Transient Hole-Burning and Free Induction Decay as a Probe of Multi-Timescale Fluctuations of a Reservoir

Abstract

Transient hole burning (THB) and free induction decay (FID) in inhomogeneously broadened ensemble of two-level quantum systems whose coherence losses are due to multi-timescale fluctuations U^t of their transition frequencies $\omega _{ab}^t = \left\langle {{\omega _{ab}}} \right\rangle + {U^t}$ are studied using the model of two Markov jump process ${U^t} = U_1^t + U_2^t$ (fast random telegraph process U ^t₁ and slow jump process U ^t₂ with lorentzian distribution of possible values) characterized by different jump rates v _l » v ₂ and distribution widths σ_l « σ₂. The examples of the systems are impurity ions in low-temperature crystals where the different timescale fluctuations U; result from the bulk and the frozen core host spin flipping or guest molecules in organic matrices with fast phonon dephasing and slow environment dynamics. Coherent transients techniques in such systems measure the homogeneous linewidth resulting mainly from short-timescale component U ^t₁ . THB technique provides additionally an information about long-timescale component U ^t₂ . We study here THB and FID consistently and fit the experiments ^1,2 in ruby undergoing to the low and high magnetic field.