Measurement of electronic splitting in PbS quantum dots by two-dimensional nonlinear spectroscopy

Quantum dots exhibit rich and complex electronic structure that makes them ideal for studying the basic physics of semiconductors in the intermediate regime between bulk materials and single atoms. The remarkable nonlinear optical properties of these nanostructures make them strong candidates for photonics applications. Here, we experimentally probe changes in the fine structure on ultrafast timescales of a colloidal solution of PbS quantum dots through their nonlinear optical response despite extensive inhomogeneous spectral broadening. Using continuum excitation and detection, we observe electronic coupling between nearly degenerate exciton states split by intervalley scattering at low exciton occupancy and a sub-100 fs frequency shift presumably due to phonon-assisted transitions. At high excitation intensities, we observe multi-exciton effects and sharp absorbance bands indicative of exciton-exciton coupling. Our experiments directly probe the nonlinear optical response of nearly degenerate quantum confined nanostructures with femtosecond temporal resolution despite extensive line broadening caused by the finite size distribution found in colloidal solutions.

Figure 1

Source of inhomogeneous broadening in the absorption spectrum of PbS quantum dots. (a) Linear absorption spectrum of PbS near the band gap at the 1S${}_{\mathrm{e}}$–1S${}_{\mathrm{h}}$ transition (black curve). Dashed blue curve is the calculated band gap for a distribution of quantum dot sizes as determined by TEM (b), revealing the dominant source of inhomogeneous broadening in ensemble measurements of the sample of PbS quantum dots. (c) Representative transient absorption spectrum upon 775-nm excitation at early population times ($T$ < 300 fs).

Figure 2

Ultrabroadband GRAPES. (a) Single-shot transient grating profile of continuum source generated by focusing the output of a Ti:sapphire amplifier into argon gas showing the spectral as well as temporal characteristics of the pulse. (b) Principle of GRAPE spectroscopy showing the emitted signal and local oscillator dispersed off a grating and imaged by a two-dimensional CCD detector. (c) Spatially encoded 2D photon echo pulse sequence samples all relevant coherence times along the unfocused axis of the beam waist. The relative angle between $k_1$ and $k_2$ (labeled α) determines the magnitude of the temporal gradient.

Figure 3

Ultrafast dynamics of PbS quantum dots at low excitation power. Absolute value of rephasing part of two-dimensional photon echo spectrum at $T$ $=$ 25, 50, 75, and 100 fs at 40 μJ/cm${}^2$ per pulse. Dotted line shows the diagonal of the 2D spectrum in which absorption and stimulated emission/excited state absorption are identical. Note that the coherence frequency, $E_{\tau }$, recorded in the rotating frame, includes the contribution from the carrier frequency in the plot. The color bar is identical for each 2D spectrum.

Figure 4

Intensity-dependent absolute value 2D rephasing electronic spectra of PbS quantum dots at $T$ $=$ 200 fs. Each spectrum is normalized to its largest feature. The relative signal amplitudes after taking into account the linear scaling with heterodyning with the local oscillator pulse are 1.00, 2.94, 9.45, 17.41, 6.52, and 6.21, indicating that up to ⟨$N$⟩ $=$ 0.6, the signal is in the third-order regime. Distinct spectral changes are observed as a function of mean exciton occupancy (⟨$N$⟩). At low intensities, the 2D spectrum reveals an excitonic fine structure and electronic coupling between distinct states. At higher intensities, distinct absorption bands are revealed, indicating exciton-exciton interactions. Cuts through different absorption bands at ⟨$N$⟩ $=$ 149 are shown to the right of the 2D spectrum. ⟨$N$⟩${}_{\mathrm{pulse}}$ was determined by taking into account the absorption cross-section per dot and the bandwidth of the continuum-generated excitation pulses.