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Journal of Experimental and Theoretical Physics

Correlation echoes in the stochastic excitation of inhomogeneously broadened two-level systems

Баруздин Сергей Анатольевич

Published Jul 1, 1997• 2 citations
Publisher

Abstract

The third-order cross-correlations between a free induction signal of an inhomogeneously broadened two-level system and white Gaussian noise exciting this system are studied. The temporal properties of the third-order cross-correlation functions are found to correspond to the characteristics of ordinary two-and three-pulse spin and light (photon) echoes excited by determinate radio pulses. The nonlinear properties of correlation echoes are studied as functions of the noise pulse parameters. It is established that the correlation echo amplitude is determined not only by the noise pulse parameters but also by the position on the time axis of the noise counts that form the given type of echo. Finally, the behavior of the spin and light correlation echoes in the appropriate ranges is discussed.

DOI
10.1134/1.558312

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The third-order cross-correlations between a free induction signal of an inhomogeneously broadened two-level system and white Gaussian noise exciting this system are studied. The temporal properties of the third-order cross-correlation functions are found to correspond to the characteristics of ordinary two-and three-pulse spin and light (photon) echoes excited by determinate radio pulses. The nonlinear properties of correlation echoes are studied as functions of the noise pulse parameters. It is established that the correlation echo amplitude is determined not only by the noise pulse parameters but also by the position on the time axis of the noise counts that form the given type of echo. Finally, the behavior of the spin and light correlation echoes in the appropriate ranges is discussed.
The excitation of a stimulated spin echo by two coherent pulses of Gaussian white noise and a δ -function-like radio pulse is studied. The mean value of the complex envelope of the echo is obtained by solving the Bloch equations. The behavior of the mean value of the envelope of the stimulated echo is investigated for a Lorentzian shape of the inhomogeneously broadened absorption line. It is shown that in an excitation regime which is linear for noise pulses the envelope corresponds to the Fourier transform of the line-shape function. Nonlinear distortions of the mean value of the envelope of a stimulated echo can arise outside the linear excitation regime.
The excitation of photon echo by noise pulses that are formed by modulation of the carrying frequency with Gauss noise is modeled. The modeling is based on optical Bloch equations the solution of which for noise pulse realizations is constructed by their stepwise approximation. In terms of the formalism of state transfer matrices, the two- and three-pulse excitation modes are analyzed. The complex envelopes of the primary and stimulated echo responses are determined. In the linear (low-level-signal) mode, the shape of the two-pulse echo corresponds to that of the time delayed and inverted noise pulse. The boundary of the linear mode, upon exceeding of which distortions of the shape of the noise pulse become noticeable, is determined. The shape of the stimulated (three-pulse) echo in the linear mode corresponds to that of the autocorrelation function of the noise pulse realization. Upon passage beyond the boundary of the linear mode, the shape of the three-pulse echo corresponds either to the cross-correlation function of distorted noise pulses (with different intensities) or to the autocorrelation function of distorted pulses (with the same intensities). The modeled photon echo excitation modes can be used in photon echo processors to process signals in the light range.
An analytical study of the photon echoes associated with the three-level system interacting resonantly with optical pulses possessing two different frequencies is performed. It is predicted that photon echoes arise at anomalous times corresponding to the correlation between the inhomogeneous broadenings for the different spectral lines as well as at the normal time expected in a simple two-level system. This new effect is caused by the coupling of the two resonant transitions through the common energy level. Furthermore, if the particle does not have inversion symmetry, the echoes with the sum or difference frequency of the exciting optical pulses can be observed in such a system. The quantitative analysis is also given for intensities, direction of propagation and polarizations of the anomalous echoes which depend upon the exciting pulses with different frequency.
The excitation of stimulated echo by two pulses of Gaussian white noise, which are originated from a single source and short coherent pulse is considered. The present work studies the nonlinear properties of average amplitude of the echo as function of the spectral power density. The mean value of the complex envelope of the echo is obtained by solving stochastic Bloch equations in Stratonovich sense. The results can be used for analysis of nonlinear excitation characteristics based on saturation effect in photon and spin processors.
A general expression for coherent transients, free induction decay and echoes, of an atomic or spin two-level system excited by resonant laser or rf field in the form of two square pulses is given by using the Fourier-transform method. This expression interprets the main characteristics of the transient signals well. An analytic expression for the shapes of two-pulse echoes is derived by assuming infinite inhomogeneity and the same Rabi frequencies for the two pulses. Two-pulse echo shapes were numerically calculated for various combinations of pulse areas by using the analytic expression. Nuclear-magnetic-resonance experiment was carried out on an inhomogeneously broadened proton spin system. Experimental two-pulse echo shapes are compared with the calculated ones. Agreement between theory and experiment is quite excellent.