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Superconducting circuits and trapped ions are promising architectures forquantum information processing. However, the natural frequencies forcontrolling these systems -- radio frequency ion control and microwave domainsuperconducting qubit control -- make direct Hamiltonian interactions betweenthem weak. In this paper we describe a technique for coupling a trapped ion'smotion to the fundamental mode of a superconducting circuit, by applying to thecircuit a carefully modulated external magnetic flux. In conjunction with anon-linear element (Josephson junction), this gives the circuit an effectivetime-dependent inductance. We then show how to tune the external flux togenerate a resonant coupling between the circuit and ion's motional mode, anddiscuss the limitations of this approach compared to using a time-dependentcapacitance.

Dynamics of an Ion Coupled to a Parametric Superconducting Circuit