Transient hole-burning and free induction decay as a probe of multi-timescale host spin dynamics in low-temperature ion-doped crystals

Transient hole-burning and free induction decay (FID) in low-temperature ion-doped crystals are studied consistently using the model of two jump processes Ut equals Ut1 + Ut2 characterized by essentially different jump rates v1 >> v2 and distribution widths (sigma) 1 << (sigma) 2 for the impurity ion optical transition frequency fluctuations Ut due to the bulk and the frozen core spin flipping. At short pump/probe pulsewidth T and short delay time (tau) d ((tau) d, T << v2-1) the calculated hole shape is narrow with the hole width determined by Ut1 process characteristics only. The hole width in this case coincides with the calculated FID rate. At long delay (tau) d >= v2-1 the hole becomes a wide lorentzian with the halfwidth 2(sigma) 2. The theory fits well the experimental data by A. Szabo et. al. on narrow hole burning and FID in ruby under low and high magnetic fields supposing the fluctuations Ut1 to be rather slow ((sigma) 21/v21 equals 0.5).