## 4 Discussion: Probing the Coherent Intradot and Interdot Dynamics in Dimer Ensembles
Scanning the delay time, \(\tau\), between the pump and the probe pulse provides direct access to the beating periods of the coherences. We present heatmaps of the transient spectra (Equation (11)) computed for the ensemble of 1000 dimers QD\({}_{\mathrm{A}}\)-QD\({}_{\mathrm{B}}\) (D\({}_{\mathrm{A}}\) = 2.7 nm, D\({}_{\mathrm{B}}\) = 3.5 nm, L = 0.2 nm, 5% size dispersion) in Figure 7, where the \(x\) axis is the delay time \(\tau\) and the y axis the frequency axis of the spectra (ordinate of Figure 6). The color is blue for emission (negative value of the spectrum in Figure 6) and red for absorption (positive value in Figure 6). Panel A is computed for a sequence of two VIS pulses and panel B for a sequence VIS-IR. The coherences between the GS and the lowest excitonic bands h1e\({}_{\mathrm{A}}\) and h1e\({}_{\mathrm{B}}\), called GS-1 and GS-4 in terms of their labeling in eigenexcitons, are excited by the pump and the probe and appear very clearly in the range 2.2 to 2.6 eV with the beating periods of \(\approx\) 2 fs. The interexciton coherences (panel B) that fall in the 0.2 to 0.6 eV range are probed by the IR pulse. Their beating periods are longer, in the 10-20 fs range. They can have an intradot (band 1-5, corresponding to zero order excitons h1e\({}_{\mathrm{B}}\) and h2e\({}_{\mathrm{B}}\), respectively, and band 4-8, corresponding to the h1e\({}_{\mathrm{A}}\) and h2e\({}_{\mathrm{A}}\) zero order exciton bands) or an interdot character (bands 1(h1e\({}_{\mathrm{B}}\))-4(h1e\({}_{\mathrm{A}}\)) and 5(h2e\({}_{\mathrm{B}}\))-8(h2e\({}_{\mathrm{A}}\))). The longer time scale interdot electronic coherences that involve weakly populated charge transfer states have periods in the dozens of fs range. They will eventually be coupled to the phonon and acoustic modes [24; 78; 79; 84]. In Figure 8, we show the transient spectra computed for an ensemble of 1000 homodimers (D\({}_{\mathrm{A}}\) = D\({}_{\mathrm{B}}\) = 2.5 nm, L = 0.55 nm and 5% size dispersion). In this case, all the exciton bands overlap and the zero order labels are no longer valid. In panel A, the fast beating electronic coherences between the two bands of eigenexcitons, 1 and 4, and the GS are effectively probed by the VIS probe. Eigenexcitons 1 and 4 are formed by the coupling of the zero order excitons eh1\({}_{\mathrm{A}}\) and eh1\({}_{\mathrm{B}}\). Their transition frequencies from the GS (y scale of the map) differ by about 0.15 eV,which reflects the strength of the interdot Coulomb coupling. Their beating periods are of the order of 2 fs, as shown by their oscillations with respect to the delay time. In panel B, the IR pulse probes the coherence between the bands of eigenexcitons 4 and 5, whose beating frequency is resonant with the frequency of the IR pulse (0.4 eV). Eigenexcitons of band 4 have their main weights on the zero order excitons h1e\({}_{\text{A}}\) and h1e\({}_{\text{B}}\) and eigenexciton of band 5 on h2e\({}_{\text{A}}\) and h2e\({}_{\text{B}}\). One can see from Figure 4C that these two eigen excitons are separated by \(\approx\) 0. 4 eV, which corresponds to a period of 10 fs along the delay time axis. This coherence has both an intra and interdot character. Figure 6: Transient absorption(TA) spectrum for an ensemble of 1000 heterodimer QD\({}_{\text{A}}\) (D\({}_{\text{A}}\) = 2.5 nm) and QD\({}_{\text{B}}\) (D\({}_{\text{B}}\) = 3.7 nm) (black) superimposed with the distribution of the energies of the eigenstates in GS to the exciton spectral region. **(A)**. Computed for a sequence of two identical VIS pulses (2.37 eV, 570 THz, \(\tau\) = 100 fs, \(\text{t}_{\text{ppump}}\) = 50 fs, \(\text{t}_{\text{probe}}\) = 150 fs, the integration time is 2 ps) **(B)** Computed for a VIS-IR sequence (VIS: 2.37 eV, 570 THz, \(\tau\) = 100 fs, IR: 0.41 eV/100 THz) where the IR probe is resonant with the low energy transition frequencies of the coherences between excitons. The inset shows the low frequency region on the same scale for the intensity.