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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Two-pulse nutational echo in spin systems

V. S. Kuz’min, Г. Г. Федорук

Published Sep 26, 1997• 2 citations
Publisher

Abstract

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.

DOI
10.1117/12.287669

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Journal of Experimental and Theoretical Physics•Jun 1, 2005•0 citations
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.
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.
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.
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.
Here, a theory of the intensity and concentration dependent damping of nutation signals observed by Boscaino et al. (Phys. Rev B 48, 7077 (1993); Phys. Rev. A 59, 4087 (1999)) and by others in various two-level spin systems is proposed. It is shown that in diluted paramagnetic solids contribution of dipole-dipole interaction to the nutation decay is negligibly small. We elaborated a cavity loss (radiation damping) mechanism that explains the intensity- and concentration dependence of the damping. It is shown that instead of ordinary Bloch's transverse T2 and longitudinal T1 damping parameters the decay of transverse and longitudinal spin components in nutation process are described by one and the same intensity-, concentration-, frequency- and time dependent damping parameter.
The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω rf is close to the Rabi frequency ω 1 in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ɛ are accompanied by higher-frequency oscillations at frequencies n ω rf and n ω rf ± ɛ, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ɛ on the sign of the detuning ω 1 − ω rf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω rf + ɛ increases, while the amplitude at the difference frequency ω rf − ɛ decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E ′ 1 centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.
Two-photon transient nutation is observed in a two-level spin system ( E ′ 1 centers in crystalline quartz) using a transverse microwave field and a linearly polarized rf field oriented along a static magnetic field in the electron paramagnetic resonance. Nutation is excited when the sum of the energies of a microwave photon and a rf photon is equal to the energy difference between two spin states. The two-photon nature of nutation is confirmed by measuring its frequency as a function of the amplitude and frequency of the rf field as well as the amplitude of the microwave field. The amplitude of the effective field of two-photon transitions is measured. It is shown that the decay rate of two-photon nutation is close to the decay rate for one-photon nutation and is determined by the spin-spin interaction between E ′ 1 centers.