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Journal of Experimental and Theoretical Physics Letters

Motion of an atom due to anisotropic filtering of its resonance fluorescence

L. V. Il’ichev

Published Jan 1, 2009• 0 citations
Publisher

Abstract

The effect of the specific anisotropy of the environment on the dynamics of a resonantly fluorescing atom is analyzed in a one-dimensional model. The environmental anisotropy, which is manifested as different spectral selectivities of the absorption of spontaneous photons emitted by the atom in different directions, results in the anisotropy of the photon emission rate giving rise to a nonzero recoil force on the atom. The effect under optimal conditions can reach one-quarter of the recoil momentum per single photon emission. This force is directed toward the weaker spectral selectivity.

DOI
10.1134/s0021364008210054

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The effect of the specific anisotropy of the environment on the dynamics of a resonantly fluorescing atom is analyzed in a one-dimensional model. The environmental anisotropy, which is manifested as different spectral selectivities of the absorption of spontaneous photons emitted by the atom in different directions, results in the anisotropy of the photon emission rate giving rise to a nonzero recoil force on the atom. The effect under optimal conditions can reach one-quarter of the recoil momentum per single photon emission. This force is directed toward the weaker spectral selectivity.
It is shown that spectral filtration of a significant fraction of radiation of a resonantly fluorescing atom changes its kinetics. The effect of a spectral observation event on the behavior of an atom is demonstrated by two examples: localization of an atom at its flight through a region occupied by a standing light wave and translatory dynamics of an atom at its motion along a standing light wave. In the first case, localization probabilities are calculated in the absence of spontaneous emission events and for one photoemission event. The arising distribution over the atomic momentum, which is sensitive to spectral filtration, is also calculated for one photoemission event. In the second example, it is shown that spectral filtration of spontaneous emission leads to the occurrence of an anomalous additive to the force acting on an atom in the standing-wave field.
The recoil effects of spontaneous photon emissions during optical pumping of a trapped three-level atom are exactly calculated. Without resort to the Lamb-Dicke approximation, and considering arbitrary detuning and saturation of the pump laser, the density of recoil shifts in phase space is derived. It is shown that this density is not of Gaussian shape, and that it becomes isotropic in phase space only for a branching ratio corresponding to fluorescence scattering but unfavorable for optical pumping. The dependence of its anisotropy on the laser saturation is discussed in the resonant case, and the mapping of moments of the atom's center-of-mass motion due to the pumping is presented. Moreover, it is shown how optimum parameters for protecting the center-of-mass quantum state from pump-induced disturbance depend on the specific property to be protected.
The resonance fluorescence of a crystalline solid consisting of two-level atoms is studied. The method of Heitler and Ma (1949) is used to solve the equations. From the calculated result, it is found that the probability of emission of photons is discrete in angular and in wavelength distributions. The emission line in the incident direction is identical in shape with the absorption line. While there is no actual trapping of radiation, the effect of photon-trapping manifests itself in both the emission and the absorption spectra.
This paper discusses the connection between the atomic-momentum distribution due to photon recoil and photon statistics. A new formulation is presented based on a Fourier transform with respect to momentum. The asymptotic approximation that is equivalent to a Fokker-Planck treatment is found. Resonance fluorescence is treated in detail. The anomalous diffusion contribution recently found by Ashkin, Gordon, and Cook is separated, and its physical significance is discussed. In particular, it is pointed out that it signifies the coherence between successive photon recoil events. It follows that to obtain the correct diffusion expression one must perform the adiabatic elimination of internal atomic degrees of freedom in the frame moving with the atom, including the deflection caused by light-pressure force. Connections to earlier work are discussed.
It is shown that the distribution of the momentum transfer to an atom in resonance fluorescence may be easily derived from the angular distribution of spontaneously emitted photons. Some general properties of the momentum distribution are found, and explicit forms of the distribution are derived for several special cases. It is shown that the distribution tends to become Gaussian after a large number n of spontaneous photon emissions, with variance proportional to n, but it is already close to the asymptotic form when n=3. When the appropriate averaging is performed to allow for the velocity spread of the atoms, the derived distributions account for the results of atomic beam deflection measurements, but much of the information about the original distributions is thereby lost. In a standing wave field both stimulated and spontaneous emissions contribute to the atomic momentum, in such a way that the variance of the momentum spread is again proportional to the number n of photon emissions.