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arXiv:1811.06731 · Physical Review Letters

Transverse Confinement of Photon Position in the Light-Atom Interaction

Jun Ying Sun, Yong-Nan Sun

Published May 26, 2021• 0 citations
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Abstract

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.

DOI
10.1103/physrevlett.126.213603

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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.
When an atom absorbs a photon from a laser beam that is not an infinite plane wave, the atom's recoil is less than variant Planck's k in the propagation direction. We show that the recoils in the transverse directions produce a lensing of the atomic wave functions, which leads to a frequency shift that is not discrete but varies linearly with the field amplitude and strongly depends on the atomic state detection. The same lensing effect is also important for microwave atomic clocks. The frequency shifts are of the order of the naive recoil shift for the transverse wave vector of the photons.
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.
A systematic shift of the photon recoil momentum due to the index of refraction of a dilute gas of atoms has been observed. The recoil frequency was determined with a two-pulse light grating interferometer using near-resonant laser light. The results show that the recoil momentum of atoms caused by the absorption of a photon is n variant Planck's k, where n is the index of refraction of the gas and k is the vacuum wave vector of the photon. This systematic effect must be accounted for in high-precision atom interferometry with light gratings.
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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.
Light carries momentum which induces on atoms a recoil for each photon absorbed. In vacuum, for a monochromatic beam of frequency ν, the global momentum per photon is bounded by general principles and is smaller than hν/c leading to a limit on the recoil. However, locally this limit can be broken. In this Letter, we give a general formula to calculate the recoil in vacuum. We show that in a laser beam with a distorted optical field, there are regions where the recoil can be higher than this limit. Using atoms placed in those regions we are able to measure directly the extra recoil.