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Physical Review Letters

Velocity-selective magnetic-resonance laser cooling

S-Q. Shang, B. Sheehy, P. van der Straten, H. Metcalf

Published Jul 16, 1990• 51 citations
Publisher

Abstract

We describe a new sub-Doppler cooling scheme that cools atoms to nonzero velocity ${\mathit{v}}_{\mathit{r}}$. 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 ${\mathit{v}}_{\mathit{r}}$=${\mathrm{\ensuremath{\omega}}}_{\mathit{Z}}$/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{}${\mathit{v}}_{\mathit{r}}$. We present a quantitative comparison between our theory and experiment and suggest some applications.

DOI
10.1103/physrevlett.65.317

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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​=\ensuremathωZ{\mathrm{\ensuremath{\omega}}}_{\mathit{Z}}\ensuremathωZ​/2k, with \ensuremathωZ{\mathrm{\ensuremath{\omega}}}_{\mathit{Z}}\ensuremathωZ​ 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 report a new cooling scheme used to actively collimate an atomic beam of 85Rb^{85}\mathrm{Rb}85Rb with one-dimensional optical molasses. The atoms' transverse velocity is damped by a standing wave of circularly polarized light in a magnetic field of \ensuremath{\sim}20 \ensuremath{\mu}T to 2 cm/s (rms), well below the Doppler velocity vD{v}_{D}vD​=(7\ensuremath{\Elzxh}\ensuremath{\gamma}/20M)1/2{)}^{1/2})1/2\ensuremath{\sim}10 cm/s for one-dimensional optical molasses. The minimum measured velocity is limited only by the experimental geometry. We have developed a model in which the mixing by the field and optical pumping combine to form a cycle that cools below the Doppler limit, in agreement with our measurements.
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 have observed a new type of sub-Doppler laser cooling with neither polarization gradients nor magnetic fields. All known sub-Doppler laser cooling methods require one of these two to resdistribute the atomic population among the energy levels. This allows the irreversible processes of optical pumping vels. This allows the irreversible processes of optical pumping (OP) to manipulate the conservative force of light shifts (e.g. resonant exchange between the two beams comprising a standing wave) into a damping force. Our scheme employs stimulated Raman transitions between ground state hyperfine levels of Rb with a bichromatic standing wave, accompanied by a momentum change of {Delta}p = 2{h_bar}k. OP, with {Delta}p = 1{h_bar}k, creates a population imbalance allowing repetition of the Raman process. When the detuning of the light from Raman resonance {delta} is properly chosen, the net momentum exchange damps the atomic motion. Changing {delta} by only {gamma}/6(1 MHz) replaces cooling by heating. This process separates the velocity selective Raman resonance and OP processes differently from others, and helps clarify the role of these different mechanisms.
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 analyze the influence of an arbitrarily directed uniform magnetic field on the laser sub-Doppler cooling of atoms. The analysis is done for a (3+5)-level atom excited by a ${\ensuremath{\sigma}}^{+}\ensuremath{-}{\ensuremath{\sigma}}^{\ensuremath{-}}$ laser field configuration. Our analysis shows that the effects of the magnetic field depend strongly on the direction of the magnetic field. In an arbitrarily directed magnetic field the laser cooling configuration produces both the main resonance existing already at zero magnetic field and additional sub-Doppler resonances caused by two-photon and higher-order multiphoton processes. These sub-Doppler resonances are, however, well separated on the velocity scale if the Zeeman shift exceeds the widths of the resonances. This allows one to use the main sub-Doppler resonance for an effective laser cooling of atoms even in the presence of the magnetic field. The effective temperature of the atomic ensemble at the velocity of the main resonance is found to be almost the same as in the absence of the magnetic field. The defined structure of the multiphoton resonances may be of importance for the sub-Doppler laser cooling of atoms, atomic extraction from magneto-optical traps, and applications related to the control of atomic motion.