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Annual Meeting Optical Society of America

Laser cooling and confining of atoms

Leo W. Hollberg, Steven Chu, John E. Bjorkholm, Alex Cable, Arthur Ashkin

Published Jan 1, 1985• 1 citation
Publisher

Abstract

Using six optical beams (+ and − directions on three orthogonal axes) tuned slightly to the red of resonance it is possible to cool sodium atoms to a few hundred microkelvin. The cooling occurs because the laser radiation pressure creates a damping force which reduces the atomic velocities to a rms value of ~60 cm/s, determined by random scattering. In this optical molasses, the laser beams propagate in all directions and the light acts as a viscous photon fluid which damps the atomic velocity. The resulting motion of the sodium atoms is diffusive until the atoms reach the edge of the laser beams where they escape. The process of atomic confinement by optical molasses can be modeled as a random walk in a viscous medium with a boundary. For a spherical volume of 0.2 cm3 the resulting confinement time is ~0.1 s for half of the atoms to escape. Direct time-of-flight measurement of the atomic temperature gives ~240 μK, which agrees with predictions of quantum limited cooling by resonance radiation pressure. With confinement times of 0.1 s and temperatures of ~240 μK this method provides a source of atoms sufficiently slow for even the highest resolution optical spectroscopy, collision studies, or optical traps.

DOI
10.1364/oam.1985.wv2

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Physical Review A•Nov 1, 1992•54 citations
Using six optical beams (+ and − directions on three orthogonal axes) tuned slightly to the red of resonance it is possible to cool sodium atoms to a few hundred microkelvin. The cooling occurs because the laser radiation pressure creates a damping force which reduces the atomic velocities to a rms value of ~60 cm/s, determined by random scattering. In this optical molasses, the laser beams propagate in all directions and the light acts as a viscous photon fluid which damps the atomic velocity. The resulting motion of the sodium atoms is diffusive until the atoms reach the edge of the laser beams where they escape. The process of atomic confinement by optical molasses can be modeled as a random walk in a viscous medium with a boundary. For a spherical volume of 0.2 cm3 the resulting confinement time is ~0.1 s for half of the atoms to escape. Direct time-of-flight measurement of the atomic temperature gives ~240 μK, which agrees with predictions of quantum limited cooling by resonance radiation pressure. With confinement times of 0.1 s and temperatures of ~240 μK this method provides a source of atoms sufficiently slow for even the highest resolution optical spectroscopy, collision studies, or optical traps.
We report the viscous confinement and cooling of neutral sodium atoms in three dimensions via the radiation pressure of counterpropagating laser beams. These atoms have a density of about \ensuremath{\sim}106{10}^{6}106 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ and a temperature of \ensuremath{\sim}240 \ensuremath{\mu}K corresponding to a rms velocity of \ensuremath{\sim}60 cm/sec. This temperature is approximately the quantum limit for this atomic transition. The decay time for half the atoms to escape a \ensuremath{\sim}0.2cm3{\mathrm{cm}}^{3}cm3 confinement volume is \ensuremath{\sim}0.1 sec.
Optical molasses is a three-dimensional (3-D) configuration of laser beams used to laser-cool and to viscously confine neutral atoms. Atoms laser cooled in optical molasses reach temperatures much lower than the limit given by the original theories of laser cooling based on the Doppler effect. This cooling below the Doppler-cooling limit is now seen as being due to new laser cooling mechanisms not considered in the original theories. The dependence of the atomic temperature on parameters such as laser intensity and detuning shows good agreement between calculations performed in 1-D and experiments performed in 3-D. For cooling of Na and Cs atoms, the lowest observed temperatures correspond to rms velocities between three and four times the single photon recoil velocity. For Cs the temperature is 2.5 ± 0.6 μK and is the lowest temperature ever measured for 3-D cooling.
We report the confinement and cooling of an optically dense cloud of neutral sodium atoms by radiation pressure. The trapping and damping forces were provided by three retroreflected laser beams propagating along orthogonal axes, with a weak magnetic field used to distinguish between the beams. We have trapped as many as 107{10}^{7}107 atoms for 2 min at densities exceeding 1011{10}^{11}1011 atoms ${\mathrm{cm}}^{\ensuremath{-}3}$. The trap was \ensuremath{\simeq}0.4 K deep and the atoms, once trapped, were cooled to less than a millikelvin and compacted into a region less than 0.5 mm in diameter.
We present a simple review of the basic physical processes allowing one to control, with laser beams, the velocity and the position of neutral atoms. The control of the velocity corresponds to a cooling of atoms, that is, a reduction of the atomic velocity spread around a given value. The control of the position means a trapping of atoms in real space. The best present performances will be given, in terms of the lowest temperatures and the highest densities. The corresponding highest quantum degeneracy will also be estimated. It is imposed by fundamental limits, which will be described briefly. We also give the general trends in this field of research and outline the new directions which look promising for observing quantum statistical effects in laser cooled atomic samples, but which are for the moment restricted by unsolved problems. Introducing the Simple Schemes The radiative forces acting on atoms in a light field can be split into two parts, a reactive one and a dissipative one. The dissipative force (radiation pressure), which basically involves scattering processes, is velocity dependent. We will see that this dependence leads to the Doppler cooling scheme and to the concept of optical molasses, and we will give the corresponding minimal achievable temperature. The dissipative force can be made position dependent, through a gradient of the magnetic field, so that the atoms are also trapped in the so-called magneto-optical trap.
The force acting on a two-level atom in a low-intensity standing laser wave is calculated. On account of this force, atoms can be trapped at the loops (antinodes) of the field. By quantizing the atomic motion near the bottom of the sinusoidal potential, we have studied the atomic behavior when they are trapped in bound states as well as when they are in the free state. Laser cooling of neutral atoms was first suggested by T. Hansh and A. Schawlow in 1975. The principle involves the Doppler effect in a detuned laser beam. The absorption rate of a photon depends on the apparent frequency of the photon that is shifted ωv/c\omega v/cωv/c from ω\omegaω, where ω\omegaω is the frequency of the laser, v is the velocity of the atom, and c is the velocity of light. For a single laser beam detuned slightly below an atomic resonance frequency, the apparent frequency for atoms moving toward the laser is closer to resonance, which causes a higher absorption rate. And these atoms lose momentum when they absorb a photon from the beam. The velocity of atoms can be decreased from 10$\sp5$ cm/sec, the velocity they have when they escape from an oven, to 10$\sp2$ cm/sec (about 1mK) by a laser beam. For further cooling, counterpropagating beams are necessary. In this study we propose a new mechanism for supercooling, that is, cooling well below the Doppler cooling limit. Within a standing laser wave there exists a force called a "dipole force", which has a sinusoidal spatial dependence. Once atoms are trapped by the potential, their motion around the minimum of the potential well is that of a simple harmonic oscillator. Restricting our attention to the two lowest quantized states, we calculate transition rates between free states and bound states, from which the average residence times in the bound states can be obtained. This first quantum treatment of an atom trapped in the sinusoidal potential is restricted to the one-dimensional case. Generalization to higher dimensions is left for future research.
We describe a numerical implementation of our semiclassical laser-cooling theory [J. Javanainen, Phys. Rev. A 44, 5857 (1991)] for an arbitrary multilevel atom and light field. There is satisfactory agreement between experiments and temperatures obtained from Langevin-equation simulations of the motion of an atom subject to light-pressure force and the accompanying diffusion in three-dimensional (3D) optical molasses in which there are three orthogonal pairs of counterpropagating waves with a common linear polarization for the two beams in a pair, but orthogonal polarizations between the pairs. However, the velocity distribution of the atoms is anisotropic and may deviate strongly from a Gaussian, heterodyne spectra may have a sideband, and the atomic density may be a maximum at the maximum of the potential of the dipole forces of the molasses beams. Subsequent velocity-linearized analysis of atomic damping and diffusion shows that the damping tensor may have a negative eigenvalue corresponding to heating in large regions of space, even though the light is red tuned for cooling. It is also found that the position-averaged damping and diffusion tensors make a poor predictor of the temperature obtained in Langevin-equation simulations and real experiments. Based on additional simulations of a simple 1D model, we formulate a hypothesis that connects our findings. The key idea is that an atom trapped in a minimum of the potential of the dipole forces is subject to a weaker-than-average damping, and therefore tends to boil out of the trap.