Stochastic theory of narrow hole-burning in low-temperature dilute ruby

Abstract

Transient hole-burning in low-temperature impurity-ion crystals is studied using the model of two jump processes U t = U t 1 + U t 2 (the random telegraph process U t 1 and the uncorrelated jump process U t 2 with a Lorentzian distribution of possible values) characterised by essentially different jump rates v 1 ⪢ v 2 and distribution widths σ 1 ⪡ σ 2 for the impurity ion optical transition frequency fluctuations U t due to the bulk and the frozen core host nuclear spins flipping. At short pump/probe pulse width T and short delay time τ d(τ d, T ⪡ v 2 −1) the calculated hole shape is narrow with the hole width determined by the U t 1 process characteristic only while at long delay τ d ≥ v 2 −1 it becomes a wide Lorentzian with the haftwidth 2σ 2. The theory fits the experimental data of Szabo et al. well on narrow hole burning in ruby under low and high magnetic field, supposing the fluctuations U t 1 to be rather slow ( σ 2 1 v 2 1 = 0.5 ).