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Physical Review A

σ+ - σ− laser-cooling configuration with broadband laser fields: Instability at zero velocity

A. S. Parkins, P. Zoller

Published May 1, 1992• 2 citations
Publisher

Abstract

We investigate theoretically laser cooling with broadband ${\mathrm{\ensuremath{\sigma}}}_{+\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{\sigma}}}_{\mathrm{\ensuremath{-}}}$ lasers acting on J=0\ensuremath{\rightarrow}J=1 and J=1\ensuremath{\rightarrow}J=2 transitions. For cross-correlated laser fluctuations an instability in the friction force at zero velocity is predicted for red laser detunings. The dependence of this instability on the cross-correlation and spectral line shape is investigated.

DOI
10.1103/physreva.45.r6161

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We investigate theoretically laser cooling with broadband {\mathrm{\ensuremath{\sigma}}}_{+\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{\sigma}}}_{\mathrm{\ensuremath{-}}} lasers acting on J=0\ensuremath{\rightarrow}J=1 and J=1\ensuremath{\rightarrow}J=2 transitions. For cross-correlated laser fluctuations an instability in the friction force at zero velocity is predicted for red laser detunings. The dependence of this instability on the cross-correlation and spectral line shape is investigated.
We describe a theoretical approach to laser cooling with broadband real Gaussian laser fields that is based on adiabatic elimination methods and the Fokker-Planck equation for the Wigner function. This approach is used to model the recent broadband cooling experiment of Zhu, Oates, and Hall [Phys. Rev. Lett. 67, 46 (1991)] and gives correct order-of-magnitude results. The theory is then applied to J=0\ensuremath{\rightarrow}J=1 and J=1\ensuremath{\rightarrow}J=2 transitions in a ${\mathrm{\ensuremath{\sigma}}}_{+\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{\sigma}}}_{\mathrm{\ensuremath{-}}}$ optical molasses configuration with correlated broadband laser fields. An instability in the cooling scheme at zero velocity is found for red laser detunings, and sub-Doppler-width velocity distributions are predicted for J=1\ensuremath{\rightarrow}J=2 transitions with both red and blue laser detunings.
A new method is proposed for laser cooling atoms with Doppler shifts an order of magnitude larger than the homogeneous linewidth of the atomic transition. Two traveling waves cross at a small angle and form standing waves whose wavelength is much longer than that of either traveling wave. This allows one to extend the region in which the laser cooling force is proportional to velocity. The resulting broadband stimulated cooling forces are predicted to stop 0.1% of the flux of a 500-K atomic sodium beam in a distance of 300 μm and a time of a few microseconds. This is more than 100 times faster than current methods. Numerical integration and the method of Gordon and Ashkin have been used to calculate the cooling forces which result when two traveling waves cross at an angle 2a. The stimulated cooling forces are reduced in intensity by sin2a but are proportional to velocity over an interval which is larger by 1/sin a. This allows one to stop a substantial fraction of an atomic beam without chirping the laser or Zeeman tuning the atoms.
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.
In the process of cooling and trapping neutral atoms, the authors investigate a new laser configuration, which consists of two counterpropagating laser beams with orthogonal sigma + and sigma - polarisations. They show that such a configuration looks more promising than an ordinary standing wave (where the two counterpropagating waves have the same polarisation), and they explain this result as being due to angular momentum conservation which prevents any coherent redistribution of photons between the two waves. The authors' conclusions are based on a quantitative calculation of the various parameters (potential depth, friction coefficient, diffusion coefficient) describing the mean value and the fluctuations of the radiative forces experienced, in such a laser configuration, by an atom with a J=0 ground state and a J=1 excited state.
Laser cooling on transitions with a linewidth Γ much narrower than the recoil shift ℏk2/m is studied numerically according to a full quantum-mechanical treatment of the photon recoil. We propose and investigate a broadband spectral configuration that has the purposes of (1) shortening the long cooling time characteristic for monochromatic laser cooling on a slow transition and (2) reducing the kinetic energy of the stationary momentum distributions considerably below the one-photon recoil energy (ℏk)2/2m. The energies of the computed stationary distributions are limited only by the energy uncertainty of the narrow transition ℏΓ ≪ (ℏk)2/2m. Applications to laser cooling of alkaline earths on the narrow intercombination lines are discussed.
We explore, theoretically and experimentally, a method for cooling a broadband heat reservoir, via its laser-assisted collisions with two-level atoms followed by their fluorescence. This method is shown to be advantageous compared to existing laser-cooling methods in terms of its cooling efficiency, the lowest attainable temperature for broadband baths, and its versatility: it can cool down any heat reservoir, provided the laser is red detuned from the atomic resonance. It is applicable to cooling down both dense gaseous and condensed media.