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Journal of Physics Condensed Matter

Stimulated nutation echo: application to the driven decoherence study

G. Bimbo, R. Boscaino, M. Cannas, F. M. Gelardi, R. N. Shakhmuratov

Published Jun 6, 2003• 3 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/15/24/315

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Physical Review Letters•Oct 20, 1997•31 citations
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.
We study experimentally the dynamical and decay properties of the Stimulated Nutation Echo (SNE) in a two-level spin system. This is the signal which appears in the transient response of the system to the second pulse at time tau_1 elapsed from its beginning 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 tau between the 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. The dependence of these decay rates on the pulse intensity is discussed, and its relationship with the anomalous (non-Bloch) decay of other coherent transients in solids is examined.
The decay of two-pulse nutational echo has been experimentally investigated in S equals 1/2 spin systems (E' centers in silica) at microwave frequency. We have found that damping is well described by single exponential decay function. When the time delay between the pulses increases the measured echo amplitude decreases with the decay rate of 1/T1, as expected from a T1-T2 model (Bloch model), and does not depend on the Rabi frequency (chi) . But with increasing of the first pulse duration t1 the measured decay rate depends on (chi) linearly. Theoretical calculations within the high-field Torrey approximation give linear dependence of the decay rate on (chi) with increasing of the duration t1. The agreement between the theoretical and experimental results is only qualitative. We assume that the strong difference between the theoretical prediction and the observed (chi) -dependence of the decay is caused by the frequency noise of the microwave radiation.
Observation of the optical analog of the delayed nutation echo [V. S. Kuz'min et al., Zh. \'Eksp. Teor. Fiz. 99, 215 (1991) [Sov. Phys. JETP 72, 121 (1991)] recently shown in nuclear magnetic resonance is reported. We call this echo a stimulatednnutationnecho (SNE) in analogy to the three-pulse-stimulated echo that is produced from a hole pattern burnt into an inhomogeneous line. In a SNE two-pulse sequence, the first pulse burns a train of holes into the inhomogeneous absorption spectrum and its duration tp{\mathrm{t}}_{\mathrm{p}}tp​ is stored. After a long delay time the second pulse burns its own train of holes. When coincidence of these holes takes place, the SNE occurs at a time t=tp{\mathrm{t}}_{\mathrm{p}}tp​ following the start of the second pulse. Thus the second pulse reads exactly the duration of the first pulse. It is shown that for a Gaussian-shaped beam, the echo becomes sharper and well recognizable. This echo may be used for Rabi frequency measurement and spectral diffusion studies.
The anomalous behavior of transient nutations is experimentally investigated in a set of two-level (S=12)(S=\frac{1}{2})(S=21​) spin systems differing only in spin concentration. Our results show that the non-Bloch power dependence of the decay rate of transient nutations is a concentration-dependent effect, which is more and more pronounced in more and more concentrated samples. The experimental results are interpreted in the framework of the recent theory by Shakhmuratov et al. [Phys. Rev. Lett. 79, 2963 (1997)] and support the hypothesis that the anomalous decay of transient nutations in solids originates from radiation-induced changes of the dipolar field, rather than from residual fluctuations of the nominally coherent field.
Pulsed radio-frequency transient phenomena of resonant two-level spins are often described by the Bloch equations where the phenomenological dipole (T2{T}_{2}T2​) and population (T1{T}_{1}T1​) decay times appear. A similar description has been carried over recently into the microwave and infrared regions as well. At visible-ultraviolet wavelengths, however, a more general solution is required because the transition levels do not constitute an isolated system and also spontaneous emission can no longer be disregarded. As a consequence, the lower (1) and upper (2) transition levels are characterized by vastly different decay rates (${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$) and the lifetime T1{T}_{1}T1​ is no longer a defined quantity. In view of laser-induced coherent transient phenomena now being observed, we present general solutions of the density-matrix equations of motion for an optically resonant two-level system in contact with a multilevel reservoir where ${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$. Particular and perturbative solutions involving intensity-dependent damping and frequency shifts are included with applications to echo and nutation phenomena.
Free induction decay and transient nutations are investigated in a system of two-level particles with an inhomogeneously broadened spectrum. The influence of the x (real) and y (imaginary) parts of the complex amplitude of the noise, induced by the driving field in the sample, is considered. It is shown that both noises affect T1{T}_{1}T1​ and T2{T}_{2}T2​ relaxation processes. When field-noise contributions to 1/T2{1/T}_{2}1/T2​ and 1/T1{1/T}_{1}1/T1​ relaxation rates are dominant and equal to each other, Bloch's saturation is changed to Redfield's saturation. This effect also accelerates transient nutation decay. Comparison with experimentally observed free induction decay and transient nutation in color centers in quartz is discussed.