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Journal of Physics B Atomic Molecular and Optical Physics

Velocity distribution for laser cooled atoms in a one-dimensional sigma+- sigma-configuration

Haocheng Wu, Christopher J. Foot

Published Oct 28, 1994• 5 citations
Publisher

Abstract

We report on fully quantum calculations of the momentum distribution of atoms cooled in the sigma + - sigma - configuration. These distributions have sharp quantum features at integer multiples of the photon momentum h(cross)k, similar to those which have been observed experimentally using linearly polarized light by Doery et al (1994). They explained their observation in terms of the band structure of the atoms in the light field which is a different point of view to that which we present here.

DOI
10.1088/0953-4075/27/20/001

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 21, 1998•0 citations
We report on fully quantum calculations of the momentum distribution of atoms cooled in the sigma + - sigma - configuration. These distributions have sharp quantum features at integer multiples of the photon momentum h(cross)k, similar to those which have been observed experimentally using linearly polarized light by Doery et al (1994). They explained their observation in terms of the band structure of the atoms in the light field which is a different point of view to that which we present here.
In relation to the newly discovered laser cooling mechanisms, the authors have studied the momentum diffusion of an atom with a j (ground)-j+1 (excited) state transition (j not=0), interacting with two counterpropagating sigma +- sigma - plane waves. A correlation between successive photon absorptions via the multi-sublevel internal atomic structure leads to a large increase of the momentum diffusion coefficient. In a simple probabilistic picture this enhanced diffusion is interpreted as a random walk with effective steps much larger than the one-photon recoil momentum k. For j=1 the authors report the results of a complete calculation (i.e. with a quantum description of the internal atomic state) showing a marked dependence upon the velocity of the atom as well as on the parameters of the laser field (detuning and power).
We describe calculations that predict and analyze distinctive features in the velocity distribution in 1D laser cooling for light shift potential well depths only a few times the recoil energy. These features can be interpreted in terms of populations of energy bands or even Bloch states in the periodic potential. They occur with a ${\mathrm{\ensuremath{\sigma}}}^{+}$ standing wave, with and without a small B field, and for lin\ensuremath{\perp}lin laser cooling. We have observed these features experimentally in a beam of metastable helium atoms cooled on the 23{2}^{3}23S1{\mathit{S}}_{1}S1​\ensuremath{\leftrightarrows}23{2}^{3}23P2{\mathit{P}}_{2}P2​ transition, with velocity resolution \ensuremath{\sim}0.3 recoil.
We extend the kinetic theory of deep laser cooling of multilevel atoms by counterpropagating laser waves to a case of linearly polarized waves and compare the results with those for circularly polarized waves. Considering the excitation of a $(3+5)\ensuremath{-}\mathrm{level}$ atom by two counterpropagating waves with orthogonal linear polarizations $(\mathrm{lin}\ensuremath{\perp}\mathrm{lin}$ configuration), we show that even-order stepwise processes composed of the two-photon optical processes are responsible for narrow structures near zero velocity in the ground-state atomic coherence, atomic populations, and optical coherences. The stepwise processes composed of the two-photon structures are shown to produce velocity structures much narrower than the two-photon structures produced by a single ${\ensuremath{\sigma}}^{+}\ensuremath{-}{\ensuremath{\sigma}}^{\ensuremath{-}}$ configuration [Phys. Rev. A 60, 3148 (1999)]. A Fokker-Planck type kinetic equation is derived for a model of a $(3+5)\ensuremath{-}\mathrm{level}$ atom interacting with two linearly polarized waves in a $\mathrm{lin}\ensuremath{\perp}\mathrm{lin}$ configuration. It is found that stepwise multiphoton coherent processes enhance considerably the radiation force at low velocities and the friction produced by the force at a negative detuning. Contrary to a case of a ${\ensuremath{\sigma}}^{+}\ensuremath{-}{\ensuremath{\sigma}}^{\ensuremath{-}}$ configuration the stepwise processes are found to increase the diffusion coefficient. The stepwise even-order processes caused by two linearly polarized waves are identified as the basic physical mechanism responsible for deep laser cooling of atoms in a $\mathrm{lin}\ensuremath{\perp}\mathrm{lin}$ configuration. The temperature of laser-cooled atoms is derived for a model of a $(3+5)\ensuremath{-}\mathrm{level}$ atom excited by a $\mathrm{lin}\ensuremath{\perp}\mathrm{lin}$ configuration and found to be asymptotically close to that for a case of ${\ensuremath{\sigma}}^{+}\ensuremath{-}{\ensuremath{\sigma}}^{\ensuremath{-}}$ configuration at large detuning.
A quantum analytic treatment of the resonant scattering of atoms with jg equals j yields je equals j (j is an integer) transitions by a pulsed (sigma) + - (sigma) - field is developed. In the approximation of motionless atoms, the atomic density matrix after action of single light pulse is evaluated with exact consideration of the recoil effects. Recurrent equations, which allow to calculate the distribution after arbitrary pulse sequences are found in the analytic form. It is shown that for discrete pulse frequencies the action of N light pulses leads to the formation and narrowing of peaks in discrete points of the momentum space, and also to the broadening of the envelope of the momentum distribution. In the case of the wide (with respect to the photon momentum) initial distribution the explicit formulae for peaks and envelope are obtained and an asymptotic behavior of the solution is analyzed. In the low-intensity limit a dependence of the scattering pattern contrast on the pulse duration is studied.