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Physical Review A

Sub-Doppler cooling of three-level Λ atoms in space-shifted standing light waves

Dmitry V. Kosachiov, Yu. Rozhdestvensky, M. K. Olsen, Lev I. Plimak, Daniel F. Walls

Published Aug 1, 1994• 3 citations
Publisher

Abstract

We present an investigation of an alternative mechanism for sub-Doppler cooling of atoms, based on a coherent population transfer in three-level \ensuremath{\Lambda} systems. The mechanism considered is that of a \ensuremath{\Lambda} atom interacting with two standing light waves with a mutual spatial phase shift cphi\ensuremath{\ne}0. The spatial dependence of the level populations of the \ensuremath{\Lambda} atom for different values of cphi is presented. For cphi\ensuremath{\ne}0, this clearly demonstrates coherent population transfer in an atom with transverse motion along the space-shifted nodes and antinodes of the two standing waves. We show that this allows translational temperatures well below the Doppler limit ${\mathit{T}}_{\mathit{D}}$=${\mathrm{\ensuremath{\Elzxh}}}_{\ensuremath{\gamma}}$/${\mathit{k}}_{\mathit{B}}$ to be achieved.

DOI
10.1103/physreva.50.1508

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•Jan 1, 1994•2 citations
We present an investigation of an alternative mechanism for sub-Doppler cooling of atoms, based on a coherent population transfer in three-level \ensuremath{\Lambda} systems. The mechanism considered is that of a \ensuremath{\Lambda} atom interacting with two standing light waves with a mutual spatial phase shift cphi\ensuremath{\ne}0. The spatial dependence of the level populations of the \ensuremath{\Lambda} atom for different values of cphi is presented. For cphi\ensuremath{\ne}0, this clearly demonstrates coherent population transfer in an atom with transverse motion along the space-shifted nodes and antinodes of the two standing waves. We show that this allows translational temperatures well below the Doppler limit TD{\mathit{T}}_{\mathit{D}}TD​=\ensuremath\Elzxh\ensuremathγ{\mathrm{\ensuremath{\Elzxh}}}_{\ensuremath{\gamma}}\ensuremath\Elzxh\ensuremathγ​/kB{\mathit{k}}_{\mathit{B}}kB​ to be achieved.
We present a general theoretical description of laser cooling of three-level atoms in a Λ configuration in two standing waves. Detunings, intensity, and spatial phase difference of the two waves are arbitrary. We demonstrate that, for a zero spatial phase shift, sub-Doppler cooling requires equal detunings. The basic mechanism is then coherent population trapping. For different detunings sub-Doppler cooling occurs only when the spatial phases of the two standing waves are different. This effect can be traced back to a mechanism of the Sisyphus type. These schemes of sub-Doppler cooling require neither polarization gradients nor magnetic fields.
We examine the laser cooling of three-level (Lambda) -atoms in the field of two standing waves when frequency detunings are considerably greater than natural width of the excited state as well as the Rabi frequencies in the system. It is shown that at the difference of frequency detunings is small when compared to the Rabi frequencies sub-Doppler cooling of the (Lambda) -atom is possible. We present the dependence of the light pressure force on the atoms velocity and dependence of cooled atoms temperature on the parameters of the exciting waves.
In Section 8.3.9, we mentioned that the recoil temperature was not the ultimate barrier to cooling. Several mechanisms have been conceived and implemented to concentrate the atomic velocity distribution in a range of values of width less than V R . In contrast to Doppler or Sisyphus cooling, these mechanisms do not appeal to a friction force, but rather to an optical pumping process (see Complement 2B), able to accumulate the atoms in this narrow range of velocities. We now present one such mechanism called ‘velocity-selective coherent population trapping’, considering only the case where the motion occurs in one space direction (the O z -axis). Note, however, that the method generalizes to two or three dimensions. Coherent population trapping Coherent population trapping is a phenomenon that occurs when an atom has a system of three energy levels in the ∧ configuration shown in Figure 8A.1, where each leg of the ∧ interacts with a laser L − or L + . This was discussed in detail in Section 2D.2 of Complement 2D. Here we consider the case where the two ground states g + and L − , have exactly the same energy, and the two lasers have frequencies ω + and ω − , very close to the resonance frequency ω 0 . In this situation, the selectivity of the interactions is obtained via the polarization selection rules (see Complement 2B): if g − , g + and e have magnetic quantum numbers m = −1, +1 and 0, respectively, the laser wave L − is right-circularly polarized (σ + polarization), while the laser wave L + is left-circularly polarized (σ − polarization).
We examine the dynamics of five-level atoms interacting with two standing waves. In our approach we describe the motion of the atoms by a Fokker-Planck equation, including the effect of velocity-dependent two-photon Raman processes within the second order rate equation approximation. By using this procedure we numerically calculate the cooled temperatures of sodium atoms. We then find two principal types of behaviour; that of two-level and three-level atomic systems. We are also able to find detunings of the standing waves for which the atoms are cooled to temperatures below the “Doppler limit”.