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

New look at non-Bloch decay of transient nutation and free induction in S=1/2 systems

R. N. Shakhmuratov, F. M. Gelardi, M. Cannas

Published Sep 26, 1997• 2 citations
Publisher

Abstract

Steady-state free induction decay (FID), hole burning (HB) and transient nutations (TN) decay are investigated in ensemble of two-level particles with inhomogeneously broadened spectrum. The influence of x- and y-noise components induced by the coherent field exciting the resonant transition is considered. It is shown that 'longitudinal' (x) and 'transverse' (y) noises give the contribution to both T1 and T2 relaxation processes. This effect accelerates TN decay and changes the saturation broadening seen in HB and FID. It is found that when field-noise contributions to 1/T2 and 1/T1 relaxation rates are dominant and equal to each other, the Bloch's saturation is changed to Redfield's saturation. Comparison with experimentally observed FID and TN in nearly ideal spin system (color centers in quartz and silica) is discussed.

DOI
10.1117/12.287679

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Journal of Physics Condensed Matter•Jun 6, 2003•3 citations
Steady-state free induction decay (FID), hole burning (HB) and transient nutations (TN) decay are investigated in ensemble of two-level particles with inhomogeneously broadened spectrum. The influence of x- and y-noise components induced by the coherent field exciting the resonant transition is considered. It is shown that 'longitudinal' (x) and 'transverse' (y) noises give the contribution to both T1 and T2 relaxation processes. This effect accelerates TN decay and changes the saturation broadening seen in HB and FID. It is found that when field-noise contributions to 1/T2 and 1/T1 relaxation rates are dominant and equal to each other, the Bloch's saturation is changed to Redfield's saturation. Comparison with experimentally observed FID and TN in nearly ideal spin system (color centers in quartz and silica) is discussed.
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.
Resonant excitation of an inhomogeneously broadened ensemble of two-level atoms (TLA) by a stochastic field with phase noise is theoretically investigated. Free-induction decay (FID), hole burning (HB), and transient nutation (TN) are studied. We consider two kinds of driving fields, one with a free walking phase and another with the phase locked in a limited domain. It is shown that the resonant excitation behavior depends strongly on the noise property. Noise induced by a walking phase gives a simple contribution to the dephasing time, T2,{T}_{2},T2​, of two-level atoms whereas phase locking qualitatively changes the laser-atom interaction. In the latter case, it is shown that even when the central part of the driving field spectrum is narrower than homogeneous absorption line of the TLA, the wide, low intensity wings of the spectrum (sidebands produced by the locked phase noise), have a strong effect on the FID, TN, and HB induced by the central, narrow part of the spectrum. The influence of sidebands on photon echoes is also discussed.
The steady-state free-induction decay (FID) has been investigated in samples of crystalline and amorphous quartz containing paramagnetic two-level electron spin centers (S=1/2). We report experimental data on the dependence of the FID rate on the Rabi frequency \ensuremath{\chi} induced during the preparative stage. Our results confirm that the decay of the FID signal is much slower than expected on the basis of the conventional Bloch equations. The range of \ensuremath{\chi} investigated here is wide enough to show the whole transition from Bloch-type behavior to the high-power Redfield limit, in which the FID rate is determined only by \ensuremath{\chi}. The experimental data are compared with theoretical results recently obtained by hypothesizing Gaussian-Markovian fluctuations of the resonance frequency. Even if agreement is poor, the comparison suggests by itself the possibility that more than one source of fluctuations may be effective. Other possible origins of the failure of the Bloch equations as well as of the stochastic theories are examined.
Transient hole-burning and free induction decay (FID) in low-temperature ion-doped crystals are studied consistently using the model of two jump processes Ut equals Ut1 + Ut2 characterized by essentially different jump rates v1 >> v2 and distribution widths (sigma) 1 << (sigma) 2 for the impurity ion optical transition frequency fluctuations Ut due to the bulk and the frozen core spin flipping. At short pump/probe pulsewidth T and short delay time (tau) d ((tau) d, T << v2-1) the calculated hole shape is narrow with the hole width determined by Ut1 process characteristics only. The hole width in this case coincides with the calculated FID rate. At long delay (tau) d >= v2-1 the hole becomes a wide lorentzian with the halfwidth 2(sigma) 2. The theory fits well the experimental data by A. Szabo et. al. on narrow hole burning and FID in ruby under low and high magnetic fields supposing the fluctuations Ut1 to be rather slow ((sigma) 21/v21 equals 0.5).
The free-induction decay (FID) after saturation by a laser radiation pulse of finite duration is studied for systems with spectral diffusion. The exact solution of the FID signal shape has been obtained in the framework of the telegraph noise model. This solution takes into account the finite duration of the saturating field and is valid at arbitrary values of the spectral exchange rate and the amplitude of the coherent field. The exact expression of the FID signal is derived in the weak-external-field limit. It is shown that the FID signal suddenly disappears after a time equal to the pulse width. This confirms the validity of the theorem on coherent transients, which has been proved for the Bloch equations [A. Schenzle, N. C. Wong, and R. G. Brewer, Phys. Rev. A 22, 635 (1980)].
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.