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Journal de Physique II

Magnetically assisted Sisyphus effect

Olivier Émile, Robin Kaiser, Christoph Gerz, Hartmut Wallis, Alain Aspect, Claude N. Cohen-Tannoudji

Published Dec 1, 1993• 23 citations
Publisher

Abstract

This paper presents an experimental and theoretical study of laser cooling in a standing wave in the presence of a small transverse magnetic field (Magnetically Assisted Sisyphus Effect: MASE). The analysis is worked out for a Jg=1 to Je=1 transition corresponding to the experiment performed on the $2^{3}\rm S_{1}\longleftrightarrow 2^{3}\rm P_{1}$ transition of metastable helium. In this situation, MASE has an effect opposed to the usual Doppler cooling effect, i.e. it produces heating for a negative detuning. Depending on the various parameters, the competition between MASE and Doppler cooling, which act on different velocity ranges, leads to interesting new effects, such as a bistable force. The velocity dependence of the total force is calculated, using a semi-classical approach. A second theoretical treatment, where the atomic motion is quantized, is used to study the time evolution of the velocity distribution. The results of these calculations are compared to experimental observations.

DOI
10.1051/jp2:1993226

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This paper presents an experimental and theoretical study of laser cooling in a standing wave in the presence of a small transverse magnetic field (Magnetically Assisted Sisyphus Effect: MASE). The analysis is worked out for a Jg=1 to Je=1 transition corresponding to the experiment performed on the 23S1⟷23P12^{3}\rm S_{1}\longleftrightarrow 2^{3}\rm P_{1}23S1​⟷23P1​ transition of metastable helium. In this situation, MASE has an effect opposed to the usual Doppler cooling effect, i.e. it produces heating for a negative detuning. Depending on the various parameters, the competition between MASE and Doppler cooling, which act on different velocity ranges, leads to interesting new effects, such as a bistable force. The velocity dependence of the total force is calculated, using a semi-classical approach. A second theoretical treatment, where the atomic motion is quantized, is used to study the time evolution of the velocity distribution. The results of these calculations are compared to experimental observations.
A theoretical analysis is given for 1-D laser cooling below the Doppler limit of J = 1/2 ground- state atoms. The laser field consists of a pair of counterpropagating, linearly polarized low- power beams, whose polarization directions differ by an angle θ (0 ≤ θ ≤ π/2). For θ ≪ 1, the effective optical pumping time is shown to increase strongly near the nodes of the standing wave and the cooling force can be much larger than that for θ ~1. Moreover, for θ ≪ 1, it can be shown that the stimulated part of the atomic diffusion is reduced considerably as compared with that for θ ~ 1. As a consequence it is possible to achieve an equilibrium atomic distribution that, for θ ≪ 1, is characterized by a mean kinetic energy lower than that predicted to occur for θ = π/2. The equilibrium velocity distribution is not necessarily Maxwellian and thus the temperature of the atomic ensemble may not be well defined. The achievable kinetic energy is so small that the cooled atoms are trapped in the vicinity of the laser field nodes. An explanation for these effects is given in terms of Sisyphus cooling.
We describe a new sub-Doppler cooling scheme that cools atoms to nonzero velocity vr{\mathit{v}}_{\mathit{r}}vr​. The atomic motion in a combined optical standing wave and constant magnetic field induces a velocity-selective magnetic resonance that produces strong cooling for negative laser detuning to vr{\mathit{v}}_{\mathit{r}}vr​=${\mathrm{\ensuremath{\omega}}}_{\mathit{Z}}$/2k, with ${\mathrm{\ensuremath{\omega}}}_{\mathit{Z}}$ the Larmor frequency. In a one-dimensinal optical molasses transverse to a thermal Rb beam we observe the bunching of the atoms into two peaks corresponding to \ifmmode\pm\else\textpm\fi{}vr{\mathit{v}}_{\mathit{r}}vr​. We present a quantitative comparison between our theory and experiment and suggest some applications.
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 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.
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.
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.