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Quantum Electronics and Laser Science Conference

Localization of atoms in light standing wave on microscopic (~λ) and macroscopic (≫λ) spatial scales

V. I. Balykin, Rudolf Grimm, Vladilen S Letokhov, Y. B. Ovchinnicov, A. I. Sidorov

Published May 12, 1991• 0 citations
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Abstract

We have investigated the localization of atoms in two configurations of laser fields: monochromatic and bichromatic standing waves. A quasi resonant monochromatic laser field creates a spatially periodic potential field with period equal to half of the wavelength. If the atomic kinetic energy is less than the height of the potential wells then atoms could be trapped in the wells. The motion of atoms in a standing wave is governed by the gradient force, friction force, and momentum diffusion. We studied one dimensional localization of sodium atoms in such a standing wave, as well as the influence of friction and diffusion on the motion of these atoms. The effect of accumulation of atoms at the bottom of potential wells (nodes of a standing wave) was observed. This leads to a new scheme of laser cooling of atoms with a minimum temperature below the Doppler limit.

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This chapter provides a brief review of the recent theoretical and experimental results of channeling of atoms in the standing wave. It considers the channeling (one dimensional localization) of atoms in two configurations of the laser fields: a monochromatic and a bichromatic one dimensional laser fields. A quasi resonant monochromatic laser field creates a spatially periodic potential field with a period equal to a half of the wavelength. When atomic beam crosses standing wave and atoms have a low enough kinetic energy, they are guided into the channels where they move along the channel and oscillate in the transverse direction. To detect this channeling the atoms have been chosen themselves as probes of their position. A scheme of a cooling of atoms through their channeling is based on the adiabatic lowering the standing wave intensity.

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Cooling and trapping of three-level atoms in a bichromatic standing wave

Han Pu, Tianwu Cai, N. P. Bigelow +2 more

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In two recent experiments Verkerk et al. and our group have observed quantization of the center-of-mass motion of laser cooled atoms in sub-wavelength sized potential wells formed by the light field of a 1-dimensional optical molasses. Our 1-dimensional optical molasses consists of a pair of counterpropagating laser beams of orthogonal, linear polarization, creating a series of potential wells separated by {lambda}/4. Polarization gradient laser cooling reduces the thermal energy of the atoms until they are trapped in well resolved vibrational levels near the bottom of the wells. Transitions between these vibrational levels are seen in a high resolution spectrum of fluorescence, where they give rise to a Rayleigh peak centered at the laser frequency, and well resolved Raman sidebands shifted by a frequency {plus_minus}{omega}, typically on the order of 100 kHz. We find quantitative agreement between the measured level separation h{omega} and the results of a calculation of the bandstructure in the periodic optical potential. Based on the observed ratio of the strength of the blue to the red sideband we determine the temperature of the atoms, and find agreement with theoretical predictions. Based on the level spacing and temperature we find the atoms to be localized to {approx}/15, withmore » up to 50-60% of the population of the trapped atoms in the vibrational ground state. We observe intriguing differences between fluorescence radiated by localized atoms, and the fluorescence radiated by non-localized atoms in a 1-dimensional optical molasses composed of a pair of counterpropagating laser beams of opposite circular polarization. The prospect of observing quantum motion and spatial order in 2 and 3 dimensions, and the consequences for the spectrum of fluorescence, will be discussed.« less

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

Quantum Trapping of Atoms in Optical Molasses.

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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 $\omega v/c$ from $\omega$, where $\omega$ 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.

•Oct 1, 1992•0 citations
We have investigated the localization of atoms in two configurations of laser fields: monochromatic and bichromatic standing waves. A quasi resonant monochromatic laser field creates a spatially periodic potential field with period equal to half of the wavelength. If the atomic kinetic energy is less than the height of the potential wells then atoms could be trapped in the wells. The motion of atoms in a standing wave is governed by the gradient force, friction force, and momentum diffusion. We studied one dimensional localization of sodium atoms in such a standing wave, as well as the influence of friction and diffusion on the motion of these atoms. The effect of accumulation of atoms at the bottom of potential wells (nodes of a standing wave) was observed. This leads to a new scheme of laser cooling of atoms with a minimum temperature below the Doppler limit.
This chapter provides a brief review of the recent theoretical and experimental results of channeling of atoms in the standing wave. It considers the channeling (one dimensional localization) of atoms in two configurations of the laser fields: a monochromatic and a bichromatic one dimensional laser fields. A quasi resonant monochromatic laser field creates a spatially periodic potential field with a period equal to a half of the wavelength. When atomic beam crosses standing wave and atoms have a low enough kinetic energy, they are guided into the channels where they move along the channel and oscillate in the transverse direction. To detect this channeling the atoms have been chosen themselves as probes of their position. A scheme of a cooling of atoms through their channeling is based on the adiabatic lowering the standing wave intensity.
We show that a three-level atom in the cascade configuration can be stably trapped and cooled in one dimension by an intense bichromatic standing wave. At the two-photon resonance, rectified dipole forces result in a deep potential well which can be used to localize the atoms in space. In the vicinity of the rectified potential minimum, the spatial dependence of the dressed state energies can lead to a velocity dependence of the force which produces damping of the atomic motion. Consideration of the heating effects of momentum diffusion indicates that cooling and stable trapping at low temperatures is possible in such a bichromatic field.
This chapter reviews the investigations performed at the Institute of Spectroscopy into this non-linear optic effect. The motion of an atom in a standing light wave is governed by the gradient force of potential nature. When the atomic transition saturation parameter is much less than unity and the atom-light-field interaction time is such that the change in the atomic momentum due to friction and diffusion is insignificant, both the friction force and atomic momentum diffusion can be disregarded. One of the manifestations of the atomic channelling effect in a standing light wave is the concentration of atoms near the nodes or loops of the wave. An atom can be localized in a spherical standing light wave if its trajectory is tangent to the wave front at the entrance point, the gradient force exceeds the centrifugal force, and the field intensity grows higher in the direction of atomic motion.
In two recent experiments Verkerk et al. and our group have observed quantization of the center-of-mass motion of laser cooled atoms in sub-wavelength sized potential wells formed by the light field of a 1-dimensional optical molasses. Our 1-dimensional optical molasses consists of a pair of counterpropagating laser beams of orthogonal, linear polarization, creating a series of potential wells separated by {lambda}/4. Polarization gradient laser cooling reduces the thermal energy of the atoms until they are trapped in well resolved vibrational levels near the bottom of the wells. Transitions between these vibrational levels are seen in a high resolution spectrum of fluorescence, where they give rise to a Rayleigh peak centered at the laser frequency, and well resolved Raman sidebands shifted by a frequency {plus_minus}{omega}, typically on the order of 100 kHz. We find quantitative agreement between the measured level separation h{omega} and the results of a calculation of the bandstructure in the periodic optical potential. Based on the observed ratio of the strength of the blue to the red sideband we determine the temperature of the atoms, and find agreement with theoretical predictions. Based on the level spacing and temperature we find the atoms to be localized to {approx}/15, withmore » up to 50-60% of the population of the trapped atoms in the vibrational ground state. We observe intriguing differences between fluorescence radiated by localized atoms, and the fluorescence radiated by non-localized atoms in a 1-dimensional optical molasses composed of a pair of counterpropagating laser beams of opposite circular polarization. The prospect of observing quantum motion and spatial order in 2 and 3 dimensions, and the consequences for the spectrum of fluorescence, will be discussed.« less
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.