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Physical Review A

Theoretical analysis of the spatial structures of atoms in magneto-optical traps

I. Guedes, Humberto F. Silva Filho, Frederico Dias Nunes

Published Jan 1, 1997• 4 citations
Publisher

Abstract

In this work, we present a theoretical study of the origin of the spatial structures in the conventional magneto-optical trap by using a numerical model based on the solutions of the equations of motion of trapped atoms, in the limit where the radiation trapping force is not relevant. Some results relating to the comparison between the experimental and theoretical data are reported. Also, we show that this same analysis can be employed to describe the spatial structures formation in atomic beams.

DOI
10.1103/physreva.55.561

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In this work, we present a theoretical study of the origin of the spatial structures in the conventional magneto-optical trap by using a numerical model based on the solutions of the equations of motion of trapped atoms, in the limit where the radiation trapping force is not relevant. Some results relating to the comparison between the experimental and theoretical data are reported. Also, we show that this same analysis can be employed to describe the spatial structures formation in atomic beams.
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.
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.
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.
A single-particle kinetic theory of the magneto-optical trap (MOT) for cold atoms is developed for a multilevel dipole interaction scheme. The theory analyzes the one-dimensional motion of (3+5)(3+5)(3+5)-level atoms in an inhomogeneous magnetic field and in the field of two counterpropagating circularly polarized laser waves. It is shown that in multilevel interaction schemes two-photon and generally even-order multiphoton processes are responsible for the formation of the narrow velocity and spatial structures in the radiation pressure force. The structures are located at zero velocity and near the origin of the trap. It is found that in the case of a (3+5)(3+5)(3+5)-level atom, single- and two-photon processes produce the two-component structure of the MOT potential well. Near the bottom of a conventional spatially broad potential well caused by one-photon processes, there is a much narrower well caused by two-photon processes. The double-structure MOT potential well is shown to be responsible for the two-component spatial distribution of the trapped atomic cloud. It is proposed that tight confinement of atoms near the narrow bottom of the MOT potential well can be used for the creation of a pointlike source of cold atoms for various applications in atom optics.
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.