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Quantum Electronics and Laser Science Conference

FPE approach to sub-Doppler cooling and atomic grating formation: analytical and numerical results

A. V. Bezverbnyĭ

Published Jun 25, 2003• 0 citations
Publisher

Abstract

Summary form only given. Kinetics of light-induced sub-Doppler cooling and spatial grating formation has been considered for atomic ensembles with dipole transitions in light spatial configurations, formed by coherent monochromatic non-collinear light beams with frequency /spl omega/. Consideration is based on a closed Fokker-Planck equation (FPE).

DOI
10.1109/qels.2002.1031151

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Summary form only given. Kinetics of light-induced sub-Doppler cooling and spatial grating formation has been considered for atomic ensembles with dipole transitions in light spatial configurations, formed by coherent monochromatic non-collinear light beams with frequency /spl omega/. Consideration is based on a closed Fokker-Planck equation (FPE).
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.
A realistic model of the dipole radiation forces in transverse Doppler cooling (with a s+-s- laser configuration) of an atomic beam of group 13 elements is studied within the quantum-kinetic equation framework. The full energy level sub-structure for such an atom with I = 0 (such as 66Ga) is analysed. Two cooling strategies are investigated; the first involving the 2P3/2 ? 2D5/2 transition and the second a dual laser cooling experiment involving transitions 2P1/2 and 2P3/2 ? 2S1/2. The latter scheme creates a velocity-independent dark-state resonance that inhibits a steady-state dipole cooling force. However, time-dependent calculations show that transient cooling forces are present that could be exploited for laser cooling purposes in pulsed laser fields.
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.
Laser cooling dynamics of neutral atoms with a closed optical transition Jg → Je in light fields with nonuniform polarization formed by counterpropagating waves with linear, circular or elliptical polarization was considered. For the case of finite interaction time of atoms with light field both mechanisms of Doppler and Sub-Doppler laser cooling affected on atoms in ensemble having different velocities were taken into account. We get qualitative relations on a base of numerical analysis in a frame of quasiclassical treatment of laser cooling. These relations allow to define optimal parameters of cooling waves, i.e. polarization, detuning from atomic resonance and intensity of light waves for the most rapid and dip laser cooling from initially wide momentum distribution for finite interaction time of atoms with laser field
We perform detailed analysis of sub-Doppler cooling limits for various atoms by direct solving quantum kinetic equation for atom density matrix in standing-wave light field generated by counterpropagating waves. It was demonstrated that the polarization gradient cooling effects are sensitive to atom recoil parameter (the ratio of recoil energy to natural linewidth) that results to limitation of sub-Doppler cooling and allows to outline the limits of well-known sub-Doppler cooling theory. We also give a comparison the cooling limits for well-known σ+−σ−σ_+-σ_-σ+​−σ−​ and lin⊥linlin\perp linlin⊥lin configurations.