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Technical Physics

Saturation of two-level systems under pulsed stochastic resonance conditions

Баруздин Сергей Анатольевич

Published Dec 1, 1999• 1 citation
Publisher

Abstract

Pulsed stochastic excitation of a two-level system described by Bloch equations is studied. An equation for the average powers of the components of the state vector of the system is obtained on the basis of the theory of stochastic differential equations, and solved. The dynamical and nonlinear properties of the response of a system under pulsed stochastic resonance conditions are analyzed and the results are compared with the corresponding stationary state. The results obtained can be used in spectroscopy and for analysis of nonlinear filters based on the saturation effect and intended for processing rf and light range signals.

DOI
10.1134/1.1259548

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Pulsed stochastic excitation of a two-level system described by Bloch equations is studied. An equation for the average powers of the components of the state vector of the system is obtained on the basis of the theory of stochastic differential equations, and solved. The dynamical and nonlinear properties of the response of a system under pulsed stochastic resonance conditions are analyzed and the results are compared with the corresponding stationary state. The results obtained can be used in spectroscopy and for analysis of nonlinear filters based on the saturation effect and intended for processing rf and light range signals.
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The saturation effect during the excitation of a two-level system by laser pulses is investigated in the framework of two approaches: excitation probability based on Karplus–Schwinger spectral profile and exact solution of Bloch equations. Simple analytical expression for the excitation probability by exponential pulse is derived. The excitation spectra obtained using this expression were compared with the result of solving the Bloch equations for various values of the pulse duration and the Rabi frequency, which describes the strength of the electromagnetic interaction. It is shown that in the case of long pulses, there is a satisfactory correspondence between the two approaches, but in short-pulse limit and strong saturation, the probability description based on Karplus–Schwinger spectral profile and perturbation theory does not provide satisfactory results.
In an approach based on the nonlinear Riccati-type differential equation for the ratio of the level population amplitudes, rather than on the optical Bloch equations, we describe the response of a two-level system to a few--cycle light pulse of intensity from the regime of extreme nonlinear optics, i.e., when the Rabi and transition frequencies are comparable.Emphasis is put on the dependence of the spectra of the scattered light on the carrier--envelope phase, duration and strength of both resonant and off-resonant pulses.
A generalized formulation is presented for determining the saturation thresholds for optical processes excited by ultrafast pulses based on the pulse area of the excitation pulse. It is demonstrated that the threshold of driving-pulse intensity for absorption and fluorescence saturation in a two-level system is inversely proportional to the square of the duration of the excitation pulse. These results are obtained from both a simplified analytical solution assuming a Gaussian excitation pulse shape and a detailed numerical calculation based on density-matrix equations. The calculation is generalized further to obtain the saturation condition for a two-photon Raman process by defining a two-photon pulse area both analytically and numerically. These results not only provide predictive capabilities for determining thresholds of signal saturation using ultrashort durations with arbitrary pulse shapes and durations but also open up possibilities for predetermining the threshold intensities of various resonant nonlinear processes.
On the basis of Bloch's equations an analytical expression is obtained for the pulsed saturation signal of a two-level quantum system with allowance for inhomogeneous line broadening. It is shown that in this case the signal drop is exponential over the initial portion and nonexponential for long times. It is found that starting from a certain time, which depends on the field magnitude, relaxation parameters, and inhomogeneous width of the line, a through appears in the line contour, the depth and width of which increases with an increase in pulse duration. At smaller durations of the pulse, when the line is bell-shaped, an exponential decay of the signal indicates saturation of homogeneously broadened line. Comparison of the results obtained in an experiment on pulsed saturation in ruby shows that at large amplitudes of the field and considerable inhomogeneous broadening, one observes a deviation from the Bloch theory manifesting itself as a biexponential drop in the pulsed saturation signal A conclusion is drawn that the Bloch theory satisfactorily describes the experiment until the effective time of energy transfer to the lattice is smaller than the time of the spectral propagation of excitation.