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physica status solidi (b)

Stimulated Echo and Vibrational Dynamics

V. Hizhnyakov

Published Apr 1, 1990• 2 citations
Publisher

Abstract

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).

DOI
10.1002/pssb.2221580233

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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.

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We study experimentally the dynamical and decay properties of the stimulated nutation echo (SNE) in a two-level spin system, the signal of which allows the observation timescale of the driven coherence relaxation to be extended. This signal appears in the transient response of the system to the second pulse at time τ 1 from its start and coinciding with the duration of the first pulse. The information about the first pulse duration is imprinted into the population difference of the inhomogeneously broadened ensemble of the two-level absorbers. The decay of the SNE signal has two contributions. One originates from the population decay during the time τ between the two pulses. Another is caused by the coherence loss during the excitation by the first pulse and the reading time of the second pulse. Experimental results on the decay properties induced by these mechanisms are presented for the first time. We investigate the dependence of these decay rates on the pulse intensity and we examine its relationship with the anomalous (non-Bloch) decay of other coherent transients in solids.

Journal of Physics Condensed Matter•Jun 6, 2003•3 citations
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).
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 phase relaxation of optically excited electronic states can be studied in fourwave mixing experiments where three excitation pulses at t = 0, t =t21, and t = T, respectively, interact via the third-order polarization of the medium to generate a nonlinear signal whose intensity depends on the dephasing time T2. For inhomogeneously broadened optical transitions the signal will be emitted as a time delayed photon echo pulse at t = T + t21 provided the pulse duration is short compared with T2. The echo amplitude decays as exp(−4t21/T2).1
Photon echoes, observed recently in ruby and in NH2{\mathrm{NH}}_{2}NH2​D gas by two-pulse laser excitation, exhibit a modulation behavior as the pulse delay time is varied. The effect, which arises in a three-level quantum system, is due to the interference of two optically coupled transitions that share a common level. In this article, the three-level echo problem is treated exactly. Wave-function solutions are incorporated that are handled conveniently by a Laplace-transform technique. We, therefore, extend the earlier theory of echo modulation by Lambert et al., by removing their restriction of on-resonance pulse excitation. This procedure allows us to examine the effect of inhomogeneous broadening on echo amplitude explicitly, and we treat the problem by numerical and also by analytical means for the case of a Doppler-broadened gas. Analytic expressions are derived either for a high or a low laser power regime corresponding to excitation of either a large or a small fraction of the Doppler linewidth. The former case is analogous to pulsed nuclear magnetic resonance and is well known, whereas the latter result is new and applies to current photon echo measurements.
It is the purpose of the present paper to study the dynamics underlying a three-pulse photon-echo process performed on a vibronic system coupled to non-Markovian baths, when a neighboring level enters into the global dynamical evolution because of broadband excitation required in these experiments. Particular emphasis is on the energy gap between the vibronic levels, but also on the fluctuation amplitudes and correlation times of their corresponding thermal baths. The photon-echo signal appears to be very sensitive to the additional interfering contributions introduced by the neighboring vibronic level. It is shown that these contributions associated to the pathways involving different vibronic states are modulated by their corresponding energy gap. As a consequence, these contributions to the integrated photon-echo signal strongly decrease for large energy gaps. Also, an oscillating behavior is observed on the time dependence of the photon-echo signal resulting from the summation of the contributions provided by the individual vibronic levels. Moreover, the influence of the non-Markovian character of the baths, accountable for inhomogeneous broadening, affects the amplitude and the time dependence of the photon-echo signal, as well as its dependence with the delay time of the laser pulses. Of course, for longer times a Markovian dynamical evolution is recovered.
We study experimentally the dynamical and decay properties of the stimulated nutation echo (SNE) in a two-level spin system, the signal of which allows the observation timescale of the driven coherence relaxation to be extended. This signal appears in the transient response of the system to the second pulse at time τ 1 from its start and coinciding with the duration of the first pulse. The information about the first pulse duration is imprinted into the population difference of the inhomogeneously broadened ensemble of the two-level absorbers. The decay of the SNE signal has two contributions. One originates from the population decay during the time τ between the two pulses. Another is caused by the coherence loss during the excitation by the first pulse and the reading time of the second pulse. Experimental results on the decay properties induced by these mechanisms are presented for the first time. We investigate the dependence of these decay rates on the pulse intensity and we examine its relationship with the anomalous (non-Bloch) decay of other coherent transients in solids.