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Physical Review A

Free-induction decay after a pulse saturation for systems with random telegraph frequency

Vladimir S. Malinovsky

Published Dec 1, 1995• 8 citations
Publisher

Abstract

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)].

DOI
10.1103/physreva.52.4921

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Journal of the Optical Society of America B•May 1, 1991•24 citations
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)].
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 a model of noncorrelated spectral exchange. The analysis accounts for the finite duration of the saturating field and is valid at an arbitrary value of the spectral exchange rate and amplitude of the coherent field. An exact expression for the FID signal is derived in the weak-external-field limit. A self-consistent explanation of the experimental field dependence of the FID rate [A. Szabo and T. Muramoto, Phys. Rev. A 39, 3992 (1989)] is obtained using a model of slow noncorrelated spectral diffusion.
The free induction decay (FID) after saturation by a laser radiation pulse of finite duration is studied for systems with spectral diffusion. The exact solutions of the FID signal shape have been obtained in the framework of telegraph noise model as well as model of noncorrelated spectral exchange. These solutions take into account the finite duration of saturating field and are valid at arbitrary value of the spectral exchange rate and the amplitude of the coherent field. A selfconsistent explanation of the field dependence of the FID rate found by Szabo and Muramoto is obtained under the slow noncorrelated spectral diffusion.
The free induction decay (FID) and light-echo kinetics are calculated under the assumption that a two-level system frequency is a purely discontinuous noncorrelated Markovian process, and its statistical distribution is a bi-Lorentzian contour. The latter assumption is primarily mathematical, but useful. The model allows one to obtain an exact solution of the FID problem, which recovers the results obtained earlier with perturbation theory (the fast modulation limit) as well as the result concerning the slow modulation limit. It is shown that only in the latter case does the field dependence of the FID rate found by De Voe and Brewer [Phys. Rev. Lett. 50, 1269 (1983)] have a self-consistent explanation.
We derive the effects of random telegraph noise on the equations of optical resonance. The random-telegraph-signal model allows some results to be found exactly, independent of the strength of the noise or the strength of the field that induces the resonant transitions. Our optical resonance equations depart from the well-known empirical optical Bloch equations in several ways. We obtain excellent agreement at high, low, and intermediate Rabi frequencies with the data of DeVoe and Brewer [Phys. Rev. Lett. 50, 1269 (1983)]. This is the first such agreement that has been reported with a value of the noise coherence time smaller than about 20 \ensuremath{\mu}sec.
Recent studies of the failure of the optical Bloch equations (OBE) in describing optical saturation in a solid are extended to test another aspect of the OBE, namely the time dependence of free-induction decay (FID) predicted by the SWB theorem on optical transients [Schenzle, Wong, and Brewer, Phys. Rev. A 22, 635 (1980)]. This theorem states that, following an arbitrarily shaped excitation pulse of length T, the FID will vanish at time T following the end of the excitation pulse. Experiments with ruby violate SWB in that FID decay at least twice as long as the excitation pulse is observed. Numerical and analytical calculations using a Gauss-Markov model for the modified OBE show an extended FID decay, however, the theoretical decay shape does not agree with experiment. Thus as with earlier studies on saturation broadening, we find that the modified OBE provides only a qualitative description of radiation-atom interaction in a solid.
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)].