Analytical description of spin-Rabi oscillation controlled electronic transitions rates between weakly coupled pairs of paramagnetic states with S=(1/2)

We study theoretically and experimentally the Fourier content, ${\mathcal {\bf F}} (s)$, of the Rabi oscillations in photoconductivity coming from pairs of spin-$\frac{1}{2}$ localized carriers. Upon increasing the ac drive, the Fourier spectrum evolves from a single peak at $s= \Omega_R$, where $\Omega_R$ is the Rabi frequency, to {\em three} peaks at $s= \Omega_R$, $s=2\Omega_R$, and at low $s\ll \Omega_R$. The crossover between the two regimes takes place when $\Omega_R$ exceeds the broadening, $\delta_0$, of Zeeman levels due to disorder, e.g., hyperfine field. We capture this crossover within the analytical treatment by calculating the shapes of all three peaks at arbitrary relation between $\Omega_R$ and $\delta_0$. When the peaks are well-developed their widths are ${\Delta} s \sim \delta_0^2/\Omega_R$. Good agreement of theory and experiment allowed us to infer the experimental value of $\delta_0$.