Field configurations for field-free RF trap networks

TL;DR

This paper introduces a constructive framework for designing RF trap networks with complex, non-smooth field-free guide lines, expanding the design possibilities for quantum charge-coupled devices.

Contribution

It provides explicit methods to create non-smooth, cusp, and lattice RF trap networks from planar data, including Fourier formulas for periodic structures.

Findings

Explicit construction of non-smooth RF guide networks

Derivation of Fourier-space formulas for periodic extensions

Design of square-lattice networks with tunable parameters

Abstract

We develop a constructive framework for designing radio-frequency (RF) trap networks from planar data and show that non-smooth field-free guide lines are possible in such networks. Given analytic Cauchy data on a symmetry plane, namely the potential and its normal derivative, Laplace's equation determines a local three-dimensional continuation. The odd subclass of this harmonic extension maps an arbitrary analytic generating function $P(x,y)$ to a harmonic potential whose in-plane radio-frequency null set is exactly $P(x,y)=0$. This yields explicit field-free guide networks beyond smooth straight-line intersections, including cusp guides, cotangential contacts, and periodic lattices. We further derive Fourier-space formulas for periodic extensions and present square-lattice network families with tunable local crossing angle and rounded connectivity. These results provide a compact parametrization for the design space for quantum charge-coupled device (QCCD) architectures.