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Optics Letters

Dynamical stabilization: a new model for supermolasses

Vanderlei Salvador Bagnato, N. P. Bigelow, Gregory I. Surdutovich, Sérgio Carlos Zílio

Published Oct 1, 1994• 10 citations
Publisher

Abstract

We present an analytical treatment of the force on a two-level atom interacting with a three-dimensional optical molasses. We show that, for small misalignment of the molasses light fields, corresponding to the so-called supermolasses configuration, there can be a dynamically induced stabilization of the atomic motion. This stabilization increases the time required for the atom to diffuse out of the molasses region and therefore provides a novel explanation of experimental observations. We describe the stabilization effect by analogy with the stabilization of the Kapitza pendulum, which is subject to a harmonic modulation of the pendulum pivot point.

DOI
10.1364/ol.19.001568

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Journal of the Optical Society of America B•Nov 1, 1989•367 citations
We present an analytical treatment of the force on a two-level atom interacting with a three-dimensional optical molasses. We show that, for small misalignment of the molasses light fields, corresponding to the so-called supermolasses configuration, there can be a dynamically induced stabilization of the atomic motion. This stabilization increases the time required for the atom to diffuse out of the molasses region and therefore provides a novel explanation of experimental observations. We describe the stabilization effect by analogy with the stabilization of the Kapitza pendulum, which is subject to a harmonic modulation of the pendulum pivot point.
Supermolasses1 which holds atoms much longer than the ordinary optical molasses and inhomogeneities in the distribution of atoms in optical molasses2 are current cases of unexpected spatial properties of optically cooled and/or trapped atom clouds. As a speculative explanation, I put forward that mixing of the wave vectors of the driving light field which takes place on a multistate atom produces long wavelength optical forces, whose effect on the motion of the atom enormously exceeds the influence of the forces familiar from two-state atomic models.
Researchers in Germany and France have bound neutral atoms in regular two- and three-dimensional lattices induced by the interference patterns of several laser beams. The work builds on the techniques of magnetooptical trapping and sub-Doppler laser cooling and on previous work in which atoms were bound in onedimensional standing waves of light. The fields of light in these techniques are called optical molasses, because atoms within them experience viscous forces, which cool the atoms to temperatures on the order of microkelvins. In the new, “crystalline” molasses, the standing waves produce a stable, regular array of potential wells—a microscopic “egg carton”— and the atoms become localized at the bottoms of the wells.
We study theoretically the spectrum of resonance fluorescence and laser-cooling dynamics corresponding to quantized atomic motion in one-dimensional optical molasses. We consider an atom with a Jg{\mathit{J}}_{\mathit{g}}Jg​=1\ensuremath{\rightarrow}Je{\mathit{J}}_{\mathit{e}}Je​=2 transition interacting with two counterpropagating laser beams. The laser light is assumed to be linearly polarized with an angle \ensuremath{\theta} between the polarization vectors. We discuss the spectrum of resonance fluorescence, the spectroscopy of band structure in the optical potentials, and the population of the vibrational quantum levels as a function of the angle between the polarization vectors.
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.
A theoretical analysis is given for laser cooling of a two-level atom with magnetic sublevels in the presence of polarization gradients. The optical Bloch equations for the multilevel system are solved numerically for four combinations of polarizations in one-dimensional optical molasses. The light-pressure force on the atom as given by a simple two-level theory is recovered in the absence of polarization gradients, whereas a spatial variation of the polarization is found to lead to a strong cooling force for slow atoms. The increased cooling force is responsible for the recent observations of atoms cooled in optical molasses to temperatures an order of magnitude below the Doppler limit.