Theory of the coplanar-waveguide Penning trap

A novel planar Penning trap is presented, which results from the projection of the well-known three-dimensional cylindrical trap onto the surface of a chip. The introduced trap is also a coplanar-waveguide cavity, similar to those used in circuit quantum electrodynamics experiments with superconducting two-level systems. It opens up the possibility of integrating a single trapped electron, or geonium atom, into quantum circuits. The trap is an elliptical Penning trap, with the magnetic field parallel to the chip's surface. A design procedure is described, which permits the compensation of electric anharmonicities up to sixth order. This should render possible the observation of a single trapped electron and the accurate measurement of its eigenfrequencies, a sine qua non requirement for a useful planar geonium technology.