Exciton-hole collision in staggered type-II ${\mathrm{Al}}_{0.34}$${\mathrm{Ga}}_{0.66}$As/AlAs multiple quantum wells

We report the phase relaxation of Γ-Γ direct excitons in staggered type-II ${\mathrm{Al}}_{0.34}$${\mathrm{Ga}}_{0.66}$As/AlAs multiple quantum wells by means of the time-resolved degenerate four-wave mixing. The dephasing rate increases with the increase in the excitation density. Its excitation density dependence sharply changes at a critical density of 0.2 μJ/${\mathrm{cm}}^2$. The dependence agrees with the excitation density dependence of the long-lived Γ-hole density studied by means of the pump-and-probe experiment. The long-lived hole density saturates at the same excitation density of 0.2 μJ/${\mathrm{cm}}^2$. These facts definitely indicate that the phase relaxation rate of Γ-Γ excitons is dominated by the collision between the excitons and long-lived holes.