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

Linear and nonsaturating effects in atomic multiplets subjected to three strong electromagnetic fields of resonance

F. F. Popescu, Florea Marica, Gabriel Lucian Radu

Published Jul 2, 1998• 0 citations
Publisher

Abstract

Analytic steady-state solutions of the density-matrix equation are discussed for multilevel spin systems in dilute paramagnetic solids at high temperature and subjected to three frequency- correlated fields at resonance. Unlike the double resonance, in the case of triple resonance, when the three microwave fields are sufficiently strong and the spectroscopic bridge conditions are satisfied, important linear and nonsaturating effects are predicted.

DOI
10.1117/12.312806

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Analytic steady-state solutions of the density-matrix equation are discussed for multilevel spin systems in dilute paramagnetic solids at high temperature and subjected to three frequency- correlated fields at resonance. Unlike the double resonance, in the case of triple resonance, when the three microwave fields are sufficiently strong and the spectroscopic bridge conditions are satisfied, important linear and nonsaturating effects are predicted.
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The resonant response of a multilevel atomic system to strong coherent radiation is analyzed using an extension of the methods of time-independent scattering theory, adapted to the density-matrix formalism in order to include thermal bath effects. General steady-state expressions are derived for self-attenuation and resonance scattering rates in strong saturating fields, as functions of the coupling strengths, relaxation parameters, and frequency detunings. Formal expressions are given for radiative-damping and collision-broadening relaxation parameters, relating the latter to scattering amplitudes. Modifications of collision-broadening parameters by the presence of very strong fields are discussed. The Bloch equations are derived by transformation to the time domain, under specified conditions.
The solution of the time-dependent wave equation describing the interaction of two coupled spins with a rotating magnetic field in the presence of a steady field, as in the usual magnetic resonance situation, has been reexamined. By extending the method previously developed by Salwen, an exact expression is derived for all components of the wave function describing a three-state system under magnetic-resonance conditions. This solution describes in analytical form all the single and multiple resonances of which the system is capable for fields of any intensity. It is shown that when zzz is the axis of quantization, the projection of the wave function on an eigenstate of Fx{F}_{x}Fx​ oscillates at twice the resonance frequency at exact double quantum resonance. An approximate form is derived for the transition probability near double quantum resonance, showing that our solution is consistent with Salwen's in the limit of well-separated single and double quantum resonances. The theory is applied to the uppermost three substates of the upper hyperfine multiplet of an alkali metal of arbitrary nuclear spin, a case of interest to the analysis of magnetic resonance in optically pumped vapors.
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We present a theoretical study of double-resonance alignment magnetometers using linearly polarized light, in which the effect of atomic high-order multipole moments is considered. Starting from the effective master equation of our system obtained by eliminating the excited state adiabatically, we derive the full evolution equations of the atomic multipole moments. The analytic solutions of resonance signals involving the four-order multipole moments effect are obtained by using the perturbation approach. We present that the four-order multipole moments effect is negligible in the weak laser field, and the results reduce to that obtained by a three-step approach. However, the role of four-order multipole moments coupled by two-order tensor moments is more significant with the increasing Rabi frequency of light, which cannot be ignored. Meanwhile, the analytic expressions of relaxation processes are also studied, which are a linear combination of the laser-induced equivalent relaxation rate Γ L and the spin-exchange collision rate Γ g . The expected domain of validity of the three-step approach on light power is roughly given by Γ L < 1 2 Γ g . In addition, the steady-state results of resonance signals are presented in a strong radio-frequency magnetic field; in that case, the physical mechanism of the splitting of resonance signals is discussed. These results are valid for arbitrary light power and for an arbitrarily oriented static magnetic field.
General expressions for the steady-state population distribution and complex susceptibilities of a three-level system interacting with two strong near-resonant electromagnetic fields are obtained using a density-matrix formalism. A complete treatment of the steady-state population distribution established in the three-level system, under the action of two strong fields with arbitrary resonance detunings is presented. The criterion for maximal populations of the exciting levels, as well as conditions in which the population of the exciting levels exceeds the population of the ground state are found. The modification of the absorption and emission lines with increasing intensity of the second (probe) field is considered. The emphasis in the present treatment, as distinct from Panock and Temkin (see IEEE J. Quantum Electron., vol.QE-13, p.476 (1977)) is on the consideration of the arbitrary distribution of the equilibrium populations of the system which exhibits a number of interesting features which have not been previously discussed.