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Journal of Physics C Solid State Physics

Dynamic Zeeman effect in paramagnetic emission and second harmonic generation

G Battaglia, G. Vetri

Published Jan 20, 1982• 3 citations
Publisher

Abstract

It is suggested that the combined effect of a resonant magnetic field (dynamic Zeeman effect) and of the fluctuations due to spin-spin and spin-lattice interactions could give rise to inelastic components in the emission spectrum of a paramagnetic system. It is also shown that a similar effect can be expected in the second harmonic emission. It is found that if the Rabi frequency is much larger than the relaxation rates, both the resonant and the second harmonic spectra show the two side lines typical of the atomic resonant fluorescence. The results are illustrated by means of a semiclassical model. Plots of expected spectra as a function of the frequency are given for some realistic parameters of paramagnetic samples.

DOI
10.1088/0022-3719/15/2/010

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It is suggested that the combined effect of a resonant magnetic field (dynamic Zeeman effect) and of the fluctuations due to spin-spin and spin-lattice interactions could give rise to inelastic components in the emission spectrum of a paramagnetic system. It is also shown that a similar effect can be expected in the second harmonic emission. It is found that if the Rabi frequency is much larger than the relaxation rates, both the resonant and the second harmonic spectra show the two side lines typical of the atomic resonant fluorescence. The results are illustrated by means of a semiclassical model. Plots of expected spectra as a function of the frequency are given for some realistic parameters of paramagnetic samples.
The frequency distribution of the second harmonic radiated by a two-level system in the presence of a two-photon resonant electromagnetic field is investigated. It is shown that the interaction of a permanent dipole with the driving field causes, in the second harmonic spectra, effects analogous to those belonging to the resonance fluorescence. The effects (dynamic Zeeman or Stark effects) are, however, of the second order in the amplitude of the driving field. The results are illustrated by using the vectorial model of Feynman, Vernon and Hellwarth (1957). Numerical results based on realistic parameters of a paramagnetic system are given.
Second-harmonic (SH) generation by paramagnetic samples at microwave frequency is considered, and the dependence of its intensity on the total number NNN of active centers is experimentally investigated. The reported results show a N2{N}^{2}N2 dependence of the SH intensity near the resonance condition and a higher NNN dependence in the far wings of the SH line. A qualitative explanation is suggested in which the observed effect is related to the internal correlations established among the spins during the SH generation process, as theoretically investigated in the following paper by Persico.
The dynamics of a paramagnetic system (S = 1/2), thermodynamically equilibrium-linked with the radiation field of a resonator is considered by the methods of the quantum theory of fields. The spectrum of the resonance frequencies of the system is found for two relations of the size of the paramagnetic sample L and the wavelengths of the radiation field k−1. It is shown that when L ≪ k−1 Fain’s result, Eq. (1), is valid for the intrinsic line width, if the Zeeman frequency ω0 ≫ck. With L ≳ k−1, (the case of a crystal resonator), and kT>ω0>ρSμB2 (ρS is the paramagnetic ion density in the crystal), the temperature behavior of the intrinsic width is described by formula (33). It is shown that the critical temperature Tc is the temperature of the Bose-Einstein condensation of photons of the resonator radiation field, which is determined only by the paramagnetic ion density in the sample. Estimates are made of the intrinsic broadening of the Zeeman line in certain paramagnetic crystal resonators with impurities of rare-earth ions.
The Stark representation of the resonator field and the first order of perturbation theory of the fluorescence field are used to study the fluorescence spectrum of one and two two-level atoms in an ideal resonator as a function of the initial excitation of the system. It is shown that in the absence of resonator photons (nc = 0) the spectrum obtained for initial excitation of one atom consists of two lines located symmetrically relative to the central frequency ωα. In all other cases the spectrum consists of the central harmonic ωα and of ωα ± 2Ω satellites (Ω is the Rabi frequency). The intensity of collective higher harmonics ωα ± 4Ω is low and it falls on increase in the resonator field as I/nc2. The nonlinearity of the interaction Hamiltonian results in parametric amplification of the ωα + 2Ω harmonics and in attenuation of the ωα–2Ω harmonics. In the case of two atoms it is possible to achieve stimulated fluorescence at the harmonics ωα ± 2Ω.
Theoretical and experimental study of influence of quadratic Zeeman effect on the structure of double radio-optical resonance is presented. A specific transition in 87 Rb atom is considered in the case of excitation with linearly polarized laser radiation and detection of the signal at the second harmonic of the AC magnetic field frequency. It is shown, that for small magnetic fields the magnetic resonance consists of a solitary line similarly to resonance in potassium [1]. However, for magnetic fields greater than 50 μT the line acquires two additional side-peaks without breaking its symmetry and changingposition of resonance center. The described scheme can be used in magnetometry.