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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Two-photon magneto-optical effects in atomic gases in resonant laser and strong magnetic fields

T. Ya. Karagodova, Alexander I. Karagodov, Andrey A. Eliseev

Published May 4, 2000• 0 citations
Publisher

Abstract

The theory of interaction of intense bichromatic field of laser radiation with multilevel atomic system in the external magnetic field is considered. The magnitudes of interaction are much larger than the width of atomic levels. The vector-potential of radiation field consisting of two monochromatic components with the frequencies resonant to adjacent transitions is taken in electric dipole approximation. The eigenvalues and eigenstates of the Hamiltonian, including spin-orbit interaction and interactions with laser radiation and external magnetic fields, are found without perturbation theory using resonant approximation. When the effects of resonantly excited radiation are considered the Hamiltonian of interaction with the weak field of scattered radiation is included also. Its eigenfunctions are found with the help of perturbation theory. We consider tow types of effects: polarization effects and effects of resonantly excited radiation. As the atomic system is multilevel we use the numerical methods. The influence of the magnetic field on coherent population trapping effect for multilevel systems is considered. Some of our theoretical results coincide with known experimental ones.

DOI
10.1117/12.384281

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 25, 1999•2 citations
The theory of interaction of intense bichromatic field of laser radiation with multilevel atomic system in the external magnetic field is considered. The magnitudes of interaction are much larger than the width of atomic levels. The vector-potential of radiation field consisting of two monochromatic components with the frequencies resonant to adjacent transitions is taken in electric dipole approximation. The eigenvalues and eigenstates of the Hamiltonian, including spin-orbit interaction and interactions with laser radiation and external magnetic fields, are found without perturbation theory using resonant approximation. When the effects of resonantly excited radiation are considered the Hamiltonian of interaction with the weak field of scattered radiation is included also. Its eigenfunctions are found with the help of perturbation theory. We consider tow types of effects: polarization effects and effects of resonantly excited radiation. As the atomic system is multilevel we use the numerical methods. The influence of the magnetic field on coherent population trapping effect for multilevel systems is considered. Some of our theoretical results coincide with known experimental ones.
The interaction of high power laser radiation with the atoms in the external magnetic field leads to the new nonlinear effects due to modifications of populations of the states of the system 'atom plus field.' From one side it can be followed by new peculiarities in the effect of the coherent population trapping and from other -- the effects of the population modifications are important for explanation of regularities of nonlinear magneto-optical effects. The modification of population dynamics due to the parameters of the system -- radiation field intensities, detunings, polarizations, magnetic field strength and orientation, relaxation constants leads to the new features in polarization effects, resonant fluorescence and resonant Raman effects. The new features of the considered theory are that it is built for multilevel atoms and has not restrictions on the probe intensity compared to the pump intensity. The theory and method permit to investigate the populations modifications depending on modifications of the parameters of the system and to find the relation between population dynamics and new nonlinear resonant magneto-optical effects. The considered system consists of atomic gas of low concentration in the constant magnetic field and two monochromatic laser fields of different intensities and polarizations. Analytically the influence of magnetic field on population dynamics of three-level systems have been considered. For real multilevel atom the computer simulations show the dependence of population dynamics on relaxation constants and the differences of this dynamics for different magnetic sublevels of the excited states of the atom. The results agree with known theoretical and experimental works.
The theory of interaction of the elementary atomic systems with resonant laser fields is well known. At the same time multilevel systems are investigated in less details. We consider T1 atoms as multilevel system due to removal of degeneracy of levels with different magnetic quantum number in strong radiation and magnetic fields. It is known that recently investigated effect, connected with the quantum interference of states is coherent population trapping (CPT). We propose the method of numerical calculations of interaction of real atoms with strong radiation fields and magnetic field, valid in the case when the values of Rabi frequencies considerably exceed the line widths. This method can be applied to investigate the CPT effect and influence of the external magnetic field on it.
The theory and method of computer simulations created formerly permits to investigate the interaction of high power laser radiation up to gigawatt on centimeter to the second power with the atoms as well as with small so with large fine structure interval in the external magnetic field. The modifications of the energies and populations of atomic levels due to such interaction lead to the new nonlinear effects. Among them besides the modifications in Raman effect and new effects of rotation of plane of polarization and circular dichroism investigated before there are such new effects as the modifications of the number, intensities, polarizations of the lines at the excitation spectra and the scattering spectra of resonant fluorescence. The real atom is multilevel system. Usually the theoretical investigations of nonlinear resonant magnetooptical effects are limited by two- or three-level approximations or by using the perturbation theory. This is justified for considering the effects in the weak magnetic fields but not sufficient for revealing and investigation the characteristics of the new nonlinear magnetooptical effects taking place in the intense radiation and magnetic fields. Such effects are related to modifications of electronic structure of atoms (level shifts and splittings, populations modifications). As the considered media is atomic gas one can reach for power density up to gigawatt on centimeter to the second power. As the considered concentrations are small it is possible to neglect the collisional relaxation. For real atom the considered system is multilevel so only numerical solution is appropriated. The simulations permit to find some new effects in the excitation spectra of Raman effect and resonant fluorescence.
Using the theory and the calculation method developed previously, numerical experiments on the study of dispersion of populations of a multilevel atomic system in strong fields of laser radiation in resonance with adjacent transitions and in a constant magnetic field are conducted. The effect of the magnetic field strength on the character of coherent population trapping in a multilevel system is studied. It is shown that the effect, depending on the magnetic field strength, may be observed for both and for one of the magnetic sublevels of the level that is doubly degenerate in the magnetic quantum number, for which resonance fluorescence is studied. The possibility of obtaining population inversion for magnetic sublevels in the excited state of a multilevel atom under an appropriate choice of parameters is demonstrated.
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.
Coherent population trapping effect is widely studied for simple three-level systems of different types ((Xi) 2, (Lambda) , V)1,2. For real atoms the situation is more complicated. Atomic levels are degenerated one and in the presence of external fields coupling of magnetic sublevels appears due to radiation, so magnetic fields leading to the systems of levels of the higher order. Our theory and method of calculation for interaction of multilevel atoms, with intense radiation fields in the presence of external magnetic fields have been applied for considering coherent population trapping effect for such systems. In the absence of magnetic field for considering sets of parameters, we can see the behavior of populations in function of time, detunings for both systems of coupled sublevels inherent to the coherent population trapping effect. In the presence of magnetic field, we can see novel features in the populations for the systems of coupled magnetic sublevels.