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physica status solidi (b)

The Exciton-Exciton Continuum and Its Contribution to Four-Wave Mixing Signals

V. M. Axt, K. Victor, T. Kühn

Published Mar 1, 1998• 45 citations
Publisher

Abstract

The combined influence of biexcitons and the two-exciton scattering continuum is analyzed. The analysis is based on a density matrix description of a two-band semiconductor accounting for mean-field contributions, bound biexcitons and the correlated parts of the two-exciton scattering continuum on a common footing. Consistent with the microscopic formulation, the influence of biexcitons as well as that of the two-exciton continuum is represented by a correlation kernel which is obtained from an integral equation. For a one-dimensional model four-wave mixing signals are calculated solving numerically the resulting coupled nonlinear equations for excitation conditions in the vicinity of the 1s resonance. A strong compensation between the exciton–exciton continuum and the mean-field contribution is found for all excitation conditions studied. Surprisingly, biexcitonic signatures turn out to be enhanced when continua are included in the description.

DOI
10.1002/(sici)1521-3951(199803)206:1<189::aid-pssb189>3.0.co;2-5

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Journal of Experimental and Theoretical Physics•Feb 1, 2006•1 citation
The combined influence of biexcitons and the two-exciton scattering continuum is analyzed. The analysis is based on a density matrix description of a two-band semiconductor accounting for mean-field contributions, bound biexcitons and the correlated parts of the two-exciton scattering continuum on a common footing. Consistent with the microscopic formulation, the influence of biexcitons as well as that of the two-exciton continuum is represented by a correlation kernel which is obtained from an integral equation. For a one-dimensional model four-wave mixing signals are calculated solving numerically the resulting coupled nonlinear equations for excitation conditions in the vicinity of the 1s resonance. A strong compensation between the exciton–exciton continuum and the mean-field contribution is found for all excitation conditions studied. Surprisingly, biexcitonic signatures turn out to be enhanced when continua are included in the description.
Four-wave-mixing signals from excitons under linear-circular polarized excitation exhibit an elliptical polarization, depending on both the pulse delay and the spectral position. Besides the resonances corresponding to excitons and exciton-biexciton transitions, a breakup of the exciton line is found reflecting the influence of correlations on the four-point level. An analysis accounting for the exciton density, the bound biexciton, and the exciton-exciton scattering continuum reveals that these features are not due to an antibound two-exciton state. Instead, they result from an interference of the correlated exciton continuum with the exciton density. In addition, the modeling shows that the signals ellipticity is highly sensitive to the influences of different correlations and, therefore, allows for a discrimination of their contributions.
The memory structure induced by coherent transitions to the exciton-exciton scattering continuum is shown to have significant influence on spectrally resolved four-wave-mixing signals even under selective excitation of 1s excitons. Comparisons between experiments and calculations that account nonperturbatively for these quantum kinetic Coulomb correlations demonstrate large compensations between mean-field contributions and transitions to the two-pair continuum. Experiments with different polarizations of the laser pulses show that two-pair continuum correlations are responsible for delay-time dependent shifts of the excitonic emission as well as for substantial deformations of the line shape.
We present a numeric calculation of the exciton–exciton correlation for a one-dimensional semiconductor model with long-range Coulomb interactions, taking into account the effect of the exciton continuum. We use the obtained correlation functions to calculate the time integrated intensity of the four wave mixing signal. Changing the central frequency of the exciting pulses we observe changes in the profile and in the rise time of the time integrated signal for negative delays in qualitative agreement with experimental results. Our results show theoretically how the exciton continuum affects the coherence of four-particle correlations.
The influence of fifth-order coherences on the spectrally resolved four-wave mixing response of predominantly homogeneously broadened quasi-two-dimensional excitons is studied. Fifth-order signatures are discussed as a function of spectral position and excitation polarization. An exciton–biexciton beating for positive delay times is the dominant effect, which is pronounced at the exciton–biexciton transition for collinearly polarized excitation and at the exciton transition for cross-linearly polarized excitation. For negative delay times and collinearly polarized excitation a pronounced exciton–biexciton beating at the exciton resonance is observed that is vanishing for long negative delays owing to the faster dephasing in the two-exciton continuum compared with the bound biexciton state. These results are in qualitative agreement with microscopic model calculations that include the coherent dynamics of one- and two-exciton resonances up to the fifth order in the optical field.
Summary form only given. Using a full microscopic many-body theory, based on the dynamics-controlled truncation (DCT) formalism, we compute four-wave mixing spectra of thin semiconductor quantum well microcavities within the lowest-order nonlinear regime (/spl chi//sup (3)/-regime). Specifically, we focus on heavy-hole 1s excitons and corresponding two-exciton correlations (coherent biexcitons and two-exciton continuum correlations). Within this approach, the linear optical response corresponding to hh-excitons with given absorption lineshapes are inputs to the calculation of the nonlinear FWM spectra.
The paper presents a description of two-pair correlations in an electron-hole system in laser-excited direct-gap semiconductors in terms of the exciton-boson formalism. The dependence of the states of quasi-particles on their angular momentum orientation is properly taken into account following group theory rules. It is shown for the example of heavy hole excitons in GaAs quantum wells that Coulomb two-exciton correlations include effective repulsion between excitons with nonzero total momenta and effective attraction between excitons with zero total momenta. They generate exciton and biexciton nonlinearities, respectively, in the exciton-biexciton system. The Heisenberg equations of motion derived are applied to four-wave mixing in the coherent mode. Two components of Coulomb two-exciton correlations were found to generate coherent four-wave mixing either separately, one at the cocircular and the other at the perpendicular-linear polarization of applied pulses, or jointly at parallel-linear polarization. General equations are obtained for the amplitude of four-wave mixing signals with time resolution in these polarization configurations, which, in the limit of ultranarrow pulses, reduce to analytic functions of time and excitation and sample parameters. These equations are used to analyze signal characteristics in every polarization configuration. The results give a correct picture of biexciton effects and the polarization dependence of coherent four-wave mixing in GaAs quantum wells.