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Journal of the Optical Society of America B

Orbital modes in low-density magneto-optical traps

D. Felinto, S. S. Vianna

Published May 1, 2000• 4 citations
Publisher

Abstract

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.

DOI
10.1364/josab.17.000681

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Annual Meeting Optical Society of America•Jan 1, 1991•0 citations
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 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.
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 results of numerical simulations to justify the origin of the width in ring-shaped atomic distributions of cold atoms held in a magneto-optical trap. We have considered the effects of laser fluctuations (phase and intensity) and the presence of recoil due to spontaneous emission. The results show that the occurrence of spontaneous emission accounts for the existence of a width in the atomic trajectory while laser fluctuations only change the average value of the atomic orbit. \textcopyright{} 1996 The American Physical Society.
We approach the problem of NNN atoms in a magneto-optical trap through a hierarchical tree method, using an algorithm originally developed by Barnes and Hut (BH) in the astrophysical context. Such an algorithm numerically takes care of the particle-particle interaction by controlling the approximation level in a way that offers more physical fidelity than the mean-field treatment and considerably less time consumption ($\ensuremath{\tau}\ensuremath{\sim}N\phantom{\rule{0.3em}{0ex}}{\mathrm{log}}_{10}\phantom{\rule{0.3em}{0ex}}N$ in the hierarchical BH method, in contrast with the $\ensuremath{\tau}\ensuremath{\sim}{N}^{2}$ and $\ensuremath{\tau}\ensuremath{\sim}{N}^{3∕2}$ dependences found in direct and mean-field approaches, respectively). Our results reproduce the experimentally reported single-ring orbital mode for $N\ensuremath{\lesssim}{10}^{6}$ atoms and also find indication of a double-ring structure for $N\ensuremath{\sim}{10}^{7}$, a situation mimicked by a N=106N={10}^{6}N=106 system with enhanced radiative force, in agreement with experimental observations. We stress that this high-density regime is not accessed by direct integration of the equations of motion, due to the enormous computing times required, and is not suitably described through mean-field approaches, due to the rather unphysical enhancement of the particle-particle interactions and the presence of a spurious numerical grid dependence.
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.