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AIP conference proceedings

Sub-Doppler laser cooling in a magnetic field

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

Published Jan 1, 1991• 1 citation
Publisher

Abstract

This paper reports on sub‐Doppler laser cooling processes in a light field of constant polarization with an applied magnetic field. A theoretical model is developed to describe these experiments that is valid for arbitrary transition schemes. Adding the magnetic field to the optical molasses gives rise to new phenomena such as cooling of atoms to a non‐zero velocity that can also be used to test the 1‐D model. (AIP)

DOI
10.1063/1.40969

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Physical Review A•Oct 4, 2002•7 citations
This paper reports on sub‐Doppler laser cooling processes in a light field of constant polarization with an applied magnetic field. A theoretical model is developed to describe these experiments that is valid for arbitrary transition schemes. Adding the magnetic field to the optical molasses gives rise to new phenomena such as cooling of atoms to a non‐zero velocity that can also be used to test the 1‐D model. (AIP)
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.
Sub-Doppler cooling has been achieved for the two closed hyperfine transitions: F = 4 → F ' = 5 and F = 3 → F ' = 2, of the cesium D 2 line. One-dimension optical molasses is experimentally investigated and compared for both j → j + 1 and j → j - 1 transitions, on different laser polarization configurations, in the presence, and absence of a static magnetic field. One remarkable point is that cooling is obtained with blue laser detuning for the j → j - 1 transition. An applied static magnetic field can also shift the sub-Doppler-cooled molasses peaks to nonzero velocities without any extra heating, for the polarization gradient configurations.
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.
An experimental investigation of the effects of magnetic field on cooling and trapping of neutral atoms is presented. Applied to optical molasses, a static magnetic field often produces spectacular effects. It can either induce a sub-Doppler cooling effect or shift a sub-Doppler-cooled atomic sample away from its zero-velocity position. Some of the effects have potential applications in the manipulation of cesium atoms (deflecting an atomic beam or launching an optical molasses into an atomic fountain) and can probably be used in the development of a future cesium atomic frequency standard. The observed experimental effects are interpreted by simple physical models and calculations.>
Sub-Doppler laser cooling can be achieved in the absence of polarization gradients when a weak transverse magnetic field is used for mixing eigenstates of the light shift operator. By contrast, Zeeman shifts from magnetic fields B{sub {ell}} along the quantization axis can add or subtract with the light shifts of those states. B{sub {ell}} thus provides an additional degree of freedom for studying magnetic effects in laser cooling since the set of sinusoidal potentials that derives from the spatially periodic light shifts in a standing wave can be manipulated with the field. For example, with circularly polarized light, a finite B{sub {ell}} can switch the normal heating to cooling, and vice versa. We have done such experiments in the F = 3 {yields} 4 transition of {sup 85}Rb at {lambda} = 780 nm with diode laser light, and have shown that sub-Doppler heating and cooling can be interchanged with opposite longitudinal ed directions, in good agreement with this model. One application of such experiments is to characterize precisely the magnetic fields seen by the atoms along their trajectories in the beam.
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.