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physica status solidi (b)

Signatures of biexcitons and triexcitons in coherent non‐degenerate semiconductor optics

T. Meier, C. Sieh, E. Finger, W. Stolz, Wolfgang W. Rühle, P. Thomas, S. W. Koch, Andreas Dirk Wieck

Published Jul 21, 2003• 9 citations
Publisher

Abstract

Abstract Signatures of exciton and two‐exciton states in semiconductor systems are investigated experimentally and theoretically. A set of quantum well samples with different well widths is studied using coherent excitation spectroscopy. The experimental results are analyzed using a microscopic model demonstrating the importance of biexciton correlations and disorder effects. Additional numerical investigations of absorption changes in small nanorings are employed to analyze optical transitions from two‐exciton to three‐exciton resonances.

DOI
10.1002/pssb.200303183

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Abstract Signatures of exciton and two‐exciton states in semiconductor systems are investigated experimentally and theoretically. A set of quantum well samples with different well widths is studied using coherent excitation spectroscopy. The experimental results are analyzed using a microscopic model demonstrating the importance of biexciton correlations and disorder effects. Additional numerical investigations of absorption changes in small nanorings are employed to analyze optical transitions from two‐exciton to three‐exciton resonances.
Exciton-biexciton coherent coupling effects are examined in semiconductor quantum dots. The exciton absorption spectrum is measured with the microphotoluminescence excitation technique in a single InGaAs quantum dot. The spectrum changes from a Lorenztian-type line shape to an unusual dip-shaped line shape with increasing excitation intensities in a higher exciton state where there is a large oscillator strength between the exciton and biexciton states. The intensity dependence of the dip energy width clearly indicates that coherent Rabi oscillation occurs between the exciton and biexciton states. The absorption properties with excitation light of different polarizations show that the dip-shaped spectra only appear when there is a large biexciton state population with linear polarization. A theoretical analysis undertaken with the density matrix method agrees well with experimental results. This agreement reveals that exciton-biexciton coherent interactions lead to unusual absorption spectra and contribute crucially to the optical properties of quantum dots. The exciton-biexciton coherent effects provide a scheme for controlling four distinguishable states, which can be applied to a demonstration of quantum gate operations.
The coherent response of excitons in semiconductor nanostructures measured in four-wave mixing (FWM) depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs/Al0.3Ga0.7As single quantum wells (SQW) and AlxGa1-xAs mixed crystals. Additional to the usual phase-space filling nonlinearity, excitation-induced dephasing (EID) and biexciton formation (BIF) are important. EID leads to a strong dependence of the signal on the angle between the linear input polarizations. We find that EID persists in inhomogeneous systems, showing that the mutual density-dependent dephasing rate difference between two subsystems within the inhomogeneous distribution is strongly dependent on their energy difference. BIF is strongly affecting the cross-linear polarized FWM response. The signal for positive delay is dominated by the transitions from the one-exciton state X to the two-exciton states. Here, the third-order polarization at X-XX is not at the same resonance as the first-order polarization at 0-X. Consequently, the rephasing of the microscopic third-order polarization to the macroscopic FWM photon echo is blurred by the non-perfect correlation of X and XX energies, leading to a fast and non-exponential signal decay in delay time. For inhomogeneous broadenings larger than the biexciton binding energy, we find an enhanced biexciton binding energy, and a quenching of the oscillator strength of the unbound biexciton.
Ultrafast nonlinear optical spectroscopy is used to study the coherent dynamics of optically excited electron-hole pairs in semiconductors. Coulomb interaction implies that the optical inter-band transitions are dominated, at least at low temperatures, by excitonic effects. They are further enhanced in quantum confined lower-dimensional systems, where exciton and biexciton effects dominate the spectra even at room temperature. The coherent dynamics of excitons are at modest densities well described by the optical Bloch equations and a number of the dynamical effects known from atomic and molecular systems are found and studied in the exciton-biexciton system of semiconductors. At densities where strong exciton interactions, or many-body effects, become dominant, the semiconductor Bloch equations present a more rigorous treatment of the phenomena. Ultrafast degenerate four-wave mixing is used as a tool to study the coherent exciton dynamics, and the importance of performing transform limited spectroscopy is demonstrated throughout.
Semiconductors systems exhibiting excitonic properties are discussed in terms of their coherent response, which is extracted using two-dimensional coherent spectroscopy. This control method allows for separation of quantum pathways that comprise the optical response, such as interactions between excitons, their dephasing rates, the effects of many-body interactions and the role of structure on the microscopic electronic environment. Additional controls, such as polarization can be used to further distinguish biexcitons and suppress many-body interactions. These result are compared and contrasted with those from a semiconductor microcavity where the excitons form polaritonic modes due to normal-mode splitting. Rephrasing spectra map the detuning dependence of the exciton-polariton branches. Increasing the detuning shifts all features to higher energy and the expected anti-crossing is observed. An isolated biexciton is seen only at negative detuning, separated by a binding energy. For positive detuning, the spectral weight of the off-diagonal features swap, as the lower polariton branch and biexciton come into resonance. This indicates that the off-diagonal features are sensitive to the interactions of the exciton-polaritons and other resonances in the system.
Great progress has been made in recent years in experimental studies of excitonic molecules, both in direct-band and indirect-band semiconductors. The exciton systems in these semiconductors differ substantially. In direct-band semiconductors with dipole-allowed optical transitions, the direct-recombination times are extremely small. Consequently the processes of binding of excitons into excitonic molecules and their decay occur under strongly nonequilibrium conditions. Hence one can obtain the fundamental information on biexcitons in these semiconductors by nonlinear optical methods. This review discusses the processes on which the various methods are based: two-photon resonance excitation of biexcitons, induced one-photon conversion of an exciton into a biexciton, two-photon resonance Raman scattering involving biexciton states, etc., and their application to studying biexcitons with the example of CdS. Problems of bistability involving biexcitons are also briefly discussed. In indirect semiconductors, where recombination occurs with the emission of a phonon, the lifetimes of excitons are large, and quasiequilibrium can be established in the exciton system. Under these conditions the information on the properties of the molecules is obtained by analyzing their radiative-decay spectra. The problem of detecting biexcitons in indirect semiconductors, radiative decay of molecules, and the effect on their stability of external electric, strain, and magnetic fields are discussed in detail with the examples of Si and Ge. Also the results of investigating the quantum statistical behavior of a dense gas of spin-oriented excitons (in a magnetic field under conditions in which the biexcitons are destabilized) are briefly presented (using the example of uniaxially compressed germanium), and the question of the possibility of their Bose condensation is discussed.