Multipolar and nonlocal effects in plasmon-mediated entanglement generation

TL;DR

This work extends plasmon-mediated qubit entanglement to incorporate multipolar and nonlocal nanoparticle responses, revealing that dark multipolar modes can strongly suppress entanglement at small MNP–QD separations and for certain nanoparticle sizes. Using a cavity-QED framework with adiabatic elimination, it derives an effective two-qubit description in the Dicke basis and demonstrates three coupling regimes (strong, intermediate, weak) with distinct entanglement behavior. It shows that dipole-only models overestimate entanglement in the strong regime, while nonlocal corrections continue to modulate entanglement in the intermediate regime; in the weak regime, predictions converge but mediated entanglement remains limited by damping. The study also quantifies sensing potential via quantum Fisher information, finding an optimum near $r\approx s\approx 30$ nm where $\mathcal{F}_Q$ surpasses the SQL, illustrating practical implications for quantum sensing and nanophotonic device design.

Abstract

The generation of quantum entanglement is important for a wide range of quantum technology protocols. In nanophotonics, a promising platform for quantum technologies, entanglement generation via plasmon-mediated coupling in quantum dot qubits is often modeled within the dipole limit, where only dipolar plasmons of the mediating nanoparticle are considered, and the local response approximation, where nonlocal corrections are ignored. However, multipolar effects manifest strongly at coupling distances less than the nanoparticle size, while nonlocal optical effects stem from a size-induced dielectric response. We investigated these two important effects in the generation of two-qubit entanglement mediated by plasmonic coupling. A cavity quantum electrodynamic approach is employed, where the induced plasmonic effects lead to modified transition rates in the dynamics of the coupled quantum dot qubits. We find that multipolar modes and size-dependent damping lead to entanglement decay at small coupling distances and limit mediated entanglement with certain particle sizes. We discuss potential implications of multipolar modes in entanglement-based quantum sensing.

Figures (7)

• Figure 1: (Color online) Model geometry of the coupled system showing two QDs, QD1 and QD2, each with ground and excited states $|g_{i}\rangle$ and $|e_{i}\rangle~ (i = 1, 2)$ and dipole moments $\bm{\mu}_{1}$ and $\bm{\mu}_{2}$, respectively, coupled to a MNP of radius $r$, and interacting with one another via plasmon-mediated interactions at an inter-qubit distance of $2d$, and experiencing effective relaxation rates. The QD-MNP-QD system is driven at the dipolar LSPR wavelength $\lambda \approx \lambda_{0}$, of the MNP, in host medium of dielectric constant, $\varepsilon_{b}$.
• Figure 2: (Color Online) Energy level diagram showing the state transitions amongst the Dicke states and the rates involved.
• Figure 3: (Color online) Comparison of the dipole and multipole analyses of the transient concurrence of the two-qubit system for qubits prepared in the initial state $\rho_{0} = |1\rangle\langle 1|$ for different values of MNP-QD surface-to-surface distance $s$, and a AgNP of radius, $r = 30$ nm.
• Figure 4: (Color online) Comparison of the dipole and multipole analyses of the transient concurrence of the two-qubit system for qubits prepared in the initial state $\rho_{0} = |3\rangle\langle 3|$ for different values of MNP-QD surface-to-surface distance $s$, and a AgNP of radius $r = 30$ nm.
• Figure 5: (Color online) Depedence of the dipole and multipole analyses of the stationary concurrence on the MNP-QD surface-to-surface distance $s$, for a AgNP of radius $30$ nm.