Estimating the Memory Time Induced by Exciton-Exciton Scattering

It is shown that lower bounds for the effective memory time induced by two-pair correlations can be estimated by monitoring changes of the shape of excitonic four-wave-mixing spectra. Experimentally we demonstrate a memory time of at least 540 fs for a ZnSe single quantum well. Microscopic calculations reveal that this lower bound is not sharp. Interactions retarded by more than 800 fs are shown to influence the dynamics, reflecting the presence of a long time tail in the memory kernel.

Figure 1

Excitonic FWM spectra after colinear excitation at negative delay times from $\Delta t=0\mathrm{p}\mathrm{s}$ (top) in steps of $\delta \Delta t=-0.05\mathrm{p}\mathrm{s}$. (a) Experiment (b) theory. Parameters: damping $\gamma =1/(2.4\mathrm{p}\mathrm{s})$; pulse area $A=0.02$; pulse duration 160 fs FWHM of the field amplitude; inhomogeneous broadening $=1\mathrm{m}\mathrm{e}\mathrm{V}$. The zero of energy in (b) is at the exciton resonance.

Figure 2

Excitonic FWM spectra calculated for conditions as in Fig. 1b but with a memory time cut to (a) ${\tau }_{\mathrm{c}\mathrm{u}\mathrm{t}}=0.8\mathrm{p}\mathrm{s}$, (b) ${\tau }_{\mathrm{c}\mathrm{u}\mathrm{t}}=0.6\mathrm{p}\mathrm{s}$. Dashed curves correspond to delays larger than the truncated memory time.

Figure 3

Absolute value of the memory kernel for exciton-exciton scattering. Shown is the component relevant for couplings of $1s$ transition amplitudes after colinear excitation. Inset: frequency representation (imaginary part).