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Physical Review A

Laser sub-Doppler cooling of atoms in an arbitrarily directed magnetic field

Soo Chang, Taeg Yong Kwon, Ho Seong Lee, Vladimir G. Minogin

Published Oct 4, 2002• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.66.043404

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Bulletin of the American Physical Society•May 1, 1993•0 citations
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 \ensuremathσ+\ensuremath−\ensuremathσ\ensuremath−{\ensuremath{\sigma}}^{+}\ensuremath{-}{\ensuremath{\sigma}}^{\ensuremath{-}}\ensuremathσ+\ensuremath−\ensuremathσ\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.
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 extend the kinetic theory of the laser cooling of atoms to four multilevel atomic schemes: (3+5)-, (5+7)-, (7+9)-, and (9+11)-level atom. In all four atomic schemes the atoms are considered to be excited by two counterpropagating circularly polarized laser waves. A comparison of four multilevel atomic schemes shows that the even-order multiphoton processes are responsible for the narrow structures near zero velocity in the atomic coherences, atomic populations, dipole radiation forces, and the diffusion coefficients. The even-order multiphoton processes in a multilevel atom with a big number of magnetic sublevels are shown to produce the velocity structures, which are much narrower than that produced by the two-photon processes in a (3+5)-level atom. It is found that the multiphoton processes enhance the radiation force at low velocities and the friction produced by the force at a negative detuning. The even-order multiphoton processes caused by the laser waves are identified as the basic physical mechanism responsible for the sub-Doppler laser cooling of atoms. The temperature of laser-cooled atoms is derived for all four models and found to be lower for atomic schemes with a larger number of magnetic sublevels.
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 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.