Free-induction decay in a fluctuating two-level system

R. Boscaino, V. M. La Bella

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.

Pavel A Apanasevich, S. Ya. Kilin, Alexander P. Nizovtsev +1 more

Masakazu Kunitomo, T. Endo, Shunsuke Nakanishi +1 more

Anatoly I. Burshtein, Vladimir S. Malinovsky

Sudden-modulation theory is used for the calculation of stationary saturation and polarization of two-level systems. The randomly fluctuating frequency of the two-level system is assumed to be a noncorrelated, purely discontinuous Markovian process. The stationary probability of field-induced transitions is calculated exactly. It is shown that if the frequency modulation is fast (or if the field is strong enough) the transition probability coincides with that obtained in the framework of perturbation theory when the latter is developed in its integrodifferential non-Markovian version. This probability differs from the kinetic probability calculated by Markovian perturbation theory (with fluctuating frequency) in its corresponding spectral wing shape and in the field dependence of its corresponding resonance width. This field dependence is smoother than that in Markovian theory and stabilizes when the resonance width is not equal to the natural transition width. Nevertheless, in the Lorentzian approximation the free-induction decay rate in the framework of exact (or non-Markovian) theory increases with the field in nearly the same way as that in Markovian theory. Almost the same is true of the field dependence of the free-induction decay amplitude in either theory, provided that the signal correlation before and after the field is switched off is neglected. The conditions are found under which the Lorentzian approximation of the transition probability is valid. These conditions are shown to break down when the theory (in the fast-frequency-modulation limit) leads to agreement with experiments reported by De Voe and Brewer [ Phys. Rev. Lett.50, 1269– 1272 ( 1983)].

Christopher Feuillade, C. Böttcher

R. Boscaino, F. M. Gelardi, G. Messina

Two-photon free-induction decay (FID) was experimentally investigated in a two-level electron-spin system by revealing the second-harmonic wave emitted by the system. Oscillatory FID signals were detected for large-area pulses of the input power, analogously to recent observations by Kunitomo et al. for single-quantum resonances. Moreover, the measured decay time of the FID signal following a steady-state preparation was found to be larger than the theoretical value by a few orders of magnitude.