Effect of Rabi splitting on the low-temperature electron paramagnetic resonance signal of anthracite.

Specific distortions of the EPR signal of bulk anthracite are observed at low temperatures. They are accompanied by variations in the microwave oscillator frequency and are explained by the manifestation of the Rabi splitting due to the strong coupling between electron spins and the cavity, combined with the use of an automatic frequency-control (AFC) system. EPR signals are recorded at negligible saturation in the temperature range of 4-300K with use of the AFC system to keep the oscillator frequency locked to the resonant frequency of the TM110 cylinder cavity loaded with the sample. For the sample with a mass of 3.6mg the line distortions are observed below 50K and increase with temperature lowering. The oscillator frequency variations are used to estimate the coupling strength as well as the number of spins in the sample. It is shown that the spin-cavity coupling strength is inversely proportional to temperature and can be used for the absolute determination of the number of spins in a sample. Our results indicate that at low temperatures even 1016 spins of the anthracite sample, with a mass of about 0.5mg, can distort the EPR line.

Multi-photon transitions and Rabi resonance in continuous wave EPR.

The study of microwave-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 the time evolution of 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.