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Physical Review Letters

Magnetic-field-induced laser cooling below the Doppler limit

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

Published Feb 19, 1990• 90 citations
Publisher

Abstract

We report a new cooling scheme used to actively collimate an atomic beam of $^{85}\mathrm{Rb}$ 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 ${v}_{D}$=(7\ensuremath{\Elzxh}\ensuremath{\gamma}/20M${)}^{1/2}$\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.

DOI
10.1103/physrevlett.64.858

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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 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 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 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 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 present two cooling mechanisms that lead to temperatures well below the Doppler limit. These mechanisms are based on laser polarization gradients and work at low laser power when the optical-pumping time between different ground-state sublevels becomes long. There is then a large time lag between the internal atomic response and the atomic motion, which leads to a large cooling force. In the simple case of one-dimensional molasses, we identify two types of polarization gradient that occur when the two counterpropagating waves have either orthogonal linear polarizations or orthogonal circular polarizations. In the first case, the light shifts of the ground-state Zeeman sublevels are spatially modulated, and optical pumping among them leads to dipole forces and to a Sisyphus effect analogous to the one that occurs in stimulated molasses. In the second case (σ+−σ− configuration), the cooling mechanism is radically different. Even at very low velocity, atomic motion produces a population difference among ground-state sublevels, which gives rise to unbalanced radiation pressures. From semiclassical optical Bloch equations, we derive for the two cases quantitative expressions for friction coefficients and velocity capture ranges. The friction coefficients are shown in both cases to be independent of the laser power, which produces an equilibrium temperature proportional to the laser power. The lowest achievable temperatures then approach the one-photon recoil energy. We briefly outline a full quantum treatment of such a limit.