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physica status solidi (b)

Discrimination between the Interband and Intraband Coherences in Pump-Probe Signals from Semiconductors

Georg Bartels, A. Stahl

Published Mar 1, 1998• 7 citations
Publisher

Abstract

We discuss coherent heavy-hole light-hole quantum beats in transient pump–probe signals from a homogeneous GaAs quantum well in the low density regime using a microscopic density matrix theory. A key feature of our theory is the inclusion of higher order correlation functions like the biexciton transition amplitude and the exciton density comprising both interband and intraband character. Our calculations show that the heavy-hole light-hole quantum beats are dominated by the longer living intraband coherent contributions for most excitation conditions. In the special case when both pump and probe are linearly polarized, forming an angle of 45°, the coherent signature is exclusively caused by the otherwise small contributions of the biexciton transition amplitude, i.e. an interband coherent correlation function. In this way the different interband and intraband dephasing times should be observable separately in PP signals, depending on the excitation conditions.

DOI
10.1002/(sici)1521-3951(199803)206:1<325::aid-pssb325>3.0.co;2-0

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Transient pump-probe signals of a GaAs/Alx{\mathrm{Al}}_{\mathrm{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As quantum well are investigated both theoretically and experimentally for different excitation conditions. The calculations are based on a microscopic density-matrix approach taking higher-order correlations into account. We present spectrally resolved transients which provide insights into the nature of the differential transmission change. Especially the complex phase signature of heavy-hole--light-hole quantum beats in dependence of the detection energy allows for an identification of different microscopic processes in the pump-probe signal. The theoretical results are verified experimentally by comparison with the coherent and incoherent parts of the time-resolved data. We find a dominant role of the Coulomb-induced correlations up to the ${\mathrm{\ensuremath{\chi}}}^{(3)}$ relevant four-point level in the coherent signature in comparison to the Pauli blocking contributions.
Time-integrated differential detection techniques are used to study quantum beats involving the light-hole and heavy-hole excitons in an optically thin InGaAs multiple quantum well. The contributions of the exciton-exciton correlations are separated from those of the intervalence-band Raman coherence and the interband (population) coherence by monitoring the signal in the probe direction and by taking advantage of the polarization selection rules for the excitonic transitions. Quantum beats are observed for pump and probe pulses with the same circular polarization, providing evidence for two-exciton correlations. A theoretical analysis based on the dynamics-controlled truncation formalism suggests that the beats for the same linear polarization arise from Raman, population, and two-exciton contributions.
We report measurements of the polarization and time-averaged intensity of four-wave mixing signals from GaAs quantum wells as functions of the pump beam polarizations, laser photon energy, and optical injection density, the latter covering a range of higher levels than has previously been reported. Excitation of heavy-hole excitons produced a sin2 variation of the signal intensity as the pump beam polarizations changed from parallel to perpendicular, while injection of light-hole excitons led to an approximately cos2 dependence. The tuning dependence of the heavy-hole-exciton signal revealed a low-energy signal which is attributed to biexcitons. The dominance of this signal for perpendicular polarization causes the observed sin2 variation of the heavy-hole-exciton signal.
We report time-resolved degenerate four-wave-mixing experiments on a high-quality single GaAs quantum well. The signals for parallel and cross-polarized exciting pulses show pronounced quantum beats with different frequencies corresponding to the heavy/light-hole splitting and the biexciton binding energy, respectively. Comparison of the experimental data with solutions of the optical Bloch equations for a phenomenological model system shows that these features result from strong contributions of the biexcitonic state. The importance of biexcitons to the nonlinear coherent response of the two-dimension exciton is further confirmed by the frequency dependence of the time-integrated four-wave-mixing signal amplitudes measured for the two polarization geometries.
We perform femtosecond spectrally resolved pump-probe differential reflectivity measurements on excitons in GaAs quantum wells in both coherent and incoherent regimes. The spectral signal is nonzero and oscillatory at $\ensuremath{-}\mathrm{ve}$ delay up to a few ps indicating persistent coherence between excitonic polarization induced by the probe pulse and the delayed pump pulse. The signal for small +ve+ve+ve and $\ensuremath{-}\mathrm{ve}$ delay $(\ensuremath{\tau})$ shows modulation caused by quantum beats due to coexcitation of heavy and light hole excitons. The rise of the signal with $\ensuremath{\tau}$ for $\ensuremath{\tau}<0$ is rather nonexponential and is sensitive to detuning of the detection energy with respect to the exciton energy. The signal decay with $\ensuremath{\tau}$ for small +ve+ve+ve $\ensuremath{\tau}$ shows dependence on pump-probe relative polarization. The excitonic reflectivity shows a large reduction caused by excitonic absorption saturation for both +ve+ve+ve and $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}$ when the pump pulse intensity is increased to large values. To compare the experimental results with theory, we obtain an expression for the PPDR signal in terms of the third order excitonic polarization. This has an additional term not considered earlier to describe pump-probe experiments. The calculations are performed using optical Bloch equations, modified to incorporate exciton inhomogeneous broadening, quantum beats, and many body effects such as local field, excitation induced energy shift, and dephasing. These effects are found essential in explaining the observed PPDR spectral data. The delay dependence of the signal near the exciton energy is mainly controlled by inhomogeneous broadening for $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}.$ The signal decay for large +ve+ve+ve $\ensuremath{\tau}$ has an exponential behavior determined by the lifetime of incoherent excitons. Experiments for collinear polarization reveal an additional exponential component for small +ve+ve+ve delay. Theoretically, this is found to be related to exciton dephasing and is present only when many body effects are included.
Quantum beats involving the light-hole and heavy-hole excitons in GaAs quantum wells are studied using both conventional and novel temporally gated differential detection techniques. The contributions of the exciton-exciton correlations are separated from those of the intervalence-band Raman coherence and the interband (population) coherence by monitoring the signal in the probe direction and by taking advantage of the polarization selection rules for the excitonic transitions. The results are shown to be in agreement with a theoretical analysis based on the dynamics-controlled truncation formalism.