Multi-photon transitions and Rabi resonance in continuous wave EPR

TL;DR

This paper develops a theoretical framework for understanding multi-photon transitions and Rabi resonance effects in continuous wave EPR spectroscopy, revealing new spectral features and transition behaviors under specific modulation conditions.

Contribution

It introduces an analytical description of multi-photon transitions under Rabi resonance in CW EPR, highlighting the effects on spectral sidebands and transition inversion.

Findings

Multi-photon transitions produce sidebands in EPR spectra when modulation exceeds linewidth.

Rabi resonance causes frequency shifts and inversion of spectral lines.

Time-resolved signals demonstrate primary and secondary Rabi resonance effects.

Abstract

The study of microwave and radiofrequency multi-photon transitions in continuous wave (CW) EPR spectroscopy is extended to a Rabi resonance condition, when the radio frequency of the magnetic-field modulation matches the Rabi frequency of a spin system in the microwave field. Using the non-secular perturbation theory based on the Bogoliubov averaging method, the analytical description of the response of the spin system is derived for all modulation frequency harmonics. When the modulation frequency exceeds the EPR linewidth, multi-photon transitions result in sidebands in absorption EPR spectra measured with phase-sensitive detection at any harmonic. The saturation of different-order multi-photon transitions is shown to be significantly different and to be sensitive to the Rabi resonance. The noticeable frequency shifts of sidebands are found to be the signatures of this resonance. The inversion of two-photon lines in some spectral intervals of the out-of-phase first-harmonic signal is predicted under passage through the Rabi resonance. The inversion indicates the transition from absorption to stimulated emission or vice versa, depending on the sideband. The manifestation of the primary and secondary Rabi resonance is also demonstrated in time-resolved steady-state EPR signals formed by all harmonics of the modulation frequency. Our results provide a theoretical framework for future developments in multi-photon CW EPR spectroscopy, which can be useful for samples with long spin relaxation times and extremely narrow EPR lines