Degenerate four-wave mixing measurements on an exciton-photon coupled system in a semiconductor microcavity

Abstract

The polarization-sensitive degenerate four-wave mixing technique is employed to study semiconductor quantum-well microcavities in the low-density limit. Frequency-domain and time-domain measurements are carried out to study exciton-polariton modes in long-͑high-Q) and short-͑low-Q) photon lifetime systems. In the high-Q system, normal-mode splitting is observed in the linear reflection as well as the degenerate fourwave mixing spectrum. In the low-Q system, though the linear reflection spectrum shows normal-mode splitting, the spectrum of the degenerate four-wave mixing is found to have a maximum only at the bare exciton resonance. Our experimental results are well reproduced by a weakly interacting boson model which accounts for the anharmonicity in the system due to exciton-exciton correlation and the phase-space filling effect. The four-wave mixing results from the high-Q system are in good agreement with the cavity polariton scattering treatment for the third-order nonlinear response of the microcavity confined excitons. The polarization sensitive frequency-domain degenerate four-wave-mixing measurements from the high-Q system enable us to obtain the ratio of the anharmonic parameters. The frequency and time-domain measurements show that the strong coupling between the exciton and photon changes the nonlinear optical response qualitatively. Incoherent effects like the excitation-induced dephasing are suppressed in the high-Q system, whereas they are more pronounced in the low-Q system. We also find differences in the signal decay rates for different polarization configurations, which is attributed to inhomogeneous broadening in the low-Q system.

Influence of Exciton-Exciton Interaction on Quantum Beats

“…This simplifies the treatment of the four-particle correlations at the semiconductor band edge drastically and is effective for a system where excitons are stable and have a large binding energy. Recently the FWM process in semiconductor microcavities has been explained using the weakly interacting boson (WIB) model [9][10][11][12]. Within the WIB model the anharmonicity of the electron-hole system is due to a spin-dependent interaction of optically active excitons [8].…”

Relation between phenomenological few-level models and microscopic theories of the nonlinear optical response of semiconductor quantum wells

“…As will be seen below, except for the incoherent contribution 55,56,60 and examples of this type of cancellation involving subsets of levels have been well known for some time. We make a detailed comparison of Eq.…”

“…In the third category, which we call bosonic models, coherent excitons are modeled as interacting bosonic excitations of the semiconductor, with some approximate Pauli blocking corrections. Successful models in this class have been developed along lines similar to the atomic few-level models 55,56 and/or lines using Hamiltonians based on bosonic operators for excitons rather than fermionic operators for electrons and holes. [57][58][59][60][61][62][63] This paper addresses the issue of possible connections between atomic few-level models ͑the first category͒ and ͑fermionic͒ microscopic theories ͑the second category͒.…”

“…[55][56][57]59,60,62 Modeling optically active excitons and biexcitons as bosons ͑with Pauli correction to the exciton-light coupling͒, these authors derived an effective few-level model up to the two-exciton sector, which has a similar level structure to the generic model considered here. Instead of being "oscillator" levels defined through measured resonances, the levels in the WIB model are physical states with fixed numbers of bosonic excitons.…”

On the Identification of Intervalence-Band Coherences in Semiconductor Quantum Wells

“…On the other hand, the beats in the TI-FWM is insensitive to q 21 . Based on the d-function pulse model one can easily see that the sole source of beats in the TI-DTS is q 21 , whereas the source of beats in the TI-FWM is both q 21 and occupation functions such as q 33 . In third order, the latter is jq 31 j 2 jq 32 j 2 , which yields the usual occupation gratings in the FWM configuration.…”