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

Magnetic resonance in a strong laser field

G. Todorov, М. П. Чайка, Vladimir A. Polischuk, Lyubomir P. Petrov, St. Georgiev, Dimitar G. Slavov, Vladimir R. Arsov

Published Nov 6, 2003• 0 citations
Publisher

Abstract

A theoretical model describing magnetic resonance in a strong laser field was proposed. The exact solution of the well known system of equations was solved for the transition between a ground state with Jφ = 1 and an exited state with Jf = 0. It was shown that in the spontaneous emission intensity from the level with Jf = 0 resonant changes will be observed when the frequency ω of the altering magnetic field becomes equal to the Larmor-frequency determined by the constant magnetic field Ho.

DOI
10.1117/12.519391

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A theoretical model describing magnetic resonance in a strong laser field was proposed. The exact solution of the well known system of equations was solved for the transition between a ground state with Jφ = 1 and an exited state with Jf = 0. It was shown that in the spontaneous emission intensity from the level with Jf = 0 resonant changes will be observed when the frequency ω of the altering magnetic field becomes equal to the Larmor-frequency determined by the constant magnetic field Ho.
Theoretical model describing the influence of a parasitic magnetic field on CPT-resonance in Hanle configuration in a strong laser field was proposed. The exact solution of the system of equations has been obtained for the transition between a ground state with Jφ=1 and an excited state with Jf=0 and/or 1. The solutions for the tensor components f k0, describing the population and longitudinal alignment of the upper level f, are obtained, and the dependences of the resonances on the different parameters and parasitic fields were analyzed. The results are in qualitative agreement with resent experimental investigations.
The theory of double-resonance phenomena, or the simultaneous action of optical transitions and rf perturbations between the Zeeman sublevels of an atom, is extended to the induced emission and absorption processes effected by the monochromatic radiation and the discrete resonances involved in the gas laser. Expressions for the probability amplitudes of the Zeeman sublevels under such conditions are derived from time-dependent perturbation theory, the lifetimes of the states being introduced in a phenomenological way. Zeeman splittings of both upper and lower states involved in the laser transition are considered, and an effective term diagram used to discuss the results. Small signal approximations are applied to consider some specific cases, which show that the light beats seen in spontaneous emission when the rf frequency ${\ensuremath{\omega}}_{0}$ equals the Larmor frequency, and in other instances, do not occur in induced emission unless such frequencies coincide with axial resonances of the laser cavity. Variations in the intensity and resonance effects are indicated at Zeeman splittings corresponding to ${\ensuremath{\omega}}_{0}$, with similar variations in the amplitude of any beat frequencies due to multiple axial resonances. Additional coherence effects occur where levels cross, which will give rise to changes in the intensity and polarization of the induced emission at the corresponding frequency.
The authors have studied resonance collisions amongst atoms dressed by a strong laser field. The equations of motion have been solved numerically to yield collisional transition rates for various values of the Rabi frequency (V) due to the laser and its detuning ( Delta ) from the atomic transition frequency ( omega 0 ). The atoms are assumed to follow classical rectilinear paths and only undergo binary collisions. The resonance interaction is taken to be the first-order dipole-dipole interaction acting within the ground and resonance levels of a pair of atoms. A qualitative explanation is offered for the results obtained by splitting the Hamiltonian into parts that represent the collision-free evolution of the system at the Rabi frequency, the 'normal' resonance interaction, and the 'dressed interaction' responsible for opening new scattering channels. The latter interaction depends upon the relative strengths of the resonance interaction (R), the generalized Rabi frequency ( Omega ) and the ratio V/ Delta .
The simultaneous action of a RF perturbation between the Zeeman sublevels of an atomic transition, which is also sustaining laser oscillations, is given further consideration. General equations are derived that describe the phenomena in a rotating effective magnetic field basis. These are valid for any level of the RF perturbation, being then solved by iteration to third order in the laser electric field and integrated exactly over the atomic velocity distribution. Results are given for single-π-mode laser operation on aJ = 1 \rightarrow 0transition and for single-mode operation on each of the well-resolved σ components of the Zeeman splitting. The extension to more complex transitions, such as aJ = 1 \rightarrow 2, is then given. A dominant resonance peak in the laser intensity occurs when the RF equals the Zeeman splitting of either the upper or lower states of the transition. Population differences amongst the upper sublevels are more effective than those between the lower sublevels and give the smallest resonance widths. For operation on the σ modes, the main effect is a reduction in the saturation coefficient β, together with smaller changes in the coupling coefficients θ between the oscillations. Such changes will affect the general behavior near the singular points of the nonlinear equations, and will change the shape of the curves of mode intensities as functions of cavity detuning and magnetic field.
In the present work we consider theoretically the influence of an arbitrary oriented additional magnetic field on the main properties of the Coherent Population Trapping (CPT) resonances in fluorescence and/or in absorption. The exact numerical solutions are obtained for the tensor components Ρk0 (ρ = f, φ) which describe the population and the longitudinal alignment of the resonant (f) levels with quantum numbers Ff 0 and Ff =1, exited with a single frequency laser field from the ground (φ) state with Fφ=l and Fφ=2. Numerical simulations was used to obtain the width and the amplitude dependences of the resonances under different parameters and parasitic fields. The results are in qualitative agreement with resent experimental investigations.
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.