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Annual Meeting Optical Society of America

Vortex forces in magneto-optical traps for cesium and sodium: justification for spatial structures

Gregory I. Surdutovich, Ritta Z. Vitlina, Marcos Oriá, Luís Gustavo Marcassa, Sérgio Carlos Zílio, Vanderlei Salvador Bagnato

Published Jan 1, 1992• 0 citations
Publisher

Abstract

In this communication we show that the existence of previously observed spatial structures—balls, rings, and rings with balls—in MOT experiments with Cs (Ref. 1) and Na (Ref. 2) can be explained from a single general viewpoint, through the use of vortex forces.1, 2 The theory uses the saturable aspect of the vortex forces that originates from shifted Gaussian laser beams in MOT experiments and the coordinate dependences of the vortex forces. Depending on the conditions of saturation, any of the above observed structures can be explained only with spontaneous radiative forces. High saturation regimes and moderate detunings provide conditions for the formation of rings with a central ball. Moderated saturation and larger detunings provide conditions for formation of rings without a central ball. We apply the present theory to the experiments of Ref. 1.

DOI
10.1364/oam.1992.thgg4

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In this communication we show that the existence of previously observed spatial structures—balls, rings, and rings with balls—in MOT experiments with Cs (Ref. 1) and Na (Ref. 2) can be explained from a single general viewpoint, through the use of vortex forces.1, 2 The theory uses the saturable aspect of the vortex forces that originates from shifted Gaussian laser beams in MOT experiments and the coordinate dependences of the vortex forces. Depending on the conditions of saturation, any of the above observed structures can be explained only with spontaneous radiative forces. High saturation regimes and moderate detunings provide conditions for the formation of rings with a central ball. Moderated saturation and larger detunings provide conditions for formation of rings without a central ball. We apply the present theory to the experiments of Ref. 1.
In this report we present the experimental observation of rings of sodium atoms in a cold vapor cell and a theoretical model based in the existence of vortex forces leading to stable circular orbits. The apparatus for this experiment consists of a Zeeman-shift spontaneous-force trap(1), similar to the one used for Cs atoms(2). The magnetic field is produced by a pair of anti-Helmholtz coils and the three circularly polarized retro-reflected laser beams are tuned to the 3S1/2 (F=2) → 3P3/2 (F=3) transition of sodium. All laser beams carry a 1712 Mz sideband frequency working as a repumper for atoms in the 3S1/2 (F=1) ground state. When all beams are well aligned with respect to the retro-reflection and magnetic field and are detuned 10 MHz below resonance, we observe a bright ball with 1 to 2 mm at the trap center. If one of the beams is misaligned by a small rotation of the retro-reflector, the initially spheric ball deforms to a dwell shape. When a second beam is also misaligned, the formation of a ring is observed. The ring increases its radius and keeps the same width as the laser is scanned to larger values of red detunings, as shown in Fig. 1. For detunings larger than Δ = 25 MHz the ring disappears. By adding a small misalignment to the third orthogonal beam we observed a change of the plane where the ring is formed.
We investigated how the size of ring-shaped clouds of cold, magneto-optically trapped sodium atoms depends on the trapping parameters: magnetic-field gradient and laser intensity, detuning, and misalignment. The experiments were carried out in the low-density regime (N < 106 atoms), and the ring radius was shown to be independent of the number of trapped atoms. The results are explained with a simple model including a coordinate-dependent vortex force and the usual magneto-optical trap forces.
We present a theoretical analysis to explain the origin of different spatial distributions of laser-cooled sodium atoms in a magneto-optical trap. Such distributions, which include spherical clouds, rings, and rings with cores, are attributed to the radiation pressure due to misaligned Gaussian beams acting on each individual atom. The predictions of this theory are confirmed by experimental observations reported earlier. We were able to construct a diagram with several domains corresponding to the stable structures observed.
Since the first proposal and the first experiment on magneto-optical trapping of atoms, magneto-optical traps (MOT) became the most popular traps for cold atoms. Despite the numerous successful applications of MOT it is still unclear what ultimate parameters could be expected for atoms trapped in MOT. We develop the theory of MOT for cold atoms under the multilevel dipole interaction schemes. Theory is based on consideration of one-dimensional motion of atoms which have three ground-state sublevels (F/sub g/=1) and five upper-state sublevels (F/sub e/=2) and are in inhomogeneous magnetic field and in the field of two counter-propagating circular polarized laser waves. It is shown that in multilevel interaction schemes two-photon processes are responsible for formation of a narrow velocity and spatial structure in the radiation force. It is found that two-photon coherent process enhances considerably the friction force and the oscillation frequency at negative detuning. Single-photon and two-photon processes are shown to produce the two-component structure of the MOT potential and accordingly the two-component coordinate distribution.