Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Two-dimensional forces and atomic motion in a sub-Doppler limit

Vladimir Finkelstein, Jingzhong Guo, P. R. Berman

Published Dec 1, 1992• 4 citations
Publisher

Abstract

A theoretical analysis is given of the interaction of a laser field consisting of two orthogonal, linearly polarized, low-power standing waves, with an ensemble of J=1/2 ground-state atoms. The atoms are assumed to move with velocities below the Doppler limit of laser cooling. The two-dimensional light-induced atomic force is calculated for the specific case when the field polarization directions differ by \ensuremath{\pi}/2. The effective optical-pumping time is shown to increase strongly near the nodes of the laser field, leading to a force that can be much larger than that in the one-dimensional case. The force is not isotropic, and can lead to the bunching of the atoms in velocity space.

DOI
10.1103/physreva.46.7108

Related papers

One-dimensional sub- Doppler laser cooling

Vladimir Finkelstein, P. R. Berman, Jingzhong Guo

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.

Annual Meeting Optical Society of America•Jan 1, 1991•0 citations

One-dimensional laser cooling below the Doppler limit

Vladimir Finkelstein, P. R. Berman, Jingzhong Guo

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.

Physical Review A•Feb 1, 1992•48 citations

Laser cooling below the Doppler limit by polarization gradients: simple theoretical models

Jean Dalibard, Claude N. Cohen-Tannoudji

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.

Journal of the Optical Society of America B•Nov 1, 1989•1,272 citations

Anomalous Doppler-Effect and Polariton-Mediated Cooling of Two-Level Atoms

P. Domokos, András Vukics, Helmut Ritsch

We consider an atom moving in a near resonant laser field with its dipole strongly coupled to a resonator field mode. As compared to the standard Doppler shift, we find a substantially different and counterintuitive linear velocity dependence of the light scattering properties. The mechanical force of the laser field exhibits strong velocity selectivity at a polariton resonance, which gives rise to an enhanced friction force and Doppler cooling even in the directions perpendicular to the resonator axis. This effect allows for sub-Doppler cooling of atoms even with a nondegenerate ground state.

Physical Review Letters•Mar 11, 2004•22 citations

One-dimensional laser cooling with linearly polarized fields

Jun Guo, P. R. Berman

We present a calculation of one-dimensional sub-Doppler cooling of neutral atoms, in which the atomic center-of-mass motion is quantized. The cooling field consists of a pair of counterpropagating, linearly polarized laser beams, with their polarizaton vectors at an angle \ensuremath{\theta} with respect to each other. The steady-state atomic density matrix is analyzed as a function of \ensuremath{\theta}. It is shown that, depending on the internal atomic level scheme, the equilibrium population of the quantized ground state of atomic center-of-mass motion can either increase or decrease significantly when \ensuremath{\theta} is reduced from \ensuremath{\pi}/2. These effects are interpreted based on the spatial localization of atoms in the light-induced potential wells.

Physical Review A•Oct 1, 1993•30 citations

One-dimensional motion of slow atoms in a standing-wave field

Y. Z. Wang, Weibin Cai, Y. D. Cheng +3 more

Using an atomic beam we have experimentally observed the one-dimensional motion of atoms in a standing-wave field. The dependence of the laser-cooling effect on the saturation parameter has been measured, and the velocity bunching of atoms has been observed. The results have been compared with the two-level theory of a light-pressure force.

Physical Review A•Oct 1, 1990•8 citations
A theoretical analysis is given of the interaction of a laser field consisting of two orthogonal, linearly polarized, low-power standing waves, with an ensemble of J=1/2 ground-state atoms. The atoms are assumed to move with velocities below the Doppler limit of laser cooling. The two-dimensional light-induced atomic force is calculated for the specific case when the field polarization directions differ by \ensuremath{\pi}/2. The effective optical-pumping time is shown to increase strongly near the nodes of the laser field, leading to a force that can be much larger than that in the one-dimensional case. The force is not isotropic, and can lead to the bunching of the atoms in velocity space.
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.
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.
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.
We consider an atom moving in a near resonant laser field with its dipole strongly coupled to a resonator field mode. As compared to the standard Doppler shift, we find a substantially different and counterintuitive linear velocity dependence of the light scattering properties. The mechanical force of the laser field exhibits strong velocity selectivity at a polariton resonance, which gives rise to an enhanced friction force and Doppler cooling even in the directions perpendicular to the resonator axis. This effect allows for sub-Doppler cooling of atoms even with a nondegenerate ground state.
We present a calculation of one-dimensional sub-Doppler cooling of neutral atoms, in which the atomic center-of-mass motion is quantized. The cooling field consists of a pair of counterpropagating, linearly polarized laser beams, with their polarizaton vectors at an angle \ensuremath{\theta} with respect to each other. The steady-state atomic density matrix is analyzed as a function of \ensuremath{\theta}. It is shown that, depending on the internal atomic level scheme, the equilibrium population of the quantized ground state of atomic center-of-mass motion can either increase or decrease significantly when \ensuremath{\theta} is reduced from \ensuremath{\pi}/2. These effects are interpreted based on the spatial localization of atoms in the light-induced potential wells.