Superconducting circuit boundary conditions beyond the Dynamical Casimir Effect

TL;DR

This paper analytically explores superconducting microwave circuit boundary conditions beyond the Dynamical Casimir Effect, revealing limitations of current models and showing that moving mirrors generate more particles and entanglement at high frequencies.

Contribution

It provides an explicit solution for time-dependent Robin boundary conditions in superconducting circuits and identifies the frequency regime where microwave models accurately simulate relativistic effects.

Findings

Robin boundary conditions differ from Dirichlet at high frequencies

Moving mirrors produce more particles than static models at high frequencies

Boundaries in microwave circuits can model relativistic effects within specific parameters

Abstract

We study analytically the time-dependent boundary conditions of superconducting microwave circuit experiments in the high plasma frequency limit, in which the conditions are Robin-type and relate the value of the field to the spatial derivative of the field. We give an explicit solution to the field evolution for boundary condition modulations that are small in magnitude but may have arbitrary time dependence, in a formalism that applies both to a semiopen waveguide and to a closed waveguide with two independently adjustable boundaries. The correspondence between the microwave Robin boundary conditions and the mechanically-moving Dirichlet boundary conditions of the Dynamical Casimir Effect is shown to break down at high field frequencies, approximately one order of magnitude above the frequencies probed in the 2011 experiment of Wilson et al. Our results bound the parameter regime in which a microwave circuit can be used to model relativistic effects in a mechanically-moving cavity, and they show that beyond this parameter regime moving mirrors produce more particles and generate more entanglement than their non-moving microwave waveguide simulations.