The two-pulse echo sequence is examined for the case in which the frequency modulation time τm of the transition is intermediate between the well known limiting cases of very fast modulation (motional narrowing) and very slow or static modulation (inhomogeneous broadening). Within this spectral diffusion regime, the interpretation of the echo decay differs markedly from standard treatments. If the frequency-frequency correlation function initially decays as 1−tβ, the echo decay time TE is proportional to τmβ/(β+2). These results reduce to those of Yan and Mukamel [J. Chem. Phys. 94, 179 (1991)] for β=1. Drawing on a viscoelastic model, the theoretical results are compared to viscosity and temperature dependent vibrational echo experiments on myoglobin–CO. A τm1/3 dependence is observed, as is predicted for an exponential decay of the frequency–frequency correlation function.
The two-pulse echo sequence is examined for the case in which the frequency modulation time τm of the transition is intermediate between the well known limiting cases of very fast modulation (motional narrowing) and very slow or static modulation (inhomogeneous broadening). Within this spectral diffusion regime, the interpretation of the echo decay differs markedly from standard treatments. If the frequency-frequency correlation function initially decays as 1−tβ, the echo decay time TE is proportional to τmβ/(β+2). These results reduce to those of Yan and Mukamel [J. Chem. Phys. 94, 179 (1991)] for β=1. Drawing on a viscoelastic model, the theoretical results are compared to viscosity and temperature dependent vibrational echo experiments on myoglobin–CO. A τm1/3 dependence is observed, as is predicted for an exponential decay of the frequency–frequency correlation function.
The time-integrated three-pulse photon echo is discussed in terms of the line-shape functions which are shown to be directly related to the solvation dynamics. By using the short-time approximation to the line-shape function, an algebraic form of the three-pulse photon echo signal S PE (τ, T ) is obtained as a function of two delay times, τ and T, between pulses. On the basis of the approximate form of the photon echo signal, the echo peak shift with respect to the second delay time (population evolution period) is derived and found to be linearly proportional to the time-dependent fluorescence Stokes shift function for times greater than the bath correlation time, τ c . In the case of intermediate inhomogeneous broadening, the asymptotic echo peak shift magnitude is found to be useful in estimating the static inhomogeneous width. To illustrate the theoretical results, an analysis of the echo peak shift measurement of IR144 in a room temperature glass, PMMA, is presented.
We have measured the spectral content of the echo radiation emitted by a two-level spin system ([AlO4]0 centers in quartz), after a two-pulse excitation sequence, ${\mathrm{\ensuremath{\theta}}}_{1}$-\ensuremath{\tau}-${\mathrm{\ensuremath{\theta}}}_{2}$. In general, the experimental spectral shapes reproduce qualitatively those calculated for an inhomogeneous system of noninteracting spins. However, we found that in certain ranges of the sequence parameters (${\mathrm{\ensuremath{\theta}}}_{1}$, ${\mathrm{\ensuremath{\theta}}}_{2}$, and \ensuremath{\tau}) the widths of the experimental spectra are less than expected by a factor that amounts up to 0.5. The observed narrowing effect involves the spin packets located in a narrow spectral bandwidth (of the order of the Rabi frequency) around the excitation frequency and occurs whenever the excitation sequence induces a transverse oscillating moment of the strictly resonant packets. The spectral narrowing is a transient effect, in the sense that the spectral widths tend to recover their theoretical values for long interpulse distances \ensuremath{\tau}. We suggest a tentative interpretation which relates the narrowing to the coherence properties of the local field generated by precessional motion of the echo-active spins. \textcopyright{} 1996 The American Physical Society.
The three pulse stimulated echo, long known in magnetic resonance (1), has more recently been demonstrated on optical transitions(2). An interesting way of looking at the stimulated-echo-formation relies on the fact that the first two excitation pulses create an "ordered" population as a function of detuning .This ordered population can also be looked upon as a " grating " in frequency space from which a probe pulse can "reflect" an echo. Since a grating in only one of the levels suffices, a corollary is that the echo may be stimulated at some entirely different frequency ω2 than the one ω1, at which the grating was prepared. We report the observation of such a connected two-color stimulated echo(C2CSE) in a solid and use it to confirm the relaxation out of the 747 cm−1 vibrational state of the S1 manifold of pentacene in naphthalene. It has also been realized (3) that after redistribution of the initially excited population grating, that the echo may be stimulated from any state into which the grating has relaxed. We report here the first observation of such a relaxed two-color stimulated echo(R2CSE) and note that this echo can be seen as the optical analogue of the cross-relaxation peak in a two-dimensional nmr spectrum. The rise and fall of this relaxed echo can be used as a probe for the vibrational deactivation pathway(s) subsequent to excitation of various vibrational levels in the S1 manifold. Prior to discussing briefly some of the results we note that from an analysis of this echo effect it is clear that a necessary prerequiste to observation of such two-color photon echoes is that the inhomogeneous broadening on the selected transitions is strongly correlated. Furthermore we note that in these echo effects interference with stimulated emission and super -fluorescence must be avoided by using small-angle excitation pulses. Some of the results are shown in Fig.1. In (A) the decay of the C2CSE is presented with the solid line being a fit to a population decay parameter of the 747 cm-1 level of 33 psec. In (B) the rise of the R2CSE is shown where the probe wavelength is at the pure electronic transition. The dashed line is the expected echo-intensity rise if the initially excited vibration would directly decay into the vibrationless state. The mismatch between the dashed curve and the experimental one shows that intermediate levels in the relaxation pathway must exist. The solid line in (B) is a fit to a model where one intermediate bottleneck level is assumed with a lifetime of 16±2 psec. Other examples will be presented at the meeting.
The effects of the finite correlation time of the external modulation on the secondary-emission spectra are clarified emphasizing the deviation from the motional narrowing limit or the impact approximation in the case of large off-resonance excitation. The dependences of the excitation spectrum of the secondary emission on the modulation parameters and on the inhomogeneous broadening are studied systematically. It is found that the excitation spectrum of the luminescence shows a faster decrease than that of the Raman scattering as the off-resonance frequency increases. The present theory is relevant for explaining the recent experiment by Watanabe, Kinoshita, and Kushida [Chem. Phys. Lett. 126, 197 (1986)] on the \ensuremath{\beta}-carotene in solutions. A general theory of the time-resolved spectra of the secondary emission is formulated to incorporate the effect of the finite correlation time. The luminescence component shows a slow temporal decay with the longitudinal relaxation rate. It is found for the first time that the difference is unexpectedly large between the transient behavior of the luminescence intensity and that of the intermediate-state population for the slow-modulation regime and that the difference indicates the effect of finite correlation time of the frequency modulation. On the other hand, the transient behavior of the Raman scattering contains a fast component that follows the envelope of the excitation-pulse intensity and the same slow component as the luminescence. The ratio of the slow component to the total intensity depends sensitively on the modulation parameters and the off-resonance frequency. The modulation parameters of the system in question can be estimated from these dependences in combination with the spectral characteristics of the emission under stationary excitation.
Abstract Stimulated echo (SE), excited in an inhomogeneously‐broadened vibronic absorption band of impurity centres by three successive pulses, is considered. SE for a small delay time t2 of the second pulse, comparable with the characteristic time of vibrational relaxation, is essentially determined by the vibrational dynamics of the excited centres. The processes of a absorption and amplification of the third exciting pulse are differently modulated by vibrations, giving different contributions to the amplitude of SE. The absorption contribution is described by the function A(t3, t2, t2), while that of the amplification by A(t2, t3, t3), where A(μ, τ, τ′), is the correlation function of the resonance secondary emission of centres. For very short t2 and t3, i. e. essentially smaller than the periods of vibrations, the latter can play a role of inhomogeneity in the system, allowing one to observe the SE on homogeneous systems, such as ionic crystals with colour centres (F‐centres).
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.