Field geometry in tip-induced plasmonic nanocavities for strongly-coupled inhomogeneous many-qubit systems via the method of images

Solid-state cavity quantum electrodynamics has attracted interest as a platform for quantum information systems. A typical scenario involves an ensemble of qubits in a plasmonic nanocavity. This talk focuses on the spatial dependence of the electromagnetic field experienced by qubits lying on the substrate of a tip-induced plasmonic nanocavity. Knowledge of a specific field distribution is necessary for modeling a specific system's dynamics.

We model the apex of the cavity tip and substrate as a conducting sphere and a half-space bounded by a plane. We solve the Laplace equation—we work in the quasistatic approximation—for this geometry using an infinite series of image charges. The magnitudes and positions of these image charges are determined by a system of finite-difference equations.

We describe application of this solution to the modeling of multiqubit systems in the presence of dissipation and noise. This model reveals the presence of certain collective behaviors of the qubits including the existence of dark states.