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Local photon momentum in an arbitrary monochromatic optical field

Jun Sun, Yong-Nan Sun

Published Nov 16, 2018• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
Abstract. In this paper we present a theory which shows that the optical force on atoms due to spontaneous processes depends upon the quantum state of the atom at the time it begins interacting with the optical field. The momentum is treated as a classical variable and the theory used to model the interaction between the atom and radiation is based on a quantum electrodynamic technique. The formalism developed is quite general and, in principle, can be applied to the determination of initial atomic states prepared by a variety of mechanisms. An example of an application of the spontaneous force is presented which shows how it is possible to use the momentum absorbed by an atom from a coherent light field to determine the density matrix of the atomic state created by a collision process. For completeness, the derivation of a stimulated force model is included where it is shown that the resulting force on atoms also depends on their initial state. 1.
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.