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Journal of Experimental and Theoretical Physics

Magnetooptical force in the resonance field formed by elliptically polarized light waves

Прудников Олег Николаевич, A. V. Taǐchenachev, Anatolii M Tumaikin, Valeriy I. Yudin

Published May 1, 2008• 1 citation
Publisher

Abstract

The dependence of the magnetooptical force on the ellipticity of the polarization of light beams is studied in terms of a one-dimensional model for closed J g → J e optical transitions. A linear velocity and magnetic-field approximation is used to find analytical expressions for the magnetooptical force for a number of transitions. In the light fields formed by waves with an elliptical polarization, qualitatively new contributions are shown to appear; they have an even dependence on the detuning of the light field and do not disappear even in the case of an exact resonance. An analysis of these results demonstrates that a magnetooptical trap can stably operate at the zero detuning of the field. Numerical methods are used to investigate the nonlinear dependence of the force on the atom velocity and the magnetic field and to estimate the characteristic atom trapping rate and the number of trapped atoms.

DOI
10.1134/s1063776108050014

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The dependence of the magnetooptical force on the ellipticity of the polarization of light beams is studied in terms of a one-dimensional model for closed J g → J e optical transitions. A linear velocity and magnetic-field approximation is used to find analytical expressions for the magnetooptical force for a number of transitions. In the light fields formed by waves with an elliptical polarization, qualitatively new contributions are shown to appear; they have an even dependence on the detuning of the light field and do not disappear even in the case of an exact resonance. An analysis of these results demonstrates that a magnetooptical trap can stably operate at the zero detuning of the field. Numerical methods are used to investigate the nonlinear dependence of the force on the atom velocity and the magnetic field and to estimate the characteristic atom trapping rate and the number of trapped atoms.
In a one-dimensional model we consider the dependence of the magneto-optical force on the elliptical polarization of laser beams for different types of closed atomic transitions ${J}_{g}\ensuremath{\rightarrow}{J}_{e}$. The linear dependencies on atomic velocity and magnetic field of the magneto-optical force are found analytically. These results establish the possibility (for Jg>0{J}_{g}>0Jg​>0) to capture atoms in a magneto-optical trap even at zero detuning (i.e., at the exact resonance of atoms with laser field) in certain $(ϵ\ensuremath{-}\ensuremath{\theta}\ensuremath{-}\overline{ϵ})$ field configurations as well as in an anomalous blue-detuned region. The nonlinear dependencies of the force on atomic velocity and magnetic field are studied numerically. The capture velocity and the number of trapped atoms are estimated.
The rectification of the force of induced light pressure in laser fields formed by elliptically polarized running waves in zero magnetic field is considered. Explicit analytic expressions for the induced and spontaneous forces of light pressure exerted on a stationary atom are obtained for two classes of closed optical transitions: J g = J → J e = J +1 and J g = J → J e = J ( J is half-integral), where J g and J e are the total angular momenta of the ground and excited energy levels. It is shown that the ellipticity of waves is the necessary condition for the emergence of the rectification of the induced force in a monochromatic field. The optimal parameters of the field and the maximum rectification coefficient are calculated for a number of optical transitions. The dependence of the rectified force on the velocity is investigated analytically and numerically for the simplest 1/2→1/2 transition.
The kinetics of atoms with degenerate energy levels in the field produced by elliptically polarized waves is considered in the semiclassical approximation. Analytic expressions for the force acting on an atom and for the diffusion coefficient in the momentum space are derived for the optical transition J g =1/2→J e = 1/2 in the slow atom approximation. These expressions are valid for an arbitrary one-dimensional configuration of the light field and for an arbitrary intensity. The peculiarities of the atomic kinetics are investigated in detail; these peculiarities are associated with ellipticity of light waves and are absent in particular configurations formed by circularly or linearly polarized waves, which were considered earlier.
A theoretical analysis is made of the resonant interaction between a traveling monochromatic light wave of arbitrary intensity and polarization and the 1/21/2 and 10 transitions in gas atoms in a magnetic field. An analysis is made of the influence of atomic collisions and coherence of the Zeeman sublevels of the terms on the structure of nonlinear magnetooptic resonances in the amplitude and polarization characteristics of the wave. Some features of nonlinear magnetooptic resonances for laser excitation of atoms from the ground state are noted. A study is made of the Faraday rotation and self-rotation of the polarization ellipse of the radiation as a function of the detuning of the wave frequency, the saturation parameter, and the optical density of the gas. The stability of the polarization of light in the medium is discussed. It is noted that these laws may be used to analyze and control the radiation characteristics of lasers and amplifiers when the level of saturation of a resonant gaseous medium in a magnetic field is high.
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.