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Optics and Spectroscopy

The influence of the orientation and strength of a magnetic field on the coherent population trapping in the Λ system

T. Ya. Karagodova

Published Aug 1, 2002• 1 citation
Publisher

Abstract

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.

DOI
10.1134/1.1503745

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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.
Abstract The theory of interaction of intense laser fields with multilevel atoms in external constant magnetic fields is applied to analysis of the dependences of the populations on time, on detuning of laser frequency, on magnetic field orientation, and strength for spontaneous decay on the levels of thermostat. Solving the Schrödinger equation for the “atom in magnetic field + radiation field” system in resonant approximation we have obtained the probability of the population of common level for a generalized Λ system (e.g., 6P1/2‐7S1/2‐6P3/2 levels of Tl atoms). The results of computer simulations permit the investigation of the peculiarities of coherent population trapping in such system. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
The effect of coherent population trapping related to quantum interference of states now is well investigated for (Lambda) -systems in which the lower levels are generated by the hyperfine structure sublevels of the ground state of the atom. At present time the majority of experimental researches of resonances of CPT are made with alkaline atoms, for which hyperfine components of the ground state have typical interval of several gigahertz. We consider CPT in (Lambda) -systems in which the fine structure sublevels of the atom generate the lower levels. Our computer simulations have been made for the thallium atom for which the distance between sublevels of fine structure components is approximately 7792 cm-1. Theoretical and computer simulations of dynamics and dispersions of population of the considered multilevel system allow to detect new peculiarities of effect and demonstrate the influence of orientation and strength of magnetic field.
We consider peculiarities of coherent population trapping (CPT) effect on magnetic sublevels of fine structure levels for Thallium (TI) atoms. The system of levels taken into account consists of eight levels. By considering spontaneous decay onto the levels of thermostat we have found the solutions of Schroedinger equation in resonant approximation and so we have found the populations of magnetic sublevels. We have considered different geometries of experiment. Among them there are the cases for which the polarization vectors of both components of radiation fields are parallel to each other and parallel or perpendicular to magnetic field, polarization vectors are perpendicular to each other (one of them is parallel to magnetic field). Also the orientation of magnetic field may be parallel or perpendicular to wave vector of radiation field. Also we have considered different initial populations of magnetic sublevels. In contrary to trivial initial populations of sublevels of the ground state of an atom we have considered the initial population of another metastable fine structure level of TI atom. This situation can take place for atomic photofragments produced in the photodissotiation of diatomic molecules.
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 dependence of the shape of resonances of coherent population trapping (CPT) on magnetic sublevels of thallium atoms, forming a generalized Λ-system with the magnetic sublevels of the fine-structure levels as lower ones, on the polarization of the radiation fields has been numerically studied. The cases of linear, elliptical, and circular polarizations have been considered. The shape and the number of CPT resonances for different polarizations have been compared. It has been concluded that the electromagnetically induced transparency can be changed by changing the polarization properties of the laser radiation. The possibility to decrease the number of observed resonances may be useful in high-resolution spectroscopy.
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.