maximum-pulse-efficiency configuration without detailed beam characterization, providing a practical route toward next-generation, time-resolved atom interferometers operating at the 10 − 5 rad noise level.
Abstract Light pulse atom interferometers (AIFs) are exquisite quantum probes of spatial inhomogeneity and gravitational curvature. Moreover, detailed measurement and calibration are necessary prerequisites for very-long-baseline atom interferometry (VLBAI). Here we provide a theoretical analysis of the phase resulting in a complex gravitational environment and introduce a novel interferometer geometry which singles out the phase shift proportional to the curvature of the gravitational potential. The scale factor depends only on well controlled quantities, namely the photon wave number, the interferometer time and the atomic recoil, which allows the curvature to be accurately inferred from a measured phase. As a case study, we numerically simulate such a gradiometric interferometer in the context of the Hannover VLBAI facility and prove the robustness of the phase shift in gravitational fields with complex spatial dependence. We define an estimator of the gravitational curvature for non-trivial gravitational fields and calculate the trade-off between signal strength and estimation accuracy with regard to spatial resolution. As a perspective, we discuss the case of a time-dependent gravitational field and corresponding measurement strategies.
The leading experimental determinations of the fine-structure constant α currently rely on atomic photon-recoil measurements from Ramsey-Bordé atom interferometry with large-momentum transfer to provide an absolute mass measurement. We propose an experimental scheme for an intermediate-scale differential atom interferometer to measure the photon recoil of neutral atomic species with a single-photon optical clock transition. We calculate trajectories for our scheme that optimize the recoil phase while nullifying the undesired gravity-gradient phase by considering independently launching two clouds of ultracold atoms with the appropriate initial conditions. For Sr and Yb, we find an atom interferometer of height 3 m to be sufficient for an absolute mass measurement precision of Δ m / m ∼ 1 × 10 − 11 with current technology. Such a precise measurement would halve the current uncertainty in α , an uncertainty that would no longer be limited by an absolute mass measurement. The removal of this limitation would allow the current uncertainty in α to be reduced by a factor of 10 by corresponding improvements in relative mass measurements, thus paving the way for higher-precision tests of the standard model of particle physics. Published by the American Physical Society 2024
This work proposed a theory model for the local photon momentum in a monochromatic optical field. We analysed the transfered momentum when an atom absorbs a photon. Based on the uncertainty principle and Fourier optics theory, we claimed that the atom localization will confine the wavefunction of the absorbed photon that will effect the transfered momentum. We applied our theory to study the systematic effect in the metrology experiment for the fine structure constant based on atom interferometry.