Exploring Pump-Probe Response in Exciton-Biexciton Quantum Dot-Metal Nanospheroid Hybrids

We study the optical susceptibility of a CdSe-based semiconductor quantum dot with a cascade exciton-biexciton configuration, which is coupled via the Coulomb interaction to a gold spheroidal nanoparticle, in the presence of a nearly resonant strong pump field and a weak probe field. We take both fields' polarization vectors to be parallel to the interparticle axis, derive the equations of motion for the density matrix, and proceed with a perturbative expansion approach to calculate the components of the density matrix associated with the effective optical susceptibility, which describes processes to first order in the probe field and to all orders in the pump field. We present spectra of the effective susceptibility and examine their dependence on the metal nanoparticle's geometric characteristics for various interparticle distances and pump field detunings, under both one- and two-photon resonance conditions. The role of the biexciton energy shift is also studied. Lastly, we introduce a dressed-state picture to elucidate the origin of the observed spectral features. Our calculations reveal that reducing the interparticle distance and increasing the metal nanoparticle aspect ratio enhance the exciton-plasmon coupling, leading to pronounced resonance splitting, spectral shifts, and broadened gain regions. Prolate nanoparticles aligned with the field polarization exhibit the strongest coupling and the widest gain bandwidth, whereas oblate geometries produce nearly overlapping resonances. Under exact resonance, the probe displays zero absorption with a negative dispersion slope, indicating slow-light behavior. These results demonstrate the tunability of hybrid CdSe-Au nanostructures for designing nanoscale optimal amplifiers, modulators, and sensors.