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Quantum Electronics and Laser Science Conference

Evidence of nonperturbative exciton-exciton scattering in four-wave-mixing signals in quantum well microcavities

N. H. Kwong, Ryu Takayama, Rolf H. Binder, I. Rumyantsev, Makoto Kuwata‐Gonokami

Published Nov 13, 2002• 0 citations
Publisher

Abstract

Summary form only given. The role of exciton-exciton scattering in the nonlinear optical response of semiconductor quantum wells is well established. However, an interesting question arising from the system's dimensionality has so far not been addressed. In the quantum theory of scattering in two dimensions, the scattering amplitude behaves non-smoothly and non-perturbatively at low energies. While the exact scattering amplitude vanishes as 1/ln (energy) as energy /spl darr/0, the second Born approximation diverges logarithmically. These properties result from the system's dimensionality and hold for any short-range well-behaved potential. One may ask whether the second Born approximation also fails for exciton-exciton scattering in two-dimensional structures and how this breakdown may be experimentally detected. In this contribution, we address this question within a microscopic theory of frequency-degenerate four-wave-mixing signals from a quantum-well microcavity. Analyzing an experiment reported in with this theory, we argue that the data are already sufficiently sensitive to show the breakdown of the second Born approximation for exciton-exciton scattering.

DOI
10.1109/qels.2001.962145

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Summary form only given. The role of exciton-exciton scattering in the nonlinear optical response of semiconductor quantum wells is well established. However, an interesting question arising from the system's dimensionality has so far not been addressed. In the quantum theory of scattering in two dimensions, the scattering amplitude behaves non-smoothly and non-perturbatively at low energies. While the exact scattering amplitude vanishes as 1/ln (energy) as energy /spl darr/0, the second Born approximation diverges logarithmically. These properties result from the system's dimensionality and hold for any short-range well-behaved potential. One may ask whether the second Born approximation also fails for exciton-exciton scattering in two-dimensional structures and how this breakdown may be experimentally detected. In this contribution, we address this question within a microscopic theory of frequency-degenerate four-wave-mixing signals from a quantum-well microcavity. Analyzing an experiment reported in with this theory, we argue that the data are already sufficiently sensitive to show the breakdown of the second Born approximation for exciton-exciton scattering.
In nonlinear semiconductor optics, two-particle scattering is often being modeled successfully within the second Born approximation (2nd BA) of the Coulomb interaction. It is shown in this paper that, at low energies, such a perturbative treatment of Coulomb correlations applied to exciton-exciton scattering in two-dimensional systems fails even qualitatively (unless phenomenological or self-consistent dephasing processes are included in the theory). We show that the failure of the 2nd BA in two dimensions can be inferred from a comparison of our theoretical results with reported experiments of four-wave mixing signals from semiconductor microcavities.
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.
A theory of degenerate four-wave mixing in a semiconductor optical cavity with quantum wells is constructed. The nonlinear response of a microcavity can be four to five orders of magnitude stronger than that of an isolated quantum well. For P 2 E -and P 3 -type nonlinearities the damped diffracted signal oscillates with a period determined by the Rabi splitting. For a biexcitonic mechanism of nonlinearity, the signal contains damped overtones of the Rabi splitting and the biexciton binding energy.
Summary form only given. Four-wave mixing processes in semiconductor quantum wells have been studied intensively for many years, because they allow for a detailed investigation of ultrafast many-body processes such as quantum correlations and quantum coherences. From a theoretical point of view one can roughly divide the existing approaches into two categories: (i) fully microscopic theories based on the bandstructure and on Coulomb interactions between electrons and holes, and (ii) phenomenological few-level models.
Summary form only given. The ultrafast nonlinear optical response of semiconductor-microcavities (SMCs) in the nonperturbative regime is attracting growing interest for exploring fundamental light-matter interactions in many-particle quantum systems, as well as for the future implementations of ultrafast photonic devices. In spite of many investigations, the coherent dynamics of excitonic nonlinear-response in the nonperturbative regime has not been fully understood. Open questions are how strong exciton-cavity coupling affects exciton-exciton (X-X) interactions, and how in turn the X-X correlation influences the nonlinear response of SmCs. We investigate these open questions and show that the nonperturbative regime provides an unprecedented tool for investigating four-particle correlations.We start from the equations for the third order exciton polarization and cavity field describing quantum optical effects and coherent nonlinear optics in SMCs, perform the semiclassical factorization and include multiple scattering processes.
Summary form only given. Four-particle correlation mediated by the Coulomb interaction has been found to play a major role in the nonlinear optical response at the semiconductor band edge at low excitation density. The attractive interaction of the excitons with opposite spins result in the formation of bound (bi-exciton) and unbound (scattered) two-exciton states. In this paper we report on the first to our knowledge, comparison of the contributions to the coherent nonlinearity from the bound and unbound two-exciton states. The polarization-sensitive four wave mixing experiment is performed in the high-Q semiconductor microcavity, in which the incoherent effects are suppressed due to strong exciton-photon coupling. The semiconductor microcavity has a single 12-nm-thick GaAs quantum well.