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Journal of Physics B Atomic and Molecular Physics

The role of the Doppler effect in the radiative interaction of atoms

J. Cooper, Derek N. Stacey

Published Nov 11, 1974• 14 citations
Publisher

Abstract

The Doppler effect reduces the radiative interaction between identical atoms so that only those for which k. Delta v <or approximately= pi Gamma can couple coherently (where Delta v is the relative velocity, k=2 pi / lambda and Gamma is the lifetime of the isolated atom). The authors conclude that this coherent interaction cannot explain the 'extrapolation anomaly' of resonance broadening.

DOI
10.1088/0022-3700/7/16/013

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The Doppler effect reduces the radiative interaction between identical atoms so that only those for which k. Delta v <or approximately= pi Gamma can couple coherently (where Delta v is the relative velocity, k=2 pi / lambda and Gamma is the lifetime of the isolated atom). The authors conclude that this coherent interaction cannot explain the 'extrapolation anomaly' of resonance broadening.
It is shown that the dispersion dependence of the rotation of the plane of polarisation of weak radiation passing through a three-level atomic medium may be free of Doppler broadening, on the account of a velocity-dependent Stark-shift which is created by saturating the wave on an adjacent transition. In the case of two-photon resonance the use of opposing light beams with different frequencies gives the possibility for an essential increase of the signal on account of the resonance gain on an intermediate transition, without additional Doppler broadening.
The emission spectrum is calculated for a system of two identical atoms, having relative coordinate r. Initially one atom is in an excited state and the other in its ground state. Both atom and field variables are fully quantized, so that the calculation automatically includes effects related to both retardation and atomic recoil on the absorption or emission of radiation. It is shown that for k0{\mathrm{k}}_{0}k0​r\ensuremath{\gg}:1 (where k0{\mathrm{k}}_{0}k0​=2\ensuremath{\pi}/\ensuremath{\lambda} and \ensuremath{\lambda} is the wavelength associated with the resonant excited- to ground-state transition), the emission spectrum can consist of a triplet. The frequency separation between the components of the triplet can be interpreted in terms of the recoil the atoms undergo individually on emitting or absorbing radiation. For k0{\mathrm{k}}_{0}k0​r\ensuremath{\ll}1, the atoms emit as a composite system and the recoil (while not resolvable) is that associated with a ``molecule'' of mass 2m, where m is the mass of one of the atoms.
The Doppler effect is one of the dominant broadening mechanisms in thermal vapor spectroscopy. For two-photon transitions one would naively expect the Doppler effect to cause a residual broadening, proportional to the wave-vector difference. In coherent population trapping (CPT), which is a two-photon narrow-band phenomenon, such broadening was not observed experimentally. This has been commonly attributed to frequent velocity-changing collisions, known to narrow Doppler-broadened one-photon absorption lines (Dicke narrowing). Here we show theoretically that such a narrowing mechanism indeed exists for CPT resonances. The narrowing factor is the ratio between the atom's mean free path and the wavelength associated with the wave-vector difference of the two radiation fields. A possible experiment to verify the theory is suggested.