Figure 1

Time evolution of the distribution of the FWHM values calculated for a set of moving-average spectra obtained for a single QD. The dots on the “horizontal” plane represent the mean values for the corresponding histograms. The solid line going through the dots is the curve $⟨\mathrm{FWHM}⟩=[0.30+0.15(t/\mathrm{s}{)}^{0.31}]\mathrm{meV}$. A line $⟨\mathrm{FWHM}⟩\propto (t/\mathrm{s}{)}^{0.5}$ is shown for comparison.Reuse & Permissions

Figure 2

Examples of “sublinear” spectral diffusion observed experimentally are shown together with superimposed theoretical curves fitted by using a least-squares criterion. The corresponding theoretical parameters and the excitation intensities are displayed in the panels. A dominant feature of $\beta \approx 0.5$ is associated with a $-3/2$ power law in Eq. (4). The parameter $\alpha$ indicates the rate at the lower cutoff in the distribution function. The upper cutoff should be at least several hertz to be consistent with experimental data at short times. (a), (c), (e), (g), and (h) show results for 4-nm ITK655 dots, (b) and (d) display diffusion of 2.5-nm ITK605 dots, and (f) represents data for a CdSe608 single dot. The QD shown in (g) is embedded in a poly(methyl methacrylate) film. In (f) and (h), the vertical dashed lines separate the regions with apparently different values of $\beta$.Reuse & Permissions

Figure 3

Numerical Monte Carlo simulations of the squared frequency displacements. The lengths of the simulated trajectories are $3\times {10}^3$ points in (a) and $3\times {10}^4$ points in (b). Relaxation rates of 500 TLS are randomly distributed across the range ${10}^{-5}\le k_s\le 10$ so that $\rho (k_s)\propto k_s^{-1.5}$ and $A_s=2$. The smooth lines are theoretical curves describing the expectation values at $\beta =0.5$. Large deviations from the expectation values result from the limited length of the data set. These deviations become significantly smaller when the data set is extended to $3\times {10}^4$ points.Reuse & Permissions