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Bulletin of the American Physical Society

Quantum calculations for one-dimensional cooling of helium

Edgar J. D. Vredenbregt, M. R. Doery, T. H. Bergeman, H. Metcalf

Published May 1, 1993• 0 citations
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Abstract

We report theoretical velocity distributions for sub-Doppler laser cooling of metastable He*(2{sup 3}S), calculated with the Density Matrix and Monte Carlo Wavefunction approaches. For low-field (B = 50 mG) magnetic-field induced laser cooling on the 2{sup 3}S {yields} (2{sup 3}P, J = 2) transition ({lambda} = 1083 nm), we get a narrow, sub-Doppler structure, consisting of three, {approximately}1 photon recoil wide peaks, spaced {approximately}1 recoil apart. With increasing field, this three-peak structure develops into two velocity-selective resonance (VSR) peaks, each {approximately}2 recoils wide. For the 2{sup 3}S {yields} (3{sup 3}P, J = 2) transition ({lambda} 389 nm), VSR peaks are predicted to appear at low field without the third, central peak, which only develops at higher field (B = 200 mG). Additional computations deal with polarization-gradient cooling. In general, we find that for one-dimensional cooling calculations, the Density Matrix method is more efficient than the Monte Carlo Wavefunction approach. Experiments are currently under way to test the results.

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We report theoretical velocity distributions for sub-Doppler laser cooling of metastable He*(2{sup 3}S), calculated with the Density Matrix and Monte Carlo Wavefunction approaches. For low-field (B = 50 mG) magnetic-field induced laser cooling on the 2{sup 3}S {yields} (2{sup 3}P, J = 2) transition ({lambda} = 1083 nm), we get a narrow, sub-Doppler structure, consisting of three, {approximately}1 photon recoil wide peaks, spaced {approximately}1 recoil apart. With increasing field, this three-peak structure develops into two velocity-selective resonance (VSR) peaks, each {approximately}2 recoils wide. For the 2{sup 3}S {yields} (3{sup 3}P, J = 2) transition ({lambda} 389 nm), VSR peaks are predicted to appear at low field without the third, central peak, which only develops at higher field (B = 200 mG). Additional computations deal with polarization-gradient cooling. In general, we find that for one-dimensional cooling calculations, the Density Matrix method is more efficient than the Monte Carlo Wavefunction approach. Experiments are currently under way to test the results.
We have observed magnetically induced laser cooling (MILC) on the J = 1 {yields} 2 component of the 2{sup 3}S {yields} 2{sup 3}P transition at {lambda} = 1.083 {mu}m in metastable helium (He*). At low magnetic field the measured widths of our atomic velocity distributions are as narrow as 2{Dirac_h}k/M corresponding to a temperature {approx_equal} 3 {mu}K (1-D Doppler limit {approx_equal} 26 {mu}K). At higher fields ({approximately}150 mG) the velocity distribution splits into two peaks of sub-Doppler width whose separation is proportional to the Zeeman splitting. Our measurements are consistent with model calculations based on the time evolution of quantum density matrices. Our experiments explore the transition regime between the quantum mechanical and semiclassical models of momentum exchange in atom-light interactions because of the large ratio (0.4) of the recoil velocity {Dirac_h}k/M to the rms of the Doppler-limited velocity distribution {radical}{Dirac_h}{gamma}/3M for this transition. We use a supersonic LN{sub 2} cooled nozzle source excited by a dc discharge for He*, and we excite the 2{sup 3}P state with a home-built diode-laser-pumped LNA laser.
We describe several one-dimensional sub-Doppler laser-cooling experiments that cool Rb to finite and zero velocities in a magnetic field and polarization gradients. We then present a physical picture that unifies these measurements in terms of coherent two-photon velocity-selective resonances between atomic ground-state sublevels (including Raman resonances). We propose several sub-Doppler cooling schemes without fields or without polarization gradients, based on VSR between nondegenerate ground states.
We report the first observation of subrecoil laser cooling in three dimensions, where we use the method of velocity-selective coherent population trapping. We have cooled a cloud of trapped metastable helium atoms to 180 nK, 22 times below the single-photon recoil temperature, with an enhancement in the momentum-space density of 16. We find that the efficiency with which the velocity-selective trap is populated can be augmented by Sisyphus-type frictional forces, while the cooling process is accompanied by the diffusion of atoms to states of very high velocity.
We have studied theoretically and experimentally the effect of a relatively strong magnetic field on sub-Doppler laser cooling in a one-dimensional optical molasses. We used the operator description of laser cooling with the Larmor precession frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{Z}}$ being much higher than the optical pumping rate. We found velocity-selective resonances (VSR) in the force at velocities vr{\mathit{v}}_{\mathit{r}}vr​=n${\mathrm{\ensuremath{\omega}}}_{\mathit{Z}}$, with n=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2 for both the scattering and redistribution force operators. These depend on the relative direction of the magnetic field and the polarization vectors of the light beams. Analytical results for the force on the atom are obtained in two cases that illustrate the effect of the VSR on the force. These formulas are compared with numerical calculations of the force. We also discovered a redistribution mechanism that relies on the gradient of the eigenstates of the light-shift operator, with eigenvalues that are independent of position so that a ``Sisyphus cooling'' picture does not apply. The theory is compared with many experimental results and excellent agreement is found. We believe that all essential features of laser cooling at low intensity are well described by this operator theory.
In sub-Doppler laser cooling of atoms, the lowest temperatures are known to occur at low (but not too low) excitation, and the temperature increases roughly linearly with laser intensity. However, under conditions for which the lowest temperatures are obtained, the small velocity capture range and low optical pumping rate limit the number of atoms that can be collected into the cold sample. In this study, we present measurements for laser cooling of Rb and metastable He atoms for two counterpropagating laser beams with orthogonal linear polarization (lin\ensuremath{\perp}lin) over a wide range of saturation parameters and laser detunings, together with results of semiclassical (Fokker-Planck) and quantum density matrix calculations. We find that at higher laser intensity, a larger number of atoms can be collected into a final velocity distribution that is significantly narrower than that given by a linear extrapolation vs the square root of laser intensity. Two cooling mechanisms are at work: the sub-Doppler Sisyphus mechanism and also Doppler cooling. Under certain conditions that we discuss, Doppler cooling aids Sisyphus cooling by collecting high-velocity atoms beyond the Sisyphus capture range. He∗{\mathrm{He}}^{*}He∗ presents a rather unusual situation in that the minimum average kinetic energy (Eav){(E}_{\mathrm{av}})(Eav​) for purely Sisyphus cooling is comparable to the minimum value of Eav{E}_{\mathrm{av}}Eav​ with Doppler cooling alone.