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Laser Cooling of Neutral Atoms.

Matthew G. McHarg

Published Dec 1, 1983• 0 citations
OpenAlex

Abstract

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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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.
Atomic beam deceleration and cooling by frequency sweep techniques is analysed by means of a Fokker-Planck equation (FPE) with time dependent drift and diffusion coefficients. The effect of compression of the velocity distribution is discussed with respect to theoretical and experimental limitations of atomic beam cooling imposed by the photon recoil. The cooling limit derived from the linear approximation of the FPE fails, if the broadening of the cooled velocity distribution peak by diffusion causes the loss of atoms from the resonant velocity range. This phenomenon is studied by numerical solutions of the FPE. The occurrence of higher final temperatures in previous Monte-Carlo calculations and in experiments is discussed. The anomalous diffusion coefficient caused by the antibunching of the scattered photons is taken into account. The possibility of transverse compression of the atomic beam is investigated by means of a reduced FPE for the transverse degrees of freedom.
In the limit of asymptotically small photon momentum, a Fokker–Planck equation for the center-of-mass Wigner function suffices to describe laser cooling of an atom. We have devised a procedure to compute the light pressure force and the diffusion tensor for an atom with an arbitrary level structure, traveling with an arbitrary velocity in any given three-dimensional light field. The scheme is based on solving a set of differential equations closely related to the density matrix equations of motion encountered in conventional recoilless laser spectroscopy. Computer programs have been written that automatically construct and solve the required equations from broad specifications of the problem, such as energies and angular momenta of the atomic levels. A Langevin equation stochastic simulation has been implemented to solve the Fokker-Planck equation of laser cooling using the computed force and diffusion. Comparisons of optical-molasses experiments and simulations carried out for a model sodium atom with a J = 2→J = 3 transition show qualitative similarities such as sub-Doppler limit temperatures, but the quantitative agreement of theory and experiment is not satisfactory.
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.
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
We present a theoretical model for the interaction of a beam of two-level atoms with a resonant laser beam. It is shown that the radiation force, while averaging to zero at resonance, produces a transverse spread of the atomic velocities. If radiative damping is ignored, this spread increases linearly with time and finally saturates towards a steady value. Although the spread has a quantum-mechanical origin, we show that it is possible, in the limit $\ensuremath{\hbar}k\ensuremath{\rightarrow}0$, to describe the phenomenon in terms of differential equations of motion for the atomic translational variables, as in the classical case. In this model it is also possible to describe the effects of radiative damping, as well as other additional effects, which may occur in a real experiment. Finally a comparison of our results with experimental data, recently obtained on an Na atomic beam, has been made. Although an order-of-magnitude fit of the experimental data could be obtained, the weights of the different causes, reducing the spread, were found to be ambiguous and have been left partly open.