Homogeneous broadening of the $S$ to $P$ transition in InGaAs/GaAs quantum dots measured by infrared absorption imaging with nanoscale resolution

Absorption of single InGaAs self-assembled quantum dots is spatially resolved in resonance with the $S$ to $P$ polaron transitions around $\lambda =25\hspace{0.5em}\mu \mathrm{m}$ wavelength. We show that the spatial resolution down to 50 nm ($\lambda /500$) combined with the analysis of the absorption nanoscopy images provides a measurement of the homogeneous broadening at room temperature. The $2.5\pm 1$ meV measured $S$-$P$ homogeneous broadening supports the calculated value accounting for acoustic phonon-induced decoherence.

Figure 1

(a) Schematic sample structure and experimental AFM configuration for the measurement of the buried QD absorption. The AFM tip and thicknesses are not to scale. (b) Mechanical oscillation amplitude (i.e., absorption signal) of the cantilever as a function of frequency for three different points on the surface. These points are labeled 1, 2, and 3. In the inset, the dots report the systematic experimental shift of the cantilever oscillation frequency with respect to the absorption signal. The violet solid line is a best linear fit to guide the eye.

Figure 2

(a) Absorption signal nanoscopy at 49.5 meV (25 $\mu \mathrm{m}$ wavelength). (b) Cantilever oscillation frequency on the same scanned surface. (c) Topography measured during the step-scan absorption signal acquisition. (d) Absorption signal nanoscopy at 91 meV (13.6 $\mu \mathrm{m}$ wavelength) in the transparent spectral region of the QDs.

Figure 3

(a) Absorption signal along a 800-nm-long scan line at 49.5 meV (red solid line) and along another scan line at 91 meV (blue dotted line). (b) Cantilever oscillation frequency along the previous scan lines at 49.5 and 91 meV energies. Points 1, 2, and 3 are referring to Fig. 1b. At 91 meV, the average frequency is different than at 49.5 meV because we have used another cantilever. Frequency discretization sampling is 0.2 kHz. The thick arrows on the right indicate the data variation in the presence of absorption. (c) Topography measured simultaneously by the AFM during the line scan at 49.5 meV. For comparison purposes, the light dotted line reports the topography measured elsewhere above a topographic dip and a topographic bump.

Figure 4

(a) Random spatial distribution of QDs in the plane for the simulation of one typical absorption nanoscopy image. (b–d) Calculated absorption images for a homogeneous Lorentzian FWHM $\hslash \gamma$ of 0.5, 2.5, and 7 meV. (e) Plot of the relative fraction in percentage (%) of absorption pixels predicted in a series of $800\times 400$ nm${}^2$ images as a function of the homogeneous Lorentzian FWHM of the $S$-$P$ intersublevel transition at 50 meV. The spatial and spectral QD distribution varies randomly from curve to curve. To guide the eye, one of the curves is singled out with open circles.