Long-Time Correlation in Non-Markovian Dephasing of an Exciton-Phonon System in InAs Quantum Dots

We have observed a time-correlated frequency fluctuation in non-Markovian dephasing of excitons in InAs quantum dots using a six-wave mixing technique. In this measurement, the arrival times of the excitation pulses were controlled to eliminate the influence of Markovian dephasing and to measure the pure non-Markovian behavior. The experimental result shows that the time correlation of the frequency fluctuation due to exciton-phonon interactions was maintained in the quantum dots for over 10 ps. This long-time correlation is caused by the modification of the phonon coupling distribution.

Figure 1

Experimental four-wave mixing intensity for delay times of 0 to 400 ps.

Figure 2

(a) Illustration of the six-wave mixing measurement. The six-wave mixing intensity is measured as a function of the delay time ${\tau }_{21}$ with a fixed delay time ${\tau }_{32}$. The upper and lower figures show the short and long conditions of the delay time ${\tau }_{21}$, respectively. Photon echo signals appear at $2{\tau }_{32}$ for both conditions. (b) Experimental six-wave mixing intensity for the first delay times of ${\tau }_{21}=0$ to 30 ps. The second delay time ${\tau }_{32}$ was set to 50 ps.

Figure 3

Theoretical six-wave mixing intensity as a function of the normalized delay time ${\tau }_{21}/{\tau }_{\mathrm{c}}$, where ${\tau }_{\mathrm{c}}$ is the correlation time of each model. (a) Six-wave mixing intensities for the simple stochastic model (dotted line) and the $T_2$ model (solid line). (b) Six-wave mixing intensities for the microscopic phonon model with ${\omega }_{\mathrm{ph}}/{\sigma }_{\mathrm{ph}}=0$ (dotted line) and 1 (solid line). The inset shows the coupling strength of phonons corresponding to ${\omega }_{\mathrm{ph}}/{\sigma }_{\mathrm{ph}}=0$ (dotted line) and 1 (solid line).

Figure 4

Theoretical six-wave mixing intensity for the first delay times of ${\tau }_{21}=0$ to 30 ps with (black solid line) and without (red dotted line) the exciton-biexciton beat. The second delay time ${\tau }_{32}$ was set to 50 ps. The inset shows the experimental (circles) and theoretical (lines) temperature dependence of the normalized six-wave mixing intensity. The second delay time ${\tau }_{32}$ was set to 40 ps. The experimental results are plotted at the delay times ${\tau }_{21}=0.9$ (open circle) and 3.9 (solid circle) ps. The intensities are normalized by the intensity at the delay time of 0.3 ps to clarify the non-Markovian behavior.