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Bulletin of the American Physical Society

Longitudinal magnetic field effects in subDoppler cooling

R.N. Gupta, Chengke Xie, S. Padua, Herman Batelaan, H. Metcalf

Published May 1, 1993• 0 citations
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Abstract

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.

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Bulletin of the American Physical Society•May 1, 1993•0 citations

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Physical Review Letters•May 24, 1993•9 citations
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 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 present an extensive set of measurements on one-dimensional sub-Doppler cooling and channeling in counterpropagating light beams. The experimental method consists of the measurement of the profile of an initially subrecoil collimated atomic beam, which is deflected by the interaction with the light field. The initial velocity of the atoms in the direction of the laser beams is varied in the range -1\ensuremath{\le}${\mathit{v}}_{\mathrm{\ensuremath{\perp}}}$(${\mathrm{ms}}^{\mathrm{\ensuremath{-}}1}$)\ensuremath{\le}1 by changing the angle between atomic and laser beams. For the orthogonal circular polarization (${\mathrm{\ensuremath{\sigma}}}^{+}$${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$) sub-Doppler cooling configuration, the force and the diffusion coefficient characterizing the cooling process have been determined as a function of the initial velocity ${\mathit{v}}_{\mathrm{\ensuremath{\perp}}}$ from the average deflection and broadening of the atomic beam profile. We observe transient effects due to the slow evolution of the distribution over the magnetic sublevels to an equilibrium. The experimental results agree very well with quantum Monte Carlo simulations and semiclassical calculations. For the orthogonal linear polarization (${\mathrm{\ensuremath{\pi}}}^{\mathit{x}}$${\mathrm{\ensuremath{\pi}}}^{\mathit{y}}$) configuration, we demonstrate the validity of the well-known Sisyphus picture for the cooling mechanism by comparing the experimental data to the results of a simple semiclassical Monte Carlo model incorporating only the dipole force and optical pumping. In weak standing waves of either circular or linear polarization, we demonstrate the characteristic features of channeling. \textcopyright{} 1996 The American Physical Society.
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 discovered a new cooling process that uses an applied magnetic field to mix differentially light shifted atomic ground state sublevels. In related experiments cooling is achieved by mixing caused by polarization gradients. Because the energy loss mechanism stems from the light shift and not the momentum transfer of a scattering event, the accessible temperature is much lower than the limit of Doppler cooling. We used this method for optical collimation of an 85Rb atomic beam to a transverse rms speed of 3 cm/s, well below the v = ( 7 ℏ γ / 20 M ) ≅ 10 cm / s of the Doppler limit for two-level atoms in this 1-D optical molasses. This low velocity, limited only by experimental geometry, is achieved only when a magnetic field of ~20 µT is applied perpendicular to the axis of the circularly polarized diode laser beam. We use a thermal beam of natural Rb produced by an oven at T ~ 150°C with an ~0.33-mm diam aperture and a defining aperture of ~0.33-mm diam about 24 cm away. The atoms are optically collimated by laser beams transverse to their motion that excite the transition at λ = 780 nm. The atomic beam profile is measured with a vertically oriented scanning hot tungsten wire, 25 µm in diameter, 1.3 m away.
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.
We observed a new type of sub-Doppler cooling that employs neither polarization gradients nor magnetic fields, and involves neither a damping force nor significant diffusive heating. Instead, light shifts combined with optical pumping (OP) to levels not coupled by the laser field gives transient cooling, and steady state is not achieved. The time scale is set by the OP rate. We observe both cooling and heating, but often with the opposite detuning from that of steady state. A semiclassical and a fully quantum mechanical calculation of transient cooling agree very well with one another and with our data.