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Journal of Experimental and Theoretical Physics

Three-dimensional theory of the magneto-optical trap

Прудников Олег Николаевич, А. В. Тайченачев, Valeriy I. Yudin

Published Apr 1, 2015• 8 citations
Publisher

Abstract

The kinetics of atoms in a three-dimensional magneto-optical trap (MOT) is considered. A three-dimensional MOT model has been constructed for an atom with the optical transition J g = 0 → J e = 1 (J g, e is the total angular momentum in the ground and excited states) in the semiclassical approximation by taking into account the influence of the relative phases of light fields on the kinetics of atoms. We show that the influence of the relative phases can be neglected only in the limit of low light field intensities. Generally, the choice of relative phases can have a strong influence on the kinetics of atoms in a MOT.

DOI
10.1134/s1063776115040147

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The kinetics of atoms in a three-dimensional magneto-optical trap (MOT) is considered. A three-dimensional MOT model has been constructed for an atom with the optical transition J g = 0 → J e = 1 (J g, e is the total angular momentum in the ground and excited states) in the semiclassical approximation by taking into account the influence of the relative phases of light fields on the kinetics of atoms. We show that the influence of the relative phases can be neglected only in the limit of low light field intensities. Generally, the choice of relative phases can have a strong influence on the kinetics of atoms in a MOT.
We present a quantum theory of a magneto-optical trap (MOT) from first principles based on the quantum kinetic equation for the atomic density matrix with taking into account the recoil effects caused by the interaction of atoms with the laser field. An efficient method for solving the quantum kinetic equation is proposed. It is shown that the steady-state solution describing the atoms in the MOT has a significantly non-equilibrium nature and can be described within the framework of a two-temperature distribution. The momentum distribution of cold atoms in the MOT depends on the magnetic field gradient and, in general, significantly differs from the momentum distribution of atoms in the optical molasses, which is usually used as an approximation to describe the MOT. We have also shown that with an increase in the magnetic field gradient, a spatial two-component distribution of atoms in the trap is formed even for a single particle approximation when interatomic interactions are neglected.
We theoretically investigate the damping and trapping forces in a three-dimensional magneto-optical trap (MOT), by numerically solving the optical Bloch equations.We focus on the case where there are dark states because the atom is driven on a 'type-II' system where the angular momentum of the excited state, F¢, is less than or equal to that of the ground state, F. For these systems we find that the force in a three-dimensional light field has very different behaviour to its one dimensional counterpart.This differs from the more commonly used 'type-I' systems (F F 1 ¢ = + ) where the 1D and 3D behaviours are similar.Unlike type-I systems where, for red-detuned light, both Doppler and sub-Doppler forces damp the atomic motion towards zero velocity, in type-II systems in 3D, the Doppler force and polarization gradient force have opposite signs.As a result, the atom is driven towards a non-zero equilibrium velocity, v 0 , where the two forces cancel.We find that v 0 2 scales linearly with the intensity of the light and is fairly insensitive to the detuning from resonance.We also discover a new magneto-optical force that alters the normal MOT force at low magnetic fields and whose influence is greatest in the type-II systems.We discuss the implications of these findings for the laser cooling and magneto-optical trapping of molecules where type-II transitions are unavoidable in realising closed optical cycling transitions.
We study the magneto-optical trap (MOT) as an optical lattice with a setup providing full phase control for all light fields. Although completely different light fields are possible for various phases, we have found experimental evidence that stored atoms are generally localized in micropotentials of the six-beam lattice. The influence of the phase variation is surprisingly small, suggesting that the robust behavior of the MOT is a consequence of this fact. We find furthermore good agreement of our experimental data with a simple theoretical model which reduces the complicated MOT to a description of steady-state atoms localized at points of the deepest adiabatic light-shift potential.
An overview of the theory of the magneto-optical trap is presented, along with measurements of the effect of an imbalance in the intensities of the trapping beams. This investigation tests the theory of the spring constant of the trap and confirms that the confining force at the center of the trap results from an induced orientation of the atomic ground state. The experimental results give the magnitude of this force, which has not yet been calculated accurately. We calculate the radiation field in the three-dimensional molasses, finding that the relative time phase of the orthogonal standing waves is significant, and we give some insight into the phenomenon of interference fringes when the beams are misaligned. We also discuss the limitation of the trapped atomic density resulting from photon scattering within the cloud, predicting that densities above 1013 atoms/cm3 could be achieved in a trap operating at low saturation of the atomic transition. Finally, we briefly consider collisional loss at low densities, finding an especially large contribution from resonant dipole–dipole scattering.
We derive a Fokker-Planck equation for the center-of-mass Wigner function of an atom moving in a Zeeman neutral-atom trap. The Zeeman structure of atomic sublevels is taken into account. Our analysis is limited to optical transitions between two sets of sublevels corresponding to angular momenta jb{\mathit{j}}_{\mathit{b}}jb​=0 and ja{\mathit{j}}_{\mathit{a}}ja​=1. Expressions for the light pressure, friction, and diffusion forces in the case of low intensity of the laser light are presented. An analytical solution for the stationary center-of-mass Wigner function as well as the size and geometry of the trap are found and discussed.