Coherent dynamics of localized excitons and trions in ZnO/(Zn,Mg)O quantum wells studied by photon echoes

We study optically the coherent evolution of trions and excitons in a $\delta$-doped 3.5 nm-thick ZnO/Zn$_{0.91}$Mg$_{0.09}$O multiple quantum well by means of time-resolved four-wave mixing at temperature of 1.5~K. Employing spectrally narrow picosecond laser pulses in the $\chi^{(3)}$ regime allows us to address differently localized trion and exciton states, thereby avoiding many-body interactions and excitation-induced dephasing. The signal in the form of photon echoes from the negatively charged A excitons (T$_\text{A}$, trions) decays with coherence times varying from 8 up to 60~ps, depending on the trion energy: more strongly localized trions reveal longer coherence dynamics. The localized neutral excitons decay on the picosecond timescale with coherence times up to $T_2=4.5$~ps. The coherent dynamics of the X$_\text{B}$ exciton and T$_\text{B}$ trion are very short ($T_2<1$~ps), which is attributed to the fast energy relaxation from the trion and exciton B states to the respective A states. The trion population dynamics is characterized by the decay time $T_1$, rising from 30~ps to 100~ps with decreasing trion energy.