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Atomic motion in a high-intensity standing wave laser field

L.F. Saez Ramdohr

Published Jan 1, 1987• 0 citations
OpenAlex

Abstract

This work discusses the effect of a high-intensity standing wave laser field on the motion of neutral atoms moving with a relatively high velocity. The analysis involves a detailed calculation of the force acting on the atoms and the calculation of the diffusion tensor associated with the fluctuations of the quantum force operator. The high-intensity laser field limit corresponds to a Rabi frequency much greater than the natural rate of the atom. The general results are valid for any atomic velocity. Results are then specialized to the case of slow and fast atoms where the Doppler shift of the laser frequency due to the atomic motion is either smaller or larger than the natural decay rate of the atom. The results obtained for the force and diffusion tensor are applied to a particular ideal experiment that studies the evolution of a fast atomic beam crossing a high-intensity laser beam. The theories developed previously, for a similar laser configuration, discuss only the low atomic velocities case and not the more realistic case of fast atoms. Here, an approximate solution of the equation for the distribution is obtained. Starting from the approximate distribution function, the deflection angle and dispersion angle for themore » atomic beam with respect to the free motion are calculated.« less

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Journal of the Optical Society of America B•Nov 1, 1985•528 citations
This work discusses the effect of a high-intensity standing wave laser field on the motion of neutral atoms moving with a relatively high velocity. The analysis involves a detailed calculation of the force acting on the atoms and the calculation of the diffusion tensor associated with the fluctuations of the quantum force operator. The high-intensity laser field limit corresponds to a Rabi frequency much greater than the natural rate of the atom. The general results are valid for any atomic velocity. Results are then specialized to the case of slow and fast atoms where the Doppler shift of the laser frequency due to the atomic motion is either smaller or larger than the natural decay rate of the atom. The results obtained for the force and diffusion tensor are applied to a particular ideal experiment that studies the evolution of a fast atomic beam crossing a high-intensity laser beam. The theories developed previously, for a similar laser configuration, discuss only the low atomic velocities case and not the more realistic case of fast atoms. Here, an approximate solution of the equation for the distribution is obtained. Starting from the approximate distribution function, the deflection angle and dispersion angle for themore » atomic beam with respect to the free motion are calculated.« less
A previous calculation of forces on atoms in external (dc) fields and in homogeneous traveling-wave laser fields is modified for the case of a standing-wave laser field. The case of intense laser fields, where the Rabi frequency is much greater than the natural decay rate of the atom, is described. A general result for any Doppler shift of the laser frequency due to the atomic motion is obtained. It is specialized to the two cases in which this shift is either much smaller or larger than the natural decay rate. In the first case, we get the same result as that of a previous calculation. The second case has not been discussed previously.
The dressed atom approach is used to investigate the evolution of atoms moving in an intense standing wave laser field. When coherences between the dressed states can be neglected, a simple expression is obtained for the radiative force acting on the atoms. The Landau-Zener model, well-known in the theory of slow atomic collisions, is here used to include coherences in an analytic treatment. At high velocities, where the simplest approach breaks down, the results are in good agreement with exact numerical calculations. Applications outside the field of laser cooling are discussed.
The momentum diffusion coefficient, as a function of position and velocity, is discussed for two-state atoms travelling through a standing-wave laser field. Equations leading to the force and diffusion coefficient have been obtained by Minogin. The authors present an alternative derivation, based on moments of the Wigner function and give numerical solutions in terms of matrix continued fractions. In strong fields, the discussion is supplemented by a derivation of the diffusion coefficient within the dressed-atom basis, and a picture of the diffusion mechanism emerges which is quite different from the one at low intensities. Calculated forces and diffusion coefficients are used in a Fokker-Planck equation to obtain stationary atomic velocity distributions.
It is conventional to describe the motion of an atom in a laser field (and other D.C fields) by a Fokker-Planck equation which is characterized by a force and a diffusion coefficient. Gordon and Ashkin have obtained a result for the diffusion coefficient in a spherically symmetric approximation. We have recently treated it as a second order tensor and have gotten a different result. The tensor has three terms. The leading term arises from the recoil of the atom during fluorescence, the second comes from gradients of the laser intensity and the D.C. fields and the last comes from a combination of the recoil term and gradients. The trace of our leading term agrees with the result of Gordon and Ashkin but there is no agreement at all with the other terms. The calculation was performed for a traveling wave laser and is being extended now to a standing wave laser by a graduate student. The experiment being undertaken here will use a swept laser frequency to compensate for the change in resonance frequency (due to the Doppler effect) of the atom as it slows down.
A semiclassical model of the force and momentum diffusion on a point particle is used to describe the motion of a two-level atom strongly coupled to a single Gaussian cavity mode. The effects of the momentum diffusion on the motion of an atom in a cavity are investigated in a regime similar to that of the experiment performed by Mabuchi et al. [Opt. Lett. 21, 1393 (1996)]. It is found that a slow atom quickly develops significant velocities along the cavity axis. The limited bandwidth in the experiment of Mabuchi et al. means that the full intensity signal due to atomic motion in the standing wave is filtered leading to the apparently smaller velocities observed. It is shown that a negative detuning of the laser and cavity from the atomic resonance would lead to nonzero dipole forces and significantly reduced velocities along the standing wave. An analysis of the intensity signal with a larger bandwidth is proposed, which would track the velocity of the atom along the cavity axis. These results are compared with a Monte Carlo wave-function simulation similar to that used to treat Doppler cooling.
We show that the dressed-atom approach provides a quantitative understanding of the main features of radiative dipole forces (mean value, fluctuations, velocity dependence) in the high-intensity limit where perturbative treatments are no longer valid. In an inhomogeneous laser beam, the energies of the dressed states vary in space, and this gives rise to dressed-state-dependent forces. Spontaneous transitions between dressed states lead to a multivalued instantaneous force fluctuating around a mean value. The velocity dependence of the mean force is related to the modification, induced by the atomic motion, of the population balance between the different dressed states. The corresponding modification of the atomic energy is associated with a change of the fluorescence spectrum emitted by the atom. The particular case of atomic motion in a standing wave is investigated, and two regimes are identified in which the mean dipole force averaged over a wavelength exhibits a simple velocity dependence. The large values of this force achievable with reasonable laser powers are pointed out with view to slowing down atoms with dipole