Harmonic Quantum Coherence of Multiple Excitons in PbS/CdS Core-Shell Nanocrystals

The generation and recombination dynamics of multiple excitons in nanocrystals (NCs) have attracted much attention from the viewpoints of fundamental physics and device applications. However, the quantum coherence of multiple exciton states in NCs still remains unclear due to a lack of experimental support. Here, we report the first observation of harmonic dipole oscillations in PbS/CdS core-shell NCs using a phase-locked interference detection method for transient absorption. From the ultrafast coherent dynamics and excitation-photon-fluence dependence of the oscillations, we found that multiple excitons cause the harmonic dipole oscillations with $\omega$, $2\omega$, and $3\omega$ oscillations, even though the excitation pulse energy is set to the exciton resonance frequency, $\omega$. This observation is closely related to the quantum coherence of multiple exciton states in NCs, providing important insights into multiple exciton generation mechanisms.

Figure 1

(a) Schematic of setup for phase-locked interference detection of transient absorption. OPA: optical parametric amplifier; PD: photodetector. (b) Transmission electron microscope image and (c) absorption spectrum of PbS/CdS core-shell nanocrystals. (d) Transient absorption signal for the probe time of $-100$ to 800 ps.

Figure 2

(a) Transient absorption signal as a function of internal and envelope times. (b) Transient absorption signal and interference intensity of the pump-pulse pair at ${\tau }_{\mathrm{pump}}=0\mathrm{fs}$. (c) Excitation-photon-fluence dependence of transient absorption signals at ${\tau }_{\mathrm{pump}}=0\mathrm{fs}$. (d) Excitation-photon-fluence dependence of the contrast calculated from the oscillating transient absorption signals. The shaded area corresponds to the contrast range expected for signals that are dominated by absorption nonlinearity.

Figure 3

Double-sided Feynman diagrams for two-pulse-pump transient absorption. The state generated by $n$-photon absorption is denoted by $|n⟩$ ($n=1$, 2, 3).

Figure 4

(a) Amplitudes of harmonic quantum coherences. Amplitudes of the first-, second-, and third-order oscillations are plotted as closed circles, triangles, and squares, respectively. The average number of absorbed photons per nanocrystal is denoted by $⟨N⟩$. The calculated generation probabilities of the oscillations are shown with the solid curves. (b) Saturated amplitudes of the harmonic quantum coherences. (c) Schematic of coherent dipole oscillations with increasing exciton density.

Figure 5

Transient absorption amplitudes of (a) nonoscillating, and (b) first-, (c) second-, and (d) third-order oscillating components. Theoretical transient absorption signals under (e) coherent and (f) incoherent conditions.