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Physical Review A

Force, diffusion, and channeling in sub-Doppler laser cooling

Maarten D. Hoogerland, H. F. P. de Bie, Herman C. W. Beijerinck, Edgar J. D. Vredenbregt, K. A. H. van Leeuwen, P. van der Straten, H. Metcalf

Published Oct 1, 1996• 13 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.54.3206

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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}v\ensuremath⊥{\mathit{v}}_{\mathrm{\ensuremath{\perp}}}v\ensuremath⊥​(ms\ensuremath−1{\mathrm{ms}}^{\mathrm{\ensuremath{-}}1}ms\ensuremath−1)\ensuremath{\le}1 by changing the angle between atomic and laser beams. For the orthogonal circular polarization ({\mathrm{\ensuremath{\sigma}}}^{+}$${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}) sub-Doppler cooling configuration, the force and the diffusion coefficient characterizing the cooling process have been determined as a function of the initial velocity v\ensuremath⊥{\mathit{v}}_{\mathrm{\ensuremath{\perp}}}v\ensuremath⊥​ from the average deflection and broadening of the atomic beam profile. We observe transient effects due to the slow evolution of the distribution over the magnetic sublevels to an equilibrium. The experimental results agree very well with quantum Monte Carlo simulations and semiclassical calculations. For the orthogonal linear polarization ({\mathrm{\ensuremath{\pi}}}^{\mathit{x}}$${\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 the first direct measurements of the velocity dependence of the average force and diffusion constant for the metastable neon atoms in a one-dimensional ${\mathrm{\ensuremath{\sigma}}}^{+}$${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$ laser cooling configuration. Force and diffusion are determined, respectively, from the deflection and broadening of a highly collimated atomic beam by its interaction with a pair of counter-running laser beams. The interaction time is much shorter than the characteristic damping time of the cooling process. The resulted force and diffusion measurements are compared with the results of both semiclassical and quantum Monte Carlo calculations.
A theoretical analysis is given for 1-D laser cooling below the Doppler limit of J = 1/2 ground- state atoms. The laser field consists of a pair of counterpropagating, linearly polarized low- power beams, whose polarization directions differ by an angle θ (0 ≤ θ ≤ π/2). For θ ≪ 1, the effective optical pumping time is shown to increase strongly near the nodes of the standing wave and the cooling force can be much larger than that for θ ~1. Moreover, for θ ≪ 1, it can be shown that the stimulated part of the atomic diffusion is reduced considerably as compared with that for θ ~ 1. As a consequence it is possible to achieve an equilibrium atomic distribution that, for θ ≪ 1, is characterized by a mean kinetic energy lower than that predicted to occur for θ = π/2. The equilibrium velocity distribution is not necessarily Maxwellian and thus the temperature of the atomic ensemble may not be well defined. The achievable kinetic energy is so small that the cooled atoms are trapped in the vicinity of the laser field nodes. An explanation for these effects is given in terms of Sisyphus cooling.
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.
A theoretical analysis is given for one-dimensional laser cooling below the Doppler limit of J=1/2 ground-state atoms. The laser field consists of a pair of counterpropagating, linearly polarized, low-power beams, whose polarization directions differ by an angle \ensuremath{\theta} (0\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}\ensuremath{\pi}/2). For \ensuremath{\theta}\ensuremath{\ll}1, the effective optical-pumping time is shown to increase strongly near the nodes of the standing wave, and the cooling force can be much larger than that for \ensuremath{\theta}=\ensuremath{\pi}/2. Moreover, for \ensuremath{\theta}\ensuremath{\ll}1, it can be shown that the stimulated part of the atomic diffusion is reduced considerably as compared with that for \ensuremath{\theta}=\ensuremath{\pi}/2. As a consequence it is possible to achieve an equilibrium atomic distribution that, for \ensuremath{\theta}\ensuremath{\ll}1, is characterized by a mean kinetic energy that is lower than that predicted to occur for \ensuremath{\theta}=\ensuremath{\pi}/2. The equilibrium velocity distribution is not necessarily Maxwellian, and thus the temperature of the atomic ensemble may not be well defined. The achievable kinetic energy is so small that the cooled atoms may be trapped in the vicinity of the laser-field nodes.
In sub-Doppler laser cooling of atoms, the lowest temperatures are known to occur at low (but not too low) excitation, and the temperature increases roughly linearly with laser intensity. However, under conditions for which the lowest temperatures are obtained, the small velocity capture range and low optical pumping rate limit the number of atoms that can be collected into the cold sample. In this study, we present measurements for laser cooling of Rb and metastable He atoms for two counterpropagating laser beams with orthogonal linear polarization (lin\ensuremath{\perp}lin) over a wide range of saturation parameters and laser detunings, together with results of semiclassical (Fokker-Planck) and quantum density matrix calculations. We find that at higher laser intensity, a larger number of atoms can be collected into a final velocity distribution that is significantly narrower than that given by a linear extrapolation vs the square root of laser intensity. Two cooling mechanisms are at work: the sub-Doppler Sisyphus mechanism and also Doppler cooling. Under certain conditions that we discuss, Doppler cooling aids Sisyphus cooling by collecting high-velocity atoms beyond the Sisyphus capture range. He∗{\mathrm{He}}^{*}He∗ presents a rather unusual situation in that the minimum average kinetic energy (Eav){(E}_{\mathrm{av}})(Eav​) for purely Sisyphus cooling is comparable to the minimum value of Eav{E}_{\mathrm{av}}Eav​ with Doppler cooling alone.
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.