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Physical review. B, Condensed matter

Pulse saturation behavior of inhomogeneously broadened lines. II. Rapid-spectral-diffusion case

Jean‐Pierre Korb, J. Maruani

Published Jun 1, 1981• 7 citations
Publisher

Abstract

A model involving two coupled thermodynamic reservoirs is used to obtain analytical expressions for inhomogeneously broadened absorption and dispersion signals under resonant and nonresonant stationary weak-pulse and strong-pulse saturation. This model allows a good reproduction of the dipolar-reservoir-like effects observed on absorption lines and predicts similar effects for dispersion signals.

DOI
10.1103/physrevb.23.5700

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The lowest energy two-dimensional exciton in GaAs/GaAlAs multiquantum wells (MQW) is inhomogeneously broadened at low temperature by fluctuations in the layer width. The broadening permits probing of the excitons as a function of position within the inhomogeneous line[1]. At high densities interaction between the excitons becomes important and leads to saturation and to an increase of the homogeneous linewidth[2]. Using the picosecond pump/probe technique we have measured the saturation behavior as a function of exciton energy within the inhomogeneously broadened line. Figure 1 shows the transmission spectrum T of a weak narrowband probe (dotted) and the change in transmission ΔT of the probe induced by the presence of a pump for two different pump wavelength for 102 Å thick layers of GaAs separated by 200 Å layers of AlGaAs. An increase in transmission (holeburning) at the pump wavelength is observed showing that the interaction between resonant excitons is much stronger than between nonresonant excitons. The strength of the hole decreases rapidly on passing through the center of the line towards the high energy side. This is consistent with an increase in the homogeneous linewidth of the higher energy excitons[1,3]. By delaying the probe we measured the rate of decay of the hole which was found to depend strongly on pump intensity. At low intensity the hole lifetime approaches the luminescent lifetime but becomes shorter at exciton densities greater than ~109 excitons/cm2/layer. We attribute this to exciton-exciton scattering leading to spectral diffusion. The behavior was similar in 51 Å and 102 Å layers. In addition to holeburning, Figure 1 shows an increased absorption in the wings of the line whose shape is almost independent of pump wavelength and which is similar to that observed in bulk GaAs[2].

International Conference on Luminescence - 1984•Jan 1, 1984•1 citation

DYNAMICS OF PULSED SATURATION IN INHOMOGENEOUSLY BROADENED TWO-LEVEL

Vladimir Kuz

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.

•Jan 1, 1997•0 citations
A model involving two coupled thermodynamic reservoirs is used to obtain analytical expressions for inhomogeneously broadened absorption and dispersion signals under resonant and nonresonant stationary weak-pulse and strong-pulse saturation. This model allows a good reproduction of the dipolar-reservoir-like effects observed on absorption lines and predicts similar effects for dispersion signals.
The simultaneous influence of homogeneous and inhomogeneous line-broadening mechanisms are investigated for a reference system embedded in a medium. An analytically solvable model is constructed which includes the interaction of the reference mode with N strongly coupled environmental states (causing an inhomogeneity) and weakly coupled bath states. The modulation of the reference mode is caused by transitions between the strongly coupled perturber states. These may be switched on with a different rate than they are switched off. Consequently, effects of energy of activation and the change in entropy for environmental transitions on the line shape can be analyzed. The spectral function as well as the relaxation function are discussed as a function of the relevant parameters such as the number of perturbers, the lifetime T1, the temperature, and transition rates.
Polarization and Rayleigh type optical mixing spectra of a homogeneously and inhomogeneously broadened two-level system are calculated. We show that the nonlinear signal has contributions from the population pulsation and saturation effect. In the homogeneous system these effects can induce an asymmetric spectrum when the probe frequency is different from the resonant value. In the inhomogeneous system the spectral response is always symmetric independent of the probe frequency value. Line saturation and dynamic stark splitting are substantially reduced in the inhomogeneous case. The mentioned differences can be used to identify the type of broadening of a given spectral line.
The lowest energy two-dimensional exciton in GaAs/GaAlAs multiquantum wells (MQW) is inhomogeneously broadened at low temperature by fluctuations in the layer width. The broadening permits probing of the excitons as a function of position within the inhomogeneous line[1]. At high densities interaction between the excitons becomes important and leads to saturation and to an increase of the homogeneous linewidth[2]. Using the picosecond pump/probe technique we have measured the saturation behavior as a function of exciton energy within the inhomogeneously broadened line. Figure 1 shows the transmission spectrum T of a weak narrowband probe (dotted) and the change in transmission ΔT of the probe induced by the presence of a pump for two different pump wavelength for 102 Å thick layers of GaAs separated by 200 Å layers of AlGaAs. An increase in transmission (holeburning) at the pump wavelength is observed showing that the interaction between resonant excitons is much stronger than between nonresonant excitons. The strength of the hole decreases rapidly on passing through the center of the line towards the high energy side. This is consistent with an increase in the homogeneous linewidth of the higher energy excitons[1,3]. By delaying the probe we measured the rate of decay of the hole which was found to depend strongly on pump intensity. At low intensity the hole lifetime approaches the luminescent lifetime but becomes shorter at exciton densities greater than ~109 excitons/cm2/layer. We attribute this to exciton-exciton scattering leading to spectral diffusion. The behavior was similar in 51 Å and 102 Å layers. In addition to holeburning, Figure 1 shows an increased absorption in the wings of the line whose shape is almost independent of pump wavelength and which is similar to that observed in bulk GaAs[2].
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.