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Physical Review A

Several asymptotic subrecoil laser-cooling behaviors in arbitrary degenerate Λ systems

Hong Yuan Ling

Published May 1, 1999• 5 citations
Publisher

Abstract

Subrecoil cooling can be achieved in three-level \ensuremath{\Lambda}-type atoms subject to counterpropagating laser beams via velocity-selective coherent population trapping [A. Aspect et al., J. Opt. Soc. Am. B 6, 2112 (1989)]. This process leads to narrow peaks in the ground but a flat structure in the excited atomic momentum distributions. By taking advantage of this difference, we construct several analytical functions from which the main cooling features (with the exception of the scaling law about the fraction of subrecoil cooled atoms) can be approximated under arbitrary parameters. This method allows us to generalize the peak-momentum width from symmetric to arbitrary degenerate \ensuremath{\Lambda} systems, and to discuss analytically the small dependence of the momentum distributions on the laser detuning near the two-photon resonance.

DOI
10.1103/physreva.59.3714

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Subrecoil cooling can be achieved in three-level \ensuremath{\Lambda}-type atoms subject to counterpropagating laser beams via velocity-selective coherent population trapping [A. Aspect et al., J. Opt. Soc. Am. B 6, 2112 (1989)]. This process leads to narrow peaks in the ground but a flat structure in the excited atomic momentum distributions. By taking advantage of this difference, we construct several analytical functions from which the main cooling features (with the exception of the scaling law about the fraction of subrecoil cooled atoms) can be approximated under arbitrary parameters. This method allows us to generalize the peak-momentum width from symmetric to arbitrary degenerate \ensuremath{\Lambda} systems, and to discuss analytically the small dependence of the momentum distributions on the laser detuning near the two-photon resonance.
The \ensuremath{\Lambda} system resulting from the interaction of counterpropagating orthogonally polarized beams of light with a Jg{\mathit{J}}_{\mathit{g}}Jg​=1\ensuremath{\rightarrow}Je{\mathit{J}}_{\mathit{e}}Je​=1 transition is known to exhibit laser cooling without the presence of a damping force, through velocity selective coherent population trapping. This occurs independent of the sign of the laser's detuning from the atomic resonance frequency. We present measurements and calculations that show a detuning-dependent transient peak or dip in the ground-state momentum distribution centered at pg{\mathit{p}}_{\mathit{g}}pg​=0, however, which is reminiscent of laser cooling by a damping force. We explain this in terms of the character of the quantum-mechanical eigenstates of the total ground-state Hamiltonian of the system, using both analytic expressions and numerical calculations.
We report the first observation of subrecoil laser cooling in two dimensions by velocity selective coherent population trapping. We have compressed the momentum distribution of a cloud of trapped metastable helium atoms along two orthogonal axes to $\ensuremath{\delta}p=\frac{\ensuremath{\hbar}k}{4}$, where $\ensuremath{\hbar}k$ is the photon momentum. The corresponding temperature, 16 times below the single-photon recoil temperature, is 250 nK. Atoms are pumped into a nonabsorbing state exhibiting four well-resolved momentum peaks with subrecoil widths. The momentum space density in the peaks is significantly greater than that in the uncooled distribution.
We present a new scheme for ID subrecoil laser cooling by velocity-selective coherent population trapping of even-even isotopes of elements found in the second group of the periodical table, particularily, zaaHg and 40Ca. The scheme envolves the transitions (a) between the ground state with the total angular momentum Pg = 0 and the excited one with Fe = 1, @) between the latter state and the second excited one with Fe* = 2. The second transition belongs to the infrared region and has a width much smaller than the transition from the ground state. The lower transition is driven by two counterpropagating o+ and U- polarized running waves. The laser beam applied in the perpendicular direction is a linearily polarized standing wave exciting the
We present a fully quantum-mechanical analysis of laser cooling of an angular momentum Jg{\mathit{J}}_{\mathit{g}}Jg​=1 to Je{\mathit{J}}_{\mathit{e}}Je​=1 transition in a laser configuration consisting of two counterpropagating linearly polarized laser beams. The essential feature of this configuration is the coexistence of velocity-selective coherent population trapping (VSCPT) and polarization-gradient cooling. The role of polarization-gradient cooling is to provide (i) for short interaction times ``precooling'' of the initial momentum distribution and (ii) in the long-time limit ``confinement of velocities.'' This eventually leads to a larger number of atoms being captured in the dark state when compared with the schme of Aspect et al. [Phys. Rev. Lett. 61, 826 (1988)]. We find that the optimum parameter values for polarization-gradient cooling and VSCPT are in a completely different parameter regime: polarization-gradient cooling works best off resonance and for low intensities, while VSCPT works best on resonance. We can combine the advantages of polarization-gradient cooling and VSCPT in a scheme where we cycle in time between the optimum cooling parameters for both cooling mechanisms.
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.