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

Dynamics and dispersion of populations for multilevel systems in the intense-radiation and external magnetic fields

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

Published May 9, 2001• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.426703

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Optics and Spectroscopy•Aug 1, 2002•1 citation
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 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.
Coherent population trapping effect is widely studied for simple three-level systems of different types ((Xi) , (Lambda) , V). For real atoms situation is more complicated. Atomic levels are degenerated one and in the presence of external fields coupling of magnetic sublevels appears due to as radiation, so magnetic fields, leading to the systems of levels of the higher order. Our theory and model of calculation for interaction of multilevel atom with intense radiation field at the presence of external magnetic field have been applied for considering coherent population trapping effect for such systems.
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.
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.
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 influence of the orientation and strength of a magnetic field on the dynamics and dispersion of the populations of the multilevel Λ system upon spontaneous decay into thermostat levels is considered. The radiation field consists of two components and is specified by the vector-potential in the electric dipole approximation. From the solution of the Schödinger equation for a system consisting of an atom in a magnetic field + radiation field, the probability of populating a common level for the generalized Λ system is determined in the resonance approximation. The calculation of the dynamics and dispersion of the populations demonstrates their dependence on the orientation of the magnetic field vector with respect to the light field polarization vector and on the relationship between the magnetic field strength and radiation field intensities. The coherent population trapping occurs only in the case when Rabi frequencies either exceed or are comparable to the Zeeman splitting of magnetic sublevels. By varying the orientation of the magnetic field, it is possible to change the dynamics and dispersion of the populations, thus affecting the coherent population trapping.