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Physical Review A

Magneto-optical rotation in atomic transitions between levels with J=0 and J=1

F. Schuller, Derek N. Stacey

Published Aug 1, 1999• 14 citations
Publisher

Abstract

We give a density-matrix account of an atom in a dilute vapor which is subject to a magnetic field and through which is propagating plane-polarized monochromatic light with frequency in the vicinity of a transition between levels of total angular momenta $J=0$ and 1, where the degeneracy may be in either the upper or lower level. The master equation approach allows saturation effects to be treated in a nonperturbative manner, and collisions are included within the context of the impact approximation. The particular case of the Voigt effect in a $(\stackrel{\ensuremath{\rightarrow}}{1}0)$ transition (lower level $J=1$) is considered in detail, and contrasted with that in $(\stackrel{\ensuremath{\rightarrow}}{0}1),$ already published; in the absence of collisions, the $(\stackrel{\ensuremath{\rightarrow}}{1}0)$ rotation spectrum is of Lorentzian form at all intensities, while if collisional relaxation is much faster than radiative decay, it takes the same form as for the $(\stackrel{\ensuremath{\rightarrow}}{0}1)$ case. The rotation produced by a magnetic field of arbitrary direction and the effects of atomic motion are also discussed.

DOI
10.1103/physreva.60.973

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•Dec 1, 1997•0 citations
We give a density-matrix account of an atom in a dilute vapor which is subject to a magnetic field and through which is propagating plane-polarized monochromatic light with frequency in the vicinity of a transition between levels of total angular momenta J=0J=0J=0 and 1, where the degeneracy may be in either the upper or lower level. The master equation approach allows saturation effects to be treated in a nonperturbative manner, and collisions are included within the context of the impact approximation. The particular case of the Voigt effect in a (1\ensuremath→0)(\stackrel{\ensuremath{\rightarrow}}{1}0)(1\ensuremath→​0) transition (lower level J=1J=1J=1) is considered in detail, and contrasted with that in (0\ensuremath→1),(\stackrel{\ensuremath{\rightarrow}}{0}1),(0\ensuremath→​1), already published; in the absence of collisions, the (1\ensuremath→0)(\stackrel{\ensuremath{\rightarrow}}{1}0)(1\ensuremath→​0) rotation spectrum is of Lorentzian form at all intensities, while if collisional relaxation is much faster than radiative decay, it takes the same form as for the (0\ensuremath→1)(\stackrel{\ensuremath{\rightarrow}}{0}1)(0\ensuremath→​1) case. The rotation produced by a magnetic field of arbitrary direction and the effects of atomic motion are also discussed.
The nonlinear magneto-optical rotation in a medium consisting of $J=1\ensuremath{\rightarrow}J=0$ atoms placed in a static magnetic field is studied. The density matrix approach and irreducible atomic basis are used to describe the state of the atomic system. The stationary propagation equations for two collinear laser beams with perpendicular circular polarizations are derived and analyzed in the case of the magnetic field perpendicular to the light propagation direction. The effect of the linear polarization rotation toward the direction parallel or perpendicular to the magnetic field vector and lossless propagation of the resulting light are predicted. The conversion of the circularly polarized beam into linearly polarized one is shown. The propagation of the leading edges of switched on cw-laser beams and their stationary propagation are analyzed numerically. The dependence of the considered effects on the light detuning and on the additional magnetic field component parallel to the light propagation direction is discussed. The destructive role of the collisional relaxation is demonstrated.
For atomic media with resonant Doppler-broadened transitions of J=0 to J'=1 or J=1 to J'=0 type and taking into account the relaxation due to depolarizing collisions a theory of nonlinear magneto-optic polarization phenomena is developed. The theory is valid in the case of both arbitrary resonance linearly-polarized radiation intensity and arbitrary external magnetic field spatial orientation. The Faraday and Voigt geometries are analysed in detail, and in the case of the Faraday geometry the effect is considered of a noncompensated magnetic field transverse component on the shape of a dependence relating the radiation polarization plane rotation angle to a magnetic field longitudinal component. In the case of the Voigt geometry an essential effect is found of the angle between the radiation initial polarization and transverse magnetic field vectors on the character of the dependence relating the radiation polarization plane rotation angle to the transverse magnetic field magnitude.
In a previous paper, I have presented a general theory of the optical pumping of atoms by a polarized multimode-laser beam, in the presence of a magnetic field. Equations of motion, valid at arbitrary laser intensities for the density matrix of the atomic system, have been obtained. In this paper, these equations are exactly solved for a linearly $\ensuremath{\sigma}$-polarized laser and levels having small angular momenta. More precisely, I consider the laser transitions ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=0$, ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=1$, and ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$. Two particular results are emphasized: (i) For $J=1\ensuremath{-}J=0$ and $J=1\ensuremath{-}J=1$ transitions and for the J=2J=2J=2 level of a $J=1\ensuremath{-}J=2$ transition, the laser-induced Hanle effects keep a Lorentzian shape, independent of the laser intensity. For the $J=1\ensuremath{-}J=1$ transition, it is shown that the depolarizing relaxation processes play a leading part in the coupling induced by the laser between the transverse alignments of the two levels. On the other hand, the power broadenings of the Hanle effects are shown to be similar. For the J=1J=1J=1 level of a $J=1\ensuremath{-}J=2$ transition, the Hanle-effect shape presents a departure from the Lorentzian one, owing to a coupling with the laser-induced hexadecapole moment in the J=2J=2J=2 level. (ii) The populations of the levels exhibit a "zero-field saturation resonance" which is due to the coupling with the Zeeman coherences. These resonances, which reproduce the Hanle effects of the transition, can be observed on the $\ensuremath{\pi}$-polarized fluorescence from the levels. In general, these resonances appear as a saturation effect, i.e., they reduce the laser-induced fluorescence of the levels in zero magnetic field. However, for the ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$ transition, the ${J}_{a}=2\ensuremath{\rightarrow}{J}_{f}=2 \ensuremath{\pi}$ fluorescence presents an anomalous behavior; the saturation resonance increases the zero-field laser-induced fluorescence. The theoretical study shows the prominent part played by the value of the Jb=1{J}_{b}=1Jb​=1 level lifetime in the interpretation of this anomaly. Other results, such as the laser-induced depolarization of the fluorescence, are also obtained. All the theoretical predictions have been experimentally checked and will be presented in forthcoming papers.
The Faraday rotation and circular dichroism of dilute gases in longitudinal magnetic fields and subject to strong radiation fields are studied. The use of irreducible tensorial sets as bare-atom states which are then dressed by the laser field allows a simple incorporation of the various multipole relaxation rates into the theory. The treatment considers magnetic fields which produce Zeeman shifts much smaller than inverse collision times but which may be greater or smaller than the multipole relaxation rates. Doppler broadening is also considered. Explicit expressions are given for dipole transitions in a two-level system with arbitrary angular momentum for strong and weak magnetic fields.
Nonlinear in laser power, near-resonant light-atom interaction leads to a number of spectacular modifications of a well-known effect -polarization plane rotation in a magnetic field applied along the direction of light propagation.In particular, the rotation can be enhanced by up to nine orders of magnitude compared to the linear case.Faraday effect [ 1 ] is the rotation of the plane of linear light polarization by a medium in a magnetic field applied in the direction of light propagation.In 1898, Macaluso and Corbino eJ, studying absorption spectra of the alkali atoms in the presence of magnetic fields, discovered that the Faraday effect in the vicinity of resonance absorption lines also had a distinct resonant character.The essence of the Macaluso-Corbino effect can be illustrated by considering a simple case of a F= 1 ~ F'=O transition (Fig. 1 ).Linearly polarized light incident on the sample can be resolved into two counter-rotating circular components ( cr~.In the absence of a magnetic field, the M=±l sublevels are degenerate and the optical resonance