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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optical pumping via a velocity-selective state

Norbert Leinfellner, Laurentius Windholz, I. E. Mazets

Published Jul 2, 1998• 0 citations
Publisher

Abstract

We present a new scheme of sub-Doppler laser cooling for atoms used in atomic frequency standards, particularly for 40Ca. We perform calculations concerning optical pumping via a velocity- selective state based upon velocity-selective coherent population trapping. Optical pumping on the Raman transition 41S0- 41P1-31D2 leads to population of the metastable singlet state followed by a decay into the metastable triplet state 4P1. The momentum distribution of atoms in that state (with a half-maximum width of about one corresponding photon recoil momentum) is a direct replica of the distribution of atoms in the 3D2 state.

DOI
10.1117/12.312805

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Physical Review Letters•Apr 1, 1996•56 citations
We present a new scheme of sub-Doppler laser cooling for atoms used in atomic frequency standards, particularly for 40Ca. We perform calculations concerning optical pumping via a velocity- selective state based upon velocity-selective coherent population trapping. Optical pumping on the Raman transition 41S0- 41P1-31D2 leads to population of the metastable singlet state followed by a decay into the metastable triplet state 4P1. The momentum distribution of atoms in that state (with a half-maximum width of about one corresponding photon recoil momentum) is a direct replica of the distribution of atoms in the 3D2 state.
We present a new laser-cooling scheme based on velocity-selective optical pumping of atoms into a nonabsorbing coherent superposition of states. This method has allowed us to achieve transverse cooling of metastable 4He^{4}\mathrm{He}4He atoms to a temperature of 2 \ensuremath{\mu}K, lower than both the usual Doppler cooling limit (23 \ensuremath{\mu}K) and the one-photon recoil energy (4 \ensuremath{\mu}K). The corresponding de Broglie wavelength (1.4 \ensuremath{\mu}m) is larger than the atomic-transition optical wavelength.
An analytical theory of optical pumping of velocity-selective coherent population trapping states in three-level Λ-atoms is presented. The theory is based on an atomic density matrix in the superpositional state representation. The representation introduced for the atomic density matrix directly describes coherent population trapping (CPT) states in a three-level Λ-atom and yields an approximate analytical description for the shape of the two-peak momentum (velocity) distribution of atoms. Optical pumping of velocity-selective CPT states is described in the superpositional state representation as a process of redistribution of atoms in the region of small velocities due to the photon recoil. Typical times of formation of velocity-selective CPT states are found to be inversely proportional to the square of the recoil energy.
We present a theoretical analysis of a new one-dimensional laser-cooling scheme that was recently demonstrated on a beam of metastable 4He atoms. Both internal and translational degrees of freedom are treated quantum mechanically. Unlike semiclassical approaches, such a treatment can be applied to situations in which the atomic coherence length is of the same order of or larger than the laser wavelength, which is the case for atoms cooled below the one-photon recoil energy. We introduce families of states that are closed with respect to absorption and stimulated emission, and we establish the generalized optical Bloch equations that are satisfied by the corresponding matrix elements. The existence of velocity-selective trapping states that are linear combinations of states with different internal and translational quantum numbers is demonstrated, and the mechanism of accumulation of atoms in these trapping states by fluorescence cycles is analyzed. From a numerical solution of the generalized optical Bloch equations, we study in detail how the final atomic-momentum distribution depends on the various physical parameters: interaction time, width of the initial distribution, laser detuning, laser power, and imbalance between the two counterpropagating waves. We show that the final temperature decreases when the interaction time increases, so that there is no fundamental limit to the lowest temperature that can be achieved by such a method. Finally, possible extensions of this method to two-dimensional cooling are presented.
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 have theoretically studied a one-dimensional light field configuration which combines velocity-selective coherent-population trapping with the action of a novel kind of sub-Doppler force providing efficient cooling below the recoil limit. The force is based on velocity-induced non-adiabatic passage of atomic population from the non-coupling state to the light-shifted coupling state. We show for 87Rb that within 0.88 ms 35% of an initial distribution of 12k width can be cooled into a 0.5k momentum interval, and that more than 90% of the initial distribution are still confined to 12k width.
We demonstrate subrecoil cooling of rubidium atoms by velocity-selective coherent population trapping. By adiabatic transfer of the cooled atoms into a spin polarized single momentum state we show the coherence of the trapped state. Our cooling scheme takes advantage of the rubidium hyperfine structure to integrate subrecoil and sub-Doppler cooling. Starting from an initial velocity distribution of twice the recoil temperature $[{T}_{\mathrm{rec}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(\ensuremath{\Elzxh}k{)}^{2}{/k}_{B}M]$, we cool down to 100 nK $(\ensuremath{\approx}\frac{1}{3}{T}_{\mathrm{rec}})$ within 1 ms, while almost completely suppressing the diffusive heating of velocity-selective coherent population trapping.