Time- and spectrally-resolved four-wave mixing in single $\mathrm{Cd}\mathrm{Te}∕\mathrm{Zn}\mathrm{Te}$ quantum dots

We present transient four-wave mixing experiments on individual excitonic transitions in self-assembled $\mathrm{Cd}\mathrm{Te}∕\mathrm{Zn}\mathrm{Te}$ quantum dots. Using a two-dimensional femtosecond spectroscopy and heterodyne detection of the nonlinear signal we study the dephasing and mutual coherent coupling of single quantum dot states. For the homogeneous linewidth of the zero-phonon line (ZPL) values of $0.06–0.1\mathrm{meV}$ $(T_2=13–20\mathrm{ps})$ are measured, and a ZPL weight in the total line shape of $Z=0.9$ at $T=7\mathrm{K}$ is estimated. We observe two linearly polarized fine-structure split exciton transitions with transition dipole moment ratios of 1.0–1.1 deduced from the four-wave mixing (FWM) amplitude, and splitting energies of $0.2–0.35\mathrm{meV}$ deduced from the FWM spectral response or quantum beat period. Coherent coupling between excitonic states is identified by off-diagonal signals in the two-dimensional spectrally-resolved FWM. The presence of an inhomogeneous broadening caused by spectral diffusion in the time ensemble is evidenced by the formation of a photon echo in the time-resolved FWM from a single transition.

Figure 1

(Color online) Top: FWM spectrum (solid line) of a ${\left(0.4\mu \mathrm{m}\right)}^2$ sample region for a delay time $\tau =3\mathrm{ps}$ and spectrum of the excitation pulses (dotted line). Bottom: $\mu \text{−}\mathrm{PL}$ from the same sample region. Inset: PL from a larger ${\left(100\mu \mathrm{m}\right)}^2$ region of the sample.

Figure 2

(Color online) FWM spectra for a delay time $\tau =2\mathrm{ps}$ for two orthogonal linear excitation polarizations along the [110] (black) and $\left[1\overline{1}0\right]$ [red (gray)] crystal direction (Ref. 17). The upper and lower graph are taken on different sample positions, each featuring an individual resonance.

Figure 3

(Color online) Top: FWM intensity averaged over $\tau =0–3\mathrm{ps}$. Inset: FWM intensity averaged over $0.4\mathrm{meV}$ (open squares) and $4\mathrm{meV}$ (filled triangles) around the resonance as function of delay $\tau$. The green (solid) and red (hollow) bars on top indicate the averaging ranges. Bottom: Intensity of the FWM field averaged over $\tau =3–20\mathrm{ps}$. Red (gray) line: magnified by a factor of 100. Dotted line: estimated shape of the acoustic phonon band.

Figure 4

(Color online) Photon echo formation from a single exciton transition. (a) Spectrally resolved FWM intensity from multiple states at $\tau =7\mathrm{ps}$. The inset shows the broadening of a single transition. The dotted line shows the filter functions used to isolated the single transition. (b) Time-dependent FWM for this single transition at various delays $\tau$. Also shown for comparison is the unfiltered FWM at $\tau =7\mathrm{ps}$.

Figure 5

(Color online) Top: spectrally resolved FWM intensity $I(\omega ,\tau )$ versus delay time $\tau$. Logarithmic gray scale over 2 orders of magnitude. The fine-structure beat shown in Fig. 6 is indicated. Bottom: Two-dimensional spectrally resolved FWM intensity $I(\omega ,{\omega }_1)$. Logarithmic gray scale over 3 orders of magnitude.

Figure 6

(Color online) Left: Delay time cut along $\omega =2.0123\mathrm{eV}$ showing beating with a period of $14\mathrm{ps}$ (solid line). Dashed line shows a fit using Eq. (3). Right: Two-dimensional spectrally resolved FWM intensity $I(\omega ,{\omega }_1)$ about the relevant spectral region. Logarithmic gray scale over 2 orders of magnitude.