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arXiv:1107.2313 · Physical Review Letters

Doppler Cooling to the Quantum Limit

Maryvonne Chalony, Anders Kastberg, Bruce G. Klappauf, David Wilkowski

Published Dec 7, 2011• 32 citations
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Abstract

Doppler cooling on a narrow transition is limited by the noise of single scattering events. It shows novel features, which are in sharp contrast with cooling on a broad transition, such as a non-gaussian momentum distribution, and divergence of its mean square value close to the resonance. We have observed those features using 1D cooling on an intercombination transition in strontium, and compared the measurements with theoretical predictions and Monte Carlo simulations. We also find that for very a narrow transition, cooling can be improved using a dipole trap, where the clock shift is canceled.

DOI
10.1103/physrevlett.107.243002

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Doppler cooling on a narrow transition is limited by the noise of single scattering events. It shows novel features, which are in sharp contrast with cooling on a broad transition, such as a non-gaussian momentum distribution, and divergence of its mean square value close to the resonance. We have observed those features using 1D cooling on an intercombination transition in strontium, and compared the measurements with theoretical predictions and Monte Carlo simulations. We also find that for very a narrow transition, cooling can be improved using a dipole trap, where the clock shift is canceled.
We present a quantum theory of one-dimensional laser cooling of free atoms using a transition with a J = 0 ground state and a J = 1 excited state. This treatment is valid both for broad lines (recoil energy small compared with the energy width ℏ Γ of the excited level) and for narrow lines. For broad lines we recover the well-known cooling limit for a two-level transition (∼ℏΓ/2), whereas for a narrow line the cooling limit is found to be of the order of the recoil energy. The stationary momentum distribution is obtained for both cases and is found to be close to the one obtained by Monte Carlo simulations.
Ultracold atoms at temperatures close to the recoil limit have been achieved by extending Doppler cooling to forbidden transitions. A cloud of (40)Ca atoms has been cooled and trapped to a temperature as low as 6 microK by operating a magnetooptical trap on the spin-forbidden intercombination transition. Quenching the long-lived excited state with an additional laser enhanced the scattering rate by a factor of 15, while a high selectivity in velocity was preserved. With this method, more than 10% of precooled atoms from a standard magnetooptical trap have been transferred to the ultracold trap. Monte Carlo simulations of the cooling process are in good agreement with the experiments.
We develop an analytical approach to Doppler cooling of atoms by one- or two-photon transitions when the natural width of the excited level is so small that the process leads to a Doppler temperature comparable with the recoil temperature. In such a limit the usual Fokker–Planck equation for Doppler cooling does not correctly describe the cooling process. We propose a generalization of the Fokker–Planck approach and derive a new model that is able to reproduce the numerical results correctly, even very close to the recoil limit. Two cases of practical interest, one-photon Doppler cooling of strontium and two-photon Doppler cooling of hydrogen, are considered. We also treat the possibility of adding a controlled quenching of the sharp line to optimize the cooling process.
Doppler cooling of calcium ions has been experimentally demonstrated using the ${S}_{1∕2}\ensuremath{\rightarrow}{D}_{5∕2}$ dipole-forbidden transition. Scattering forces and fluorescence levels a factor of 5 smaller than for the usual Doppler cooling on the dipole-allowed ${S}_{1∕2}\ensuremath{\rightarrow}{P}_{1∕2}$ transition have been achieved. Since the light scattered from the ions can be monitored at (violet) wavelengths that are very different from the excitation wavelengths, single ions can be detected with an essentially zero background level. This, as well as other features of the cooling scheme, can be extremely valuable for ion-trap-based quantum-information processing.