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Chinese Journal of Physics

Two-Photon Doppler Cooling of Rubidium Atoms to the Recoil Limit Using Cascade Transitions

Lei Tan, C-K. Zhong, C-L. Zhang, Q. Zhang

Published Jun 1, 2006• 2 citations
OpenAlex

Abstract

A model is presented for calculating the two-photon Doppler cooling of a three-level atom in a ladder configuration. This model is then applied to cool rubidium. atoms, using the combined action of two lasers to excite the 5(2) S-1/2 - 5(2) P-3/2 - 5(2) D-5/2 cascade transitions to an effective temperature of 300 nK, less than the single photon recoil temperature.

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A model is presented for calculating the two-photon Doppler cooling of a three-level atom in a ladder configuration. This model is then applied to cool rubidium. atoms, using the combined action of two lasers to excite the 5(2) S-1/2 - 5(2) P-3/2 - 5(2) D-5/2 cascade transitions to an effective temperature of 300 nK, less than the single photon recoil temperature.
We demonstrate a new cooling technique which is used to cool sodium atoms in one dimension to an effective temperature of 100 nK, less than 1/10 of the single photon recoil temperature kB{\mathit{k}}_{\mathit{B}}kB​Trec{\mathit{T}}_{\mathrm{rec}}Trec​=(\ensuremath{\Elzxh}k)2{)}^{2})2/2M.
We employ semiclassical theoretical analysis to study laser cooling of free atoms using three-level cascade transitions, where the upper transition is much weaker than the lower one. This represents an alternate cooling scheme, particularly useful for group II atoms. We find that temperatures below the Doppler limits associated with each of these transitions are expected. The lowest temperatures arise from a remarkable increase in damping and reduced diffusion compared to two-level cooling. They are reached at the two-photon resonance, where there is a crossing between the narrow and the partially dark dressed states, and can be estimated simply by the usual Doppler limit considering the decay rate of the optical coherence between these states.
Radiation pressure and laser cooling of a moving three-level ladder-type atom in bichromatic travelling fields are considered. The dependence of the force on parameters such as detunings, Rabi frequencies and spontaneous decay rates is calculated numerically and shown graphically and analytical expressions for the force are obtained for some special parameter values. It is shown that the radiation pressure shows Doppler-shifted resonance peaks resulting respectively from one-photon and two-photon transitions. Using the present scheme, Doppler cooling of sodium exploiting the 3 2 S 1/2 –3 2 P 3/2 –3 2 D 5/2 cascade transitions is investigated. It is found that temperatures lower than the Doppler limit can be achieved.
Summary form only given. We consider laser cooling of free atoms with simultaneous two-color excitation of three-level cascade transitions [1], [2], [3], [4], [5], [6] finding theoretically that temperatures below the Doppler limits associated with each one of the individual transitions are obtained. We use standard laser cooling analysis [7], [8] and the dressed state picture in order to identify different cooling regions, and determining optimum parameters for guiding further experiments. These new “sub-Doppler” limits are reached at the two-photon resonance where a significant increase of the damping coefficient and decrease of the diffusion take place. In the dressed state picture, this point corresponds to a crossing of the narrow and a (partially) dark state.Figure 1 shows a plot of temperature (normalized to the Doppler limit for cooling only on the lower transition) as function of single-photon detunings, for the 1S0-1P1-1D2 transition of Magnesium, in which the lower 1S0-1P1 transition is the usual cooling one (λ1 = 2πc/ω1 = 285 nm, λ2 = 2πc/ω2 = 881 nm, γ1 = 2π 78.8 MHz, γ2 = 2π 2.2 MHz). A minimum temperature of 38 μK is predicted. This temperature is lower than the Doppler temperature of the lower and upper transitions, TD = γ/k = 1.9 mK and 49 μK respectively. Due to the asymmetric absorption profile of the dressed atom, there is a remarkable increase in the damping coefficient (α) associated with the narrow transition, in comparison with the broad transition (two-level cooling). The cooling and damping times, inversely proportional to α, are reduced by the same amount. Since the curve for the diffusion coefficient (D) has the same shape as the curve for the absorption coefficient or the population of the intermediate state, D is also reduced with respect to the broad resonance, We analyze situations previously implemented experimentally in alkaline-Earth atoms using cascade transitions, and also discuss prospects for Aand V-type three-level systems.
Laser cooling is theoretically investigated in a cascade three-level scheme, where the excited state of a laser-driven transition is coupled by a second laser to a top, more stable level, as for alkaline-earth-metal atoms. The second laser action modifies the atomic scattering cross section and produces temperatures lower than those reached by Doppler cooling on the lower transition. When multiphoton processes due to the second laser are relevant, an electromagnetic-induced transparency modifies the absorption of the first laser, and the final temperature is controlled by the second laser parameters. When the intermediate state is only virtually excited, the dynamics is dominated by the two-photon process and the final temperature is determined by the spontaneous decay rate of the top state.
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.