We report a quantitative study of spectral diffusion in a solid-state system by measuring the stimulated echo relaxation. The spectral diffusion process in ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_{3}$ at low temperatures (2.0 K) is found to be dominated by the relaxation of the ``frozen core'' of nearest neighboring Al spins. The decay of the echo signal is found to be fully described by a simple spin-flip diffusion model and by a first-principle calculation. The complete understanding of the spectral diffusion process in this simple model system establishes a quantitative basis for using coherent optical techniques to study slow dynamics in complex systems.
We report a quantitative study of spectral diffusion in a solid-state system by measuring the stimulated echo relaxation. The spectral diffusion process in Pr3+:YAlO3 at low temperatures (2.0 K) is found to be dominated by the relaxation of the ``frozen core'' of nearest neighboring Al spins. The decay of the echo signal is found to be fully described by a simple spin-flip diffusion model and by a first-principle calculation. The complete understanding of the spectral diffusion process in this simple model system establishes a quantitative basis for using coherent optical techniques to study slow dynamics in complex systems.
Systematic measurements of stimulated-photon-echo intensities as a function of the first-to-second (\ensuremath{\tau}) and second-to-third (T) pulse separations allow the investigation of the dynamical properties of the spectral diffusion for the 7F0${\mathrm{\ensuremath{-}}}^{5}$D0 transition of a cryogenic Eu3+:YAlO3 sample. The existence of spectral diffusion was verified by the significant broadening (from 1.2 to 7.2 kHz) of the homogeneous linewidth (\ensuremath{\Gamma}) as T increases from microseconds to milliseconds, the effect being attributed to the flip flop of nearby aluminum nuclear spins surrounding the Eu3+ ion. A similar broadening effect (from 0.61 kHz, to a few kHz) was also observed in the presence of a static magnetic field H0=137 G, but with a much slower diffusion rate. To explain these observations, we use three theoretical models: the Bai-Fayer model, the diffusion-equation model, and the Monte Carlo model. Each agrees reasonably well with the experimental data and indicates the flip rates of sub-kHz order at H0=0 and an order of magnitude lower at 137 G.
The mechanisms and effects of spectral diffusion for optical transitions of paramagnetic ions have been explored using the inhomogeneously broadened 1536 nm $^{4}\mathrm{I}_{15∕2}\ensuremath{\rightarrow}^{4}\mathrm{I}_{13∕2}$ transition in Er3+:Y2SiO5. Using photon echo spectroscopy, spectral diffusion was measured by observing the evolution of the effective coherence lifetimes over time scales from $1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ to 20 ms for magnetic-field strengths from 0.3 to 6.0 T, temperatures from 1.6 to 6.5 K, and nominal Er3+ concentrations of 0.0015%, 0.005%, and 0.02%. To understand the effect of spectral diffusion on material decoherence for different environmental conditions and material compositions, data and models were compared to identify spectral diffusion mechanisms and microscopic spin dynamics. Observations were successfully modeled by ${\mathrm{Er}}^{3+}\ensuremath{-}{\mathrm{Er}}^{3+}$ magnetic dipole interactions and Er3+ electron spin flips driven by the one-phonon direct process. At temperatures of 4.2 K and higher, spectral diffusion due to 89Y nuclear spin flips was also observed. The success in describing our extensive experimental results using simple models provides an important capability for exploring larger parameter spaces, accelerating the design and optimization of materials for spatial-spectral holography, and spectral hole-burning devices. The broad insight into spectral diffusion mechanisms and dynamics is applicable to other paramagnetic materials, such as those containing Yb3+ or Nd3+.
Random frequency modulations exist in many systems, such as magnetic system and glasses at low temperature, dye solution. In magnetic systems, spin flips of doped ions or nuclei in the host lattice can cause the magnetic fluctuations at the impurity site, and hence the stochastic change of the transition frequency of the impurity ions. It is the main source of doped ions' optical dephasing at low temperature. Because the interactions have various time scales and strengths, they can lead to a time dependent broadening spectral line (heterogeneous line), the process is socalled spectral diffusion. Several theoretical methods have been used to explain this phenomenon. They all divided the interactions into only two time scales, the fast one results from spin flipping of the bulk nuclei, and the slow one comes from the contributions of the nearby nuclear spins in a frozen core. However, to describe the complete dynamic process in practical systems, these two time scales are obviously not enough. In addition, spectral diffusion is a typical frequency domain process, but almost no theoretical work started from the pure frequency domain point.In this paper , the spectral diffusion in paramagnetic ions doped system at high field, in which has the modulation frequency dependent jump rates, is studied in both frequency and time domains. In general, the spectral diffusion goes as [1-exp(- WT w )] x . Without frozen core, the values of x are 1/2 and 1 for frequency and time domains, respectively. Considering frozen core effect, the spectral diffusions are slow down by the factor of ( ω eff / ω 0) 2, where ω 0 is the frequency characterized frozen core, and ω eff are ω max and H ∞ for frequency and time domains, respectively. When the frozen core is large enough, the spectral diffusions in two domains tend to have the same form as x ≈0 22.
Photon echo measurements made at 2 °K on the 3H4 - 1D2 transition in Pr3+:LaF3 show that magnetic dipolar couplings between the Pr and F nuclei account for the 56 kHz homogeneous linewidth of this transition.1 The homogeneous broadening arises from the enhanced 141Pr nuclear moment (I=5/2) interacting with the local field fluctuations of the 19F nuclear moments undergoing mutual spin flip transitions. Such resonant fluctuations should, in the absence of a fluorine spin diffusion barrier, produce a homogeneous linewidth of about 200 kHz which is, in fact, roughly what is observed for the inhomogeneous broadening of the Pr3+ hyperfine levels and is considerably broader than that obtained by the photon echo measurements. Shelby et al2 proposed a simple model analogous to the spin diffusion barriers responsible for narrowing the homogeneous lines in certain electron paramagnetic resonance transitions3. In such systems, the field produced by the electron magnetic dipole moment (2-3 orders of magnitude larger than the enhanced nuclear moment associated with the ground state of Pr3+ in LaF3) de-tunes the nearest neighbors from each other, prohibiting mutual spin flips among them. Thus, the fields produced by the neighboring spins are static and their interaction with the paramagnetic ion contributes to the inhomogeneous linewidth and not to homogeneous broadening. The de-tuned neighbors are referred to as the "frozen core." Application of this picture to the case of Pr3+:LaF3 is supported by the calculation of Devoe et al.4 Their Monte Carlo calculation of the Pr3+ optical dephasing times shows that the observed homogeneous linewidth could be explained by deleting the nearest neighbor F spins from the lattice of rapidly fluctuating fluorine moments, in effect, treating them as part of a frozen core.
Two-pulse photon-echo measurements on the 0.1 at. % Pr3+:YAlO33H4${\mathrm{\ensuremath{-}}}^{1}$D2 transition suggest that the relaxation time depends on the density of excited states created by the excitation pulses. The dependence of the relaxation time on the intensity of each excitation pulse shows that our results are inconsistent with instantaneous spectral diffusion, a model often invoked in this type of experiment, where excited states created by the second pulse chiefly influence the relaxation time. A homogeneous linewidth contribution, noted in previous work as being of unknown origin, is eliminated at low excitation fluences.