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Physical Review Letters

Evidence of Nonperturbative Continuum Correlations in Two-Dimensional Exciton Systems in Semiconductor Microcavities

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

Published Jun 22, 2001• 57 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.87.027402

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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. 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.
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.
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.
We show that the exciton–exciton scattering continuum has a significant influence on the transient non-linear optical response of semiconductor microcavities. Comparison between transient shifts observed in pump and probe experiments and calculations demonstrates almost complete cancellation between mean-field and two-exciton continuum contributions. Moreover, we show that suppression of non-linear absorption of the lower polariton observed in many experiments is determined by the specific spectral shape of these correlations. In particular, we find that the pump induced dephasing of polariton resonances is proportional to the spectrum of four-particle correlations calculated at the energy sum of the pumped and probed polaritons.
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.
Nonperturbative phenomena in four-wave mixing spectra of semiconductors are studied using the exact solution of a widely used phenomenological nonlinear equation of motion of the exciton polarization. It is shown that the Coulomb interaction, included in the nonlinearity, leads to two characteristic effects, which are essentially of dynamical origin---a split of the exciton peak and a nonmonotonous dependence of the response at the exciton frequency on the magnitude of the external field. Relations between the spectral features and the parameters of the system are obtained. It is found that the transition from perturbative to nonperturbative regimes is controlled by parameters inversely proportional to the decay rate. It implies that the condition of low excitation density does not necessarily warrant applicability of the perturbational approach.