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DYNAMICS OF PULSED SATURATION IN INHOMOGENEOUSLY BROADENED TWO-LEVEL

Vladimir Kuz

Published Jan 1, 1997• 0 citations
OpenAlex

Abstract

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.

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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.
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.
We present a numerical method for solving the Maxwell-Bloch equations describing pulse propagation for a two-level medium. The method is accurate, efficient, stable, and well suited for this type of simultaneous equations. By applying the numerical scheme we investigate the evolutions of pulse area, pulse propagation, pulse velocity, and spectral shapes under both homogeneous and inhomogeneous broadening conditions. The results show that the area evolution and pulse-reshaping procedure are significantly influenced by detuning and inhomogeneous line shape, which also impact the oscillation tail and pulse peak. In addition, the pulse-peak traces indicated the pulse velocity always increases with greater deviation in pulse-area value from the value 2\ensuremath{\pi}. We also demonstrate the pulse velocity increased for a larger detuning or a wider inhomogeneous line shape. Furthermore, the spectral feature shows that pulse spectra evolve into an oscillating shape.
It is shown that induced transitions of an ensemble of two-level articles with an inhomogeneously broadened line in the field of a phase-modulated pulse are analogous to Landau-Zener inelastic transitions in molecules when their terms cross. Even for T% T:, where T and T: are, respectively, the pulse width and the inhomogeneous relaxation time of the medium, a transition of particles of the entire spectrum ( T:) - ' from an upper to a lower level is possible, signifying the complete removal by the pulse of the energy stored in the active medium. Analysis of the dynamics of a phase-modulated pulse by means of the Maxwell-Bloch equations shows, in addition, the possibility of amplifying it without the development of field-amplitude oscillations.
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.
Bloch equations are used to derive an analytic expression for the integral nutation-signal decay rate in a two-level quantum system. It is found that when inhomogeneous line broadening is taken into account, the temporal decay of the response is due not only to coherent suppression but also to additional decay whose rate depends on the ratio of the Rabi frequency to the inhomogeneous linewidth. The results are used to explain the anomalous (Rabi-frequency-dependent) EPR-nutation decay detected in quartz in the experiments of R. Boscaino, F. M. Gelardi, and J. P. Corb [Phys. Rev. B 48 , 7077 (1993)]. Contrary to the statement made by these researchers that this decay is non-Bloch, it is found that the process can be described by Bloch equations without any modification.
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)].