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Soviet Journal of Quantum Electronics

Theory of a radiative atomic trap

Vladimir G. Minogin

Published Mar 31, 1982• 9 citations
Publisher

Abstract

A theory of atomic motion in arbitrary resonant laser fields is put forward. It is shown that when the natural line width of an atomic transition is greater than the recoil energy, the microscopic equations for the atomic density matrix can be reduced to the Fokker–Planck equation for the atomic distribution function and, in the case of slow atoms, the latter can be reduced to the Smoluchowski equation for the atomic density. The macroscopic Smoluchowski equation is used to find laser field configurations which ensure stable trapping of atoms. An extremely simple radiative atomic trap is described and its main parameters are given.

DOI
10.1070/qe1982v012n03abeh012095

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A theory of atomic motion in arbitrary resonant laser fields is put forward. It is shown that when the natural line width of an atomic transition is greater than the recoil energy, the microscopic equations for the atomic density matrix can be reduced to the Fokker–Planck equation for the atomic distribution function and, in the case of slow atoms, the latter can be reduced to the Smoluchowski equation for the atomic density. The macroscopic Smoluchowski equation is used to find laser field configurations which ensure stable trapping of atoms. An extremely simple radiative atomic trap is described and its main parameters are given.
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We have derived reduced-density-matrix equations of motion for a pair of two identical atoms moving in the radiation field as the first step in establishing a theory of collisional redistribution of light from neutral-atom traps. We use the Zwanzig projection-operator technique to average over spontaneous field modes and establish the conditions under which Born and Markov approximations can be applied to the system of moving atoms. It follows from these considerations that when these conditions hold, the reduced-density-matrix equation for moving atoms has the same form as that for the stationary case: time dependence is introduced into the decay rates and interaction potentials by making the substitution R=R(t).
The quantum kinetic equation describing slow atomic motion in laser light is derived by an operational method which provides mathematical expressions with a transparent physical structure. The authors prove in a general way that the coefficients appearing in this equation, which is of a Fokker-Planck type, are simply related to the mean value and to the correlation functions of the Heisenberg radiative force of the semiclassical approach, where the atomic position is treated classically. They derive in particular a new theoretical expression for the damping force responsible for radiative cooling and they interpret it in terms of linear response theory. The authors also obtain a new crossed r-p derivative term, which does not appear in semiclassical treatments, but which they find to be very small in most situations. Finally, all the theoretical expressions derived are valid for any J g to J e transitions and are not restricted to two-level atoms.
The theory of the resonance radiation force is studied as it applies to the slowing of a two-level atom using a swept frequency laser. The theory is developed in detail for this case. A single partial differential equation called the Fokker-Planck equation is found to describe the atomic motion for many cases. This equation is solved numerically for a one dimensional geometry. Results from this numerical solution are found to be within 10% of experimental results. Analysis of this problem in one dimension leads to the prediction that for fixed amounts of frequency sweeping, a faster scan rate will yield smaller full width at half maximum (FWHM) spread in the velocity distribution for the atomic beam. This program also predicts that the atoms can be slowed arbitrarily close to 0 m/sec using this technique. The program used for this analysis is included. Keywords: Resonance radiation force; Slowing an atomic beam; Laser cooling of atoms; Fokker Planck equation; Thesis.
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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