Mesoscopic Modeling of Superconducting Devices: Towards a Rabi-Meissner Response

Abstract

The increasing complexity and applicability of superconducting circuit-based quantum devices motivates the need for a new mesoscopic physical model to describe their behavior. We desire a theory with the spatial resolution and accuracy of BCS theory, but the simplicity and numerical solvability of traditional phenomenological models like the Ginzburg-Landau or London equations. Here we use nonrelativistic scalar electrodynamics to model superconducting devices as a many body system of charged spinless bosons using a multimode approximation for the matter. We formulate a variational problem to numerically solve for the steady state ground state of a system of two superconducting islands, and show how the parameters of the effective charge qubit Hamiltonian depend on geometry from first principles. We then use these solutions as an initial condition for a dynamical simulation of a charge qubit interacting with an AC electromagnetic drive. Using semiclassical equations of motion derived from our effective bosonic field theory, we can simultaneously show the Meissner screening of the electromagnetic drive from the bulk of the superconductor, while driving Rabi oscillations on the effective charge qubit.