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Journal of Physics B Atomic Molecular and Optical Physics

Interference effects in the two-photon polarization spectra of alkali atoms in intermediate strength magnetic fields

P. C. Stancil, G. E. Copeland

Published Jul 14, 1994• 6 citations
Publisher

Abstract

The degree of linear polarization P L for two-photon absorption of alkali atoms in intermediate strength magnetic fields has been computationally investigated. Polarization spectra were obtained for n a s 2 S 1/2 to n b s 2 S 1/2 transitions with the photons in near resonance with intermediate 2 P j levels. Previous experiments and calculations in the absence of a magnetic held revealed a complete polarization reversal (P L approximately -100%) for frequencies near resonance between the 2 P 1/2 and 2 P 3/2 levels due to fine-structure coherence. Application of weak to intermediate strength fields induce additional depolarization features as a result of anomalous Zeeman splitting. The fine-structure depolarization feature disappears for strong fields (Paschen-Back regime), while the calculations predict that Zeeman depolarization persists though the transitions become forbidden. Magnetic-field-dependent polarization spectra can be measured in the laboratory with high precision and it should prove interesting to trace through the weak, intermediate, and strong field regimes.

DOI
10.1088/0953-4075/27/13/010

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The degree of linear polarization P L for two-photon absorption of alkali atoms in intermediate strength magnetic fields has been computationally investigated. Polarization spectra were obtained for n a s 2 S 1/2 to n b s 2 S 1/2 transitions with the photons in near resonance with intermediate 2 P j levels. Previous experiments and calculations in the absence of a magnetic held revealed a complete polarization reversal (P L approximately -100%) for frequencies near resonance between the 2 P 1/2 and 2 P 3/2 levels due to fine-structure coherence. Application of weak to intermediate strength fields induce additional depolarization features as a result of anomalous Zeeman splitting. The fine-structure depolarization feature disappears for strong fields (Paschen-Back regime), while the calculations predict that Zeeman depolarization persists though the transitions become forbidden. Magnetic-field-dependent polarization spectra can be measured in the laboratory with high precision and it should prove interesting to trace through the weak, intermediate, and strong field regimes.
The method of computer simulations on nonlinear resonant magnetooptical effects developed for real multi-level atoms in the two laser fields of arbitrary intensity and external magnetic field is applied for the polarization effects of different types calculations and investigations of the dependence of the characteristics of these effects on magnetic field strength, intensities, polarization and detunings of laser fields for alkaline atoms. The essence of the method consists in simulations and analysis of the plots of dependence of quasi energies on parameters, which are obtained with the help of sorting subprogram, and selection of suitable algorithms for calculations of characteristics of nonlinear resonant magnetooptical effects. One photon and two photon resonant effects are investigated for wide range of magnetic field strength from Zeeman to Paschen Back effects. Some new features in the spectra of rotation of plane of polarization and circular dichroism of different types are predicted. The results show the agreement with known experiments. Such calculations of nonlinear resonant magnetooptical effects in the intense laser fields resonant to adjacent transitions and magnetic field show the opportunity of investigation the modifications of electronic structure due to intense radiation fields and strong external magnetic field in atomic gases and also may be used for the treatment of new methods of phase-polarization selection of modes of tunable lasers.
The method of computer simulations on nonlinear resonant magneto-optical effects developed for real multi-level atoms in the two laser fields of arbitrary intensity and external magnetic field is applied for the polarization effects of different types calculations and investigations of the dependence of the characteristics of these effects on magnetic field strength, intensities, polarizations and detunings of laser fields for alkaline atoms. The essence of the method consists in simulations and analysis of the plots of dependence of quasienergies on parameters (detunings and intensities of radiation fields, magnetic field strength), which are obtained with the help of sorting subprogram, and selection of suitable algorithms for calculations of characteristics of nonlinear resonant magneto-optical effects. One-photon and two photon resonant effects are investigated for wide range of magnetic field strength from Zeeman to Paschen Back effects. Some new features in the spectra of rotation of plane of polarization and circular dicohroizm of different types are predicted. The results show the agreement with known experiments. Such calculations of nonlinear resonant magneto-optical effects in the intense laser fields resonant to adjacent transitions and magnetic field show the opportunity of investigation the modifications of electronic structure due to intense radiation fields and strong external magnetic field in atomic gases and also may be used for the treatment of new methods of phase-polarization selection of modes of tunable lasers.
The features of nonlinear magnetooptical effects of fine-structure levels of an alkali atom, including effects in strong magnetic fields, as well as under conditions of two-photon resonance, are considered. The spectra of magnetooptical rotation and of magnetic circular dichroism have been obtained for the first time for the nontrivial initial population of magnetic sublevels of excited electronic states of an alkali atom, as well as under conditions of two-photon resonance. The decrease in the amplitude of resonances of initially populated fine-structure levels is explained by population transfer, taking place in strong fields. This transfer affects the rotation of the plane of polarization. The lower the initial population, the more pronounced the population transfer. Numerical experiments have shown that analysis of the resonance shapes in the spectra of magnetooptical rotation can yield information on the initial population of magnetic sublevels of excited electronic states of atoms.
Quantum-mechanical interference is found in the two-photon excitation of an atomic 1S^{1}\mathrm{S}1S through the nonresonant sequence 11^{1}\mathrm{}^{1}11P\ensuremath{\leftarrow}1{\mathrm{}}^{1}1S, since the magnetic sublevels of the intermediate 1P^{1}\mathrm{P}1P state provide multiple pathways for absorption. Depending on the relative polarization of the two incident light beams, the interference can be either constructive or destructive. When the electric vectors of the light beams are linearly polarized and orthogonal, the interference is purely destructive and two-photon transitions are forbidden. Application of an external magnetic field, however, lifts the degeneracy of the intermediate state giving a two-photon absorption rate proportional to the square of the magnetic field strength. These effects are reported for the (7s)1{)}^{1})1S\ensuremath{\leftarrow}(5s2{\mathrm{s}}^{2}s2)1{)\mathrm{}}^{1})1S transition of atomic Sr excited by two dye lasers operating at different wavelengths.
We precisely investigate the Zeeman and Paschen-Back effects of the hyperfine structure during the rubidium $5{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ two-photon transition. Owing to the high sensitivity of the DDD state of atoms to a magnetic field, the splittings of the spectra of the DDD state are sufficiently large in a weak magnetic field of <10<10<10 G. We experimentally observe how in the hyperfine coupling in the 52D5/25{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}52D5/2​ state is disrupted even in weak magnetic fields around 10 G and the energy levels are arranged according to their total angular momentum JJJ and nuclear spin III. The transient of the spectra known as the Paschen-Back effect is observed even in a weak magnetic field with an order of magnitude of several tens of gauss. The results of theoretical calculations for energy shifts and transition intensities under a magnetic field are in quantitative agreement with the experimental results.
Polarization dependence of amplitude for resonant magnetic-field-induced coherent mixing of two collinear laser waves may be used for separating M1 and E2 contributions to n1 2P1/2(3/2) - n2 2P3/2(1/2) dipole-forbidden transition in atoms. The interference between E2 and Ml terms of the amplitude may cause linear polarization and circular dichroism effects. The dependencies of the two effects on the width and splitting of resonance levels, on resonance detuning, on relative directions of steady and alternating field vectors are determined. Numerical data are presented for frequency summation of two laser waves on Cs, Rb and K atoms.