Nanoscale transmission of quantum excitations in quantum information technologies must preserve the quantum character of the information. One proposed realization for nanoscale quantum information transfer uses hybrid systems of metallic nanoparticles (MNP) and semiconductor quantum dots (QD), with plasmons in MNPs moving qubits from QD to QD. Ultimately, a quantum description of the entire system, treating the MNPs and QDs on an equal footing, is needed to fully account for size quantization, quantized plasmons, coherent coupling, interparticle tunneling and nonlocal and nonlinear response. To achieve this, a quantum description of the MNPs is needed.
To this end, we use real-space time-dependent density functional theory (TDDFT) for a quantum description of MNPs. The MNPs are Au jellium nanospheres. We consider the limit of small MNPs where size quantization plays a key role. So far, it has proven difficult to clearly distinguish MNP excitations as single-particle transition or plasmonic modes, because the excitations have hybrid character. Previously, we showed that individual, small MNPs support “quantum core plasmons”, charge oscillations primarily localized near the MNP core, and “classical surface plasmons”, charge oscillations more at the MNP surface. Both of these are collective oscillations. We discuss more detailed analysis of the time dependence of driven systems to characterize more fully these excitations. Both types of modes have a “sloshing” character with charge oscillating between filled energy shells just below the Fermi level and empty shells just above the Fermi level. At the same time, both types have “inversion” character with charge continuously emptying from levels far below the Fermi level and filling shells far above the Fermi level. The sloshing character is dominant in classical surface plasmon modes. The inversion character is more single-particle like and is dominant for core plasmons.
While TDDFT yields information about the nature of the excitations in MNPs, DFT can’t address the quantum character of these excitations, ie whether the excitations are harmonic-like, bosonic, fermionic. Such information is necessary for building good models for quantized plasmons in MNPs. To begin to address these issues, we have explored simple models for interacting electrons on a linear chain. For short chains, the eigenmodes of the interacting electrons in the system are found exactly. As expected, the ground state shows a Mott transition as the hopping along the chain is varied. For the hopping regime where the interacting ground state of the system is metallic, we discuss initial results that analyze the character of the excitations. We use the results to identify which excitations are fermionic/bosonic, which are collective, which are harmonic oscillator-like, when nonlinear effects appear. Implications for plasmon quantization in small systems are discussed.