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Physical Review A

Magnetic inhibition of polarization-gradient laser cooling in σ+ - σ− optical molasses

M. Walhout, Uwe Sterr, S. L. Rolston

Published Sep 1, 1996• 22 citations
Publisher

Abstract

Xenon atoms are released from a magneto-optical trap and equilibrate in a one-dimensional, ${\mathrm{\ensuremath{\sigma}}}_{+}$-${\mathrm{\ensuremath{\sigma}}}_{\mathrm{\ensuremath{-}}}$ optical molasses, along which a uniform magnetic field is applied. In the rest frame of the ``corkscrew'' pattern of laser polarization, the magnetic field induces a nonzero average atomic velocity. Introducing a moving molasses through a relative difference in the two laser-beam frequencies allows straightforward, accurate measurements of the molasses-frame velocity distribution over a large range of magnetic fields. The measurements reveal the loss of polarization-gradient cooling in fields higher than \ensuremath{\sim}0.2 mT, in quantitative agreement with theoretical predictions. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.2275

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Xenon atoms are released from a magneto-optical trap and equilibrate in a one-dimensional, \ensuremathσ+{\mathrm{\ensuremath{\sigma}}}_{+}\ensuremathσ+​-\ensuremathσ\ensuremath−{\mathrm{\ensuremath{\sigma}}}_{\mathrm{\ensuremath{-}}}\ensuremathσ\ensuremath−​ optical molasses, along which a uniform magnetic field is applied. In the rest frame of the ``corkscrew'' pattern of laser polarization, the magnetic field induces a nonzero average atomic velocity. Introducing a moving molasses through a relative difference in the two laser-beam frequencies allows straightforward, accurate measurements of the molasses-frame velocity distribution over a large range of magnetic fields. The measurements reveal the loss of polarization-gradient cooling in fields higher than \ensuremath{\sim}0.2 mT, in quantitative agreement with theoretical predictions. \textcopyright{} 1996 The American Physical Society.
The force on a multilevel atom in a 1D magneto-optical molasses with imbalanced laser intensities is theoretically investigated. The authors employ a full quantum treatment to obtain the stationary momentum distribution of the atoms, for arbitrary parameters. The force exerted the counterpropagating laser beams balances for a nonzero locking velocity. The dependence of this velocity on the intensity imbalance is found to be reduced by polarization gradient cooling. For certain values of the imbalance there are two stable velocities, and a splitting of the velocity distribution occurs. A small imbalance, or a magnetic field along the laser beams, can cause the subDoppler cooling to be lost. However, by the correct choice of parameters these effects can be made to cancel, and the sub-Doppler cooling is regained.
We investigate the effect of a longitudinal magnetic field on the orientational cooling mechanism that operates both in σ+–σ− optical molasses and in a magneto-optical trap. For an atom with different Landé g factors in its ground and excited states, single-photon scattering and stimulated Raman scattering are resonant at different field-dependent velocities. The sharp polarization-gradient feature in the force-versus-velocity curve may therefore be translated to a velocity at which the Doppler force is dominant. In addition to this, we find that the momentum diffusion coefficient can grow as the field is increased. By numerically solving a semiclassical Fokker–Planck equation, we show that these effects lead to a field-induced inhibition of efficient sub-Doppler cooling for atoms with unequal g factors. Our treatment also enables us to discuss other phenomena that are accessible only if both Doppler and polarization-gradient effects are included in the calculation.
We report a new cooling scheme used to actively collimate an atomic beam of 85Rb^{85}\mathrm{Rb}85Rb with one-dimensional optical molasses. The atoms' transverse velocity is damped by a standing wave of circularly polarized light in a magnetic field of \ensuremath{\sim}20 \ensuremath{\mu}T to 2 cm/s (rms), well below the Doppler velocity vD{v}_{D}vD​=(7\ensuremath{\Elzxh}\ensuremath{\gamma}/20M)1/2{)}^{1/2})1/2\ensuremath{\sim}10 cm/s for one-dimensional optical molasses. The minimum measured velocity is limited only by the experimental geometry. We have developed a model in which the mixing by the field and optical pumping combine to form a cycle that cools below the Doppler limit, in agreement with our measurements.
We have studied theoretically and experimentally the effect of a relatively strong magnetic field on sub-Doppler laser cooling in a one-dimensional optical molasses. We used the operator description of laser cooling with the Larmor precession frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{Z}}$ being much higher than the optical pumping rate. We found velocity-selective resonances (VSR) in the force at velocities vr{\mathit{v}}_{\mathit{r}}vr​=n${\mathrm{\ensuremath{\omega}}}_{\mathit{Z}}$, with n=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2 for both the scattering and redistribution force operators. These depend on the relative direction of the magnetic field and the polarization vectors of the light beams. Analytical results for the force on the atom are obtained in two cases that illustrate the effect of the VSR on the force. These formulas are compared with numerical calculations of the force. We also discovered a redistribution mechanism that relies on the gradient of the eigenstates of the light-shift operator, with eigenvalues that are independent of position so that a ``Sisyphus cooling'' picture does not apply. The theory is compared with many experimental results and excellent agreement is found. We believe that all essential features of laser cooling at low intensity are well described by this operator theory.
Sub-Doppler cooling has been achieved for the two closed hyperfine transitions: F = 4 → F ' = 5 and F = 3 → F ' = 2, of the cesium D 2 line. One-dimension optical molasses is experimentally investigated and compared for both j → j + 1 and j → j - 1 transitions, on different laser polarization configurations, in the presence, and absence of a static magnetic field. One remarkable point is that cooling is obtained with blue laser detuning for the j → j - 1 transition. An applied static magnetic field can also shift the sub-Doppler-cooled molasses peaks to nonzero velocities without any extra heating, for the polarization gradient configurations.
By the moving molasses technique we have extracted laser-cooled cesium atoms in a continuous way directly from an optical molasses. The mean launching velocity is precisely tunable from 1 to 12 m/s. The atomic beam has a flux of $1.3\ifmmode\times\else\texttimes\fi{}{10}^{8} \mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}/\mathrm{s}$ at 7 m/s and a longitudinal temperature of $70 \ensuremath{\mu}\mathrm{K},$ which represents the highest flux and lowest velocity spread obtained so far in a continuous beam of cold atoms. These features makes it well suited for atomic fountains. The atomic flux can be slightly increased in a two-dimensional magneto-optical trap operation (+40(+40%).(+40 A simple model accounts for the observed dependence of the flux with the magnetic-field gradient.