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arXiv:physics/0010024 · Physical Review A

Continuous-wave Doppler cooling of hydrogen atoms with two-photon transitions

Véronique Zehnlé, Jean Claude Garreau

Published Jan 17, 2001• 17 citations
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Abstract

We propose and analyze the possibility of performing two-photon continuous-wave Doppler cooling of hydrogen atoms using the $1S\ensuremath{-}2S$ transition. ``Quenching'' of the $2S$ level (by coupling with the $2P$ state) is used to increase the cycling frequency, and to control the equilibrium temperature. Theoretical and numerical studies of the heating effect due to Doppler-free two-photon transitions evidence an increase of the temperature by a factor of 2. The equilibrium temperature decreases with the effective (quenching-dependent) width of the excited state and can thus be adjusted up to values close to the recoil temperature.

DOI
10.1103/physreva.63.021402

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We propose and analyze the possibility of performing two-photon continuous-wave Doppler cooling of hydrogen atoms using the 1S\ensuremath−2S1S\ensuremath{-}2S1S\ensuremath−2S transition. ``Quenching'' of the 2S2S2S level (by coupling with the 2P2P2P state) is used to increase the cycling frequency, and to control the equilibrium temperature. Theoretical and numerical studies of the heating effect due to Doppler-free two-photon transitions evidence an increase of the temperature by a factor of 2. The equilibrium temperature decreases with the effective (quenching-dependent) width of the excited state and can thus be adjusted up to values close to the recoil temperature.
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.
A two-photon mechanism for cooling atoms below the Doppler temperature is analyzed. We consider the magnesium ladder system $(3{s}^{2})^{1}S_{0}\ensuremath{\rightarrow}(3s3p)^{1}P_{1}$ at 285.2nm285.2\phantom{\rule{0.3em}{0ex}}\mathrm{nm}285.2nm followed by the $(3s3p)^{1}P_{1}\ensuremath{\rightarrow}(3s3d)^{1}D_{2}$ transition at 880.7nm880.7\phantom{\rule{0.3em}{0ex}}\mathrm{nm}880.7nm. For the ladder system quantum coherence effects may become important. Combined with the basic two-level Doppler cooling process this allows for reduction of the atomic sample temperature by more than a factor of 10 over a broad frequency range. First experimental evidence for the two-photon cooling process is presented and compared to model calculations. Agreement between theory and experiment is excellent. In addition, by properly choosing the Rabi frequencies of the two optical transitions a velocity independent atomic dark state is observed.
A new possibility of laser cooling of Calcium atoms using a two-photon transition is analyzed We investigate the possibility of Doppler cooling of Calcium using its two-photon (4s 2 ) 1 S0 - (4s5s) 1 S0 transition, with excitation in near resonance with the (4s4p) 1 P1 level. The two-photon absorption of l aser beams at 423 and 1 034 nm greatly increases the two-photon rate, allowing an effective transfer of momentum. The ex perimental i mplementation o f t his technique is discussed a nd we show that two-photon cooling can be used to achieve a temperature limit of about 1/7 of the onephoton Doppler limit reached in a conventional MOT.
We report on laser cooling of neutral rubidium atoms by using a single mode of a frequency comb. Cooling is achieved on a dipole-allowed transition at 780 nm in a one-dimensional retro-reflected beam geometry. Temperatures are measured using standard time-of-flight imaging. We show the dependence of the temperature on the cooling time, intensity and detuning of the frequency comb. The lowest temperature achieved is approximately equal to the Doppler temperature and is limited by the intensity of the comb mode driving the cooling transition. Additionally, we verify the analogy between frequency comb and continuous-wave laser cooling. Our work is a step towards laser cooling of atoms with strong cycling transitions in the vacuum ultraviolet, such as hydrogen, deuterium and antihydrogen, where generation of continuous-wave laser light is limited by current laser technology. Achieving efficient cooling at these wavelengths would significantly improve the precision of optical frequency standards, enable measurements of fundamental constants with unprecedented accuracy, improve tests of charge, parity, and time reversal symmetry, and open the way to achieving quantum degeneracy width new atomic species.
The possibility of laser cooling of alkaline-earth-metal atoms and ytterbium atoms using a two-photon transition is analyzed. We consider a ${}^{1}{S}_{0}{\ensuremath{-}}^{1}{S}_{0}$ transition with excitation in near resonance with the 1P1{}^{1}{P}_{1}1P1​ level. This greatly increases the two-photon transition rate, allowing an effective transfer of momentum. The experimental implementation of this technique is discussed and we show that for calcium, for example, two-photon cooling can be used to achieve a Doppler limit of $123\ensuremath{\mu}\mathrm{K}.$ The efficiency of this cooling scheme and the main loss mechanisms are analyzed.