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Journal of the Physical Society of Japan

Asymmetrical Recoil of an Atom with an Optical Absorption Coefficient Depending on the Incident Direction

Norio Inui

Published Jan 19, 2021• 0 citations
Publisher

Abstract

The recoil of a neutral atom irradiated by counter-propagating light with the same frequency and intensity is studied. The expectation value of the momentum transferred from the light to the atom with spherical symmetry at rest is usually zero because of symmetry. However, if the optical absorption coefficient of the atom depends on the incident light direction due to the magnetoelectric effect, as is the case in materials with nonreciprocal directional dichroism, the momentum transfer between the atom and photons depends on the incident direction. This allows even a standing electromagnetic wave to break the symmetry of the recoil of an atom.

DOI
10.7566/jpsj.90.024706

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The recoil of a neutral atom irradiated by counter-propagating light with the same frequency and intensity is studied. The expectation value of the momentum transferred from the light to the atom with spherical symmetry at rest is usually zero because of symmetry. However, if the optical absorption coefficient of the atom depends on the incident light direction due to the magnetoelectric effect, as is the case in materials with nonreciprocal directional dichroism, the momentum transfer between the atom and photons depends on the incident direction. This allows even a standing electromagnetic wave to break the symmetry of the recoil of an atom.
A method of calculation of the absorption coefficient in the terms of quantum optics with regard for the quantization of the electromagnetic field and the Doppler effect is presented. It is shown that the local value of the absorption coefficient non-linearly depends on the atomic density and initial intensity. The analytically derived results are demonstrated in graphs for the the local absorption coefficient as a function of the frequency. The relatively strong dependence of the absorptance on the path length of an optical light beam is caused by the interatomic coupling through the intermediary of an electromagnetic field. The splitting of the absorption line induced by the Doppler effect in the system placed between mirrors is demonstrated.
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.
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.
In our recent research1, it was suggested that counter-propagating laser beams in a Kerr-nonlinear medium can induce intensity-dependent nonreciprocity which consists in different changes of refractive indecies for both of the waves. Under some conditions, this can result in such directionally asymmetrical effects as (i) directional bistability in a nonlinear ring resonator which allows one to switch the direction of propagation of a dominant mode and (ii) enhancement of the Sagnac effect in a rotating ring resonator.
The stationary momentum and coordinate distributions of two-level atoms in the field of a one-dimensional standing light wave have been studied. A qualitatively new effect—the predominant concentration of atoms outside of the minima of the optical potential—has been detected in the regime of moderate saturation of an atomic transition and red frequency detuning. This effect has been qualitatively interpreted. Calculations have been performed using the quantum kinetic equation for the atomic density matrix with the complete inclusion of recoil and localization effects in an arbitrary-intensity light field. In addition to theoretical significance, the results can be useful for atomic nanolithography and frequency standards based on optical gratings.
We consider an atomic beam at normal incidence with a standing wave of light with phase fluctuations and we evaluate the momentum distribution of the diffracted atoms after passing through the light beam. We consider the independent-increment model or the random-jump model for the phase of the light, and the random-jump model for the light frequency. In each of these three cases we distinguish the situation of independent or identical phases of the two counter-running light waves that compose the standing wave. For identical phases, the momentum distribution seems to be sensitive mainly to the spectrum of the light, whereas for independent phases higher correlation functions are also important.