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Physical Review A

Influence of the number of atoms in a ring-shaped magneto-optical trap: Observation of bifurcation

D. Felinto, Luís Gustavo Marcassa, Vanderlei Salvador Bagnato, S. S. Vianna

Published Sep 1, 1999• 11 citations
Publisher

Abstract

The spatial ring-shaped distribution of atoms in a magneto-optical trap, produced by misaligned Gaussian laser beams, is investigated with respect to the increase in the number of trapped atoms. Experimental observation of the bifurcation of a single ring into a double-ring structure is reported and explained using a model that includes radiation force due to reabsorption of photons together with the conventional radiative force.

DOI
10.1103/physreva.60.2591

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Annual Meeting Optical Society of America•Jan 1, 1991•0 citations
The spatial ring-shaped distribution of atoms in a magneto-optical trap, produced by misaligned Gaussian laser beams, is investigated with respect to the increase in the number of trapped atoms. Experimental observation of the bifurcation of a single ring into a double-ring structure is reported and explained using a model that includes radiation force due to reabsorption of photons together with the conventional radiative force.
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.
The different orbital modes that appear from the misalignment of the laser beams in the xy plane of a low-density magneto-optical trap are studied. Using the circular motion approximation, one can obtain a qualitative description of the phenomenon and can calculate the ring radii, the atom’s velocity in the ring, and the trap parameters in which the rings appear. A careful analysis of some theories previously employed in researching this topic shows that they have extrapolation problems that led to unreasonable conclusions. In particular, we compare the results of the circular motion approximation itself with those obtained from a direct numerical integration of the atomic trajectory. Within this approximation the influence of the increase in the number of trapped atoms over the ring is also investigated, and we observe an instability in a ring-shaped structure when the interaction between the atoms is included.
We present the observation of double stable clouds of cold trapped atoms in a magneto-optical trap and its explanation with a simple model based on radiative forces. This structure occurs for a specific misalignment of the trapping laser beams whose Gaussian profiles introduce an extra term in the equation of motion for the trapped atom. We were able to obtain simple analytical expressions for the trap potential and for the separation of the clouds, and carried out a numerical calculation which agrees well with the experimental observations.
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 apply a three-dimensional Doppler Monte Carlo simulation to study fluctuation in magneto-optical traps with various laser beam configurations. First, the temperature and the radius of a lithium trap are calculated with the assumption of exactly counterpropagating beams. The results are compared with previously reported experimental data [Opt. Commun.158, 263 (1998)]. Subsequently, the role of fluctuation in the transition from a ball- to a ring-shaped spatial distribution of atoms is investigated. This transition occurs when the laser beams in the xy plane are progressively misaligned. Finally, the temperature of the atoms in a ring-shaped distribution is determined, and its dependence with the misalignment of the beams is analyzed.
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.