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RESEARCH PRODUCT

Double-quantum nutations in a two-level spin system

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The transient oscillatory behavior of the nonlinear response of a two-level electron-spin system is experimentally investigated in a sample of glassy silica with ${E}_{1}^{\mathcal{'}}$ centers (S=(1/2)) at microwave frequency at T=4.2 K. The transient regime, excited by an intense step-modulated radiation tuned to double-quantum (DQ) resonance, is monitored by revealing the second-harmonic (SH) wave radiated by the spins undergoing DQ transitions. Time- and frequency-domain results show that the emitted SH wave has two components: the former, which vanishes at the DQ resonance, exhibits an overdamped transient regime, the latter consists of damped oscillations at a frequency which depends on the intensity and the polarization of the input radiation but not on its detuning from the DQ resonance condition. Using a vectorial model of the DQ resonance in an S=1/2 spin system we relate the observed oscillatory behavior to the transient nutations induced by the DQ processes; the calculated DQ Rabi frequency and its dependence on the input radiation are found in quantitative agreement with the experimental results. Moreover, we calculate that the inhomogeneous broadening of the resonance line strongly affects the time dependence and the spectral content of the emitted radiation, and in particular it makes its oscillation frequency independent of the input radiation detuning, in agreement with the experimentally observed behavior. The relationship, with recent discussions on the suitability of Bloch equations to describe coherent effects in randomly diluted solids, is also examined.