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

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 four-wave 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.