Eur. Phys. J. B 25, 445-462 (2002)
https://doi.org/10.1140/epjb/e20020051

T-matrix analysis of biexcitonic correlations in the nonlinear optical response of semiconductor quantum wells

¹ Cooperative Excitation Project, ERATO, Japan Science and Technology Corporation, Optical Sciences Center, University of Arizona, Tucson, AZ 85721, USA
² Optical Sciences Center, University of Arizona, Tucson, AZ 85721, USA
³ Cooperative Excitation Project, ERATO, Japan Science and Technology Corporation, Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

Corresponding author: ^a takayama@u.arizona.edu

Received: 3 August 2001
Revised: 26 December 2001
Published online: 15 February 2002

Abstract

A detailed numerical analysis of exciton-exciton interactions in semiconductor quantum wells is presented. The theory is based on the dynamics-controlled truncation formalism and evaluated for the case of resonant excitation of 1s-heavy-hole excitons. It is formulated in terms of standard concepts of scattering theory, such as the forward-scattering amplitude (or T-matrix). The numerical diagonalization of the exciton-exciton interaction matrix in the 1s-approximation yields the excitonic T-matrix. We discuss the role of the direct and exchange interaction in the effective two-exciton Hamiltonian, which determines the T-matrix, evaluated within the 1s-subspace, and also analyze the effects of the excitonic wave function overlap matrix. Inclusion of the latter is shown to effectively prevent the 1s-approximation from making the Hamiltonian non-hermitian, but a critical discussion shows that other artefacts may be avoided by not including the overlap matrix. We also present a detailed analysis of the correspondence between the excitonic T-matrix in the 1s-approximation and the well-known T-matrix governing two-particle interactions in two dimensional systems via short-range potentials.