Wigner Time Delay Induced by a Single Quantum Dot

Resonant scattering of weak coherent laser pulses on a single two-level system realized in a semiconductor quantum dot is investigated with respect to a time delay between incoming and scattered light. This type of time delay was predicted by Wigner in 1955 for purely coherent scattering and was confirmed for an atomic system in 2013 [R. Bourgain et al., Opt. Lett. 38, 1963 (2013)]. In the presence of electron-phonon interaction, we observe deviations from Wigner’s theory related to incoherent and strongly non-Markovian scattering processes which are hard to quantify via a detuning-independent pure dephasing time. We observe detuning-dependent Wigner delays of up to 530 ps in our experiments which are supported quantitatively by microscopic theory allowing for pure dephasing times of up to 950 ps.

Figure 1

Optical characterization of a single InGaAs QD under strict resonant excitation. (a) Fluorescence signal as a function of laser frequency at an excitation power of 80 nW. The experimental data are well described by a Lorentzian line shape with a width $6.6\mu \mathrm{eV}$ (FWHM) (red trace). (b) Upper (lower) panel: Power-dependent measurements of fluorescence intensity (linewidth). The minimum observed linewidth is $(2.96\pm 0.11)\mu \mathrm{eV}$. (c) Intensity autocorrelation measurement at 0.07 $P_{\mathrm{sat}}$.

Figure 2

(a) Red: Laser pulse used for exciting the QD. Black: Pulse scattered by QD for a laser detuning of $\mathrm{\Delta }=0.5\mu \mathrm{eV}$. The observed delay between the pulses is 530 ps. (b) Time delay as a function of excitation power for zero detuning between the laser and the TLS. The experimental data (black bullets) show a pronounced decrease of the time delay for excitation powers exceeding 600 nW, which is well described by our microscopic theory (black line) taking non-Markovian dynamics into account.

Figure 3

(a) Scattered pulses for three different laser detunings (black, $0.5\mu \mathrm{eV}$; red, $2.6\mu \mathrm{eV}$; green, $4.7\mu \mathrm{eV}$). (b) Simulation of the pulse detuned by $0.5\mu \mathrm{eV}$. The non-Markovian simulation (black line) allows one to identify coherent (gray line) and incoherent contributions (orange line).

Figure 4

Time delay as a function of spectral detuning between the laser and the TLS. The experiment (black bullets) is well described by our model taking non-Markovian dynamics into account (red line), while simple Markovian dynamics (blue and green lines) fails to reproduce the experimental data. Inset: Integrated intensity of the scattered pulses as a function of detuning together with simulations with the same color code as in the main part of the figure.