Spurious Antenna Modes of the Transmon Qubit

Abstract: Superconducting qubits are resonant absorbers of pair-breaking radiation. The metal pads that form the qubit capacitance support standing wave modes at frequencies of order 100~GHz; these modes are strongly coupled to free-space impedance through their electric dipole moment. While the antenna mode of the 3D transmon qubit is easily seen to be a resonant dipole, other 2D qubit types can be understood as the aperture duals of wire loop antennas or folded dipoles. For typical Josephson junction parameters, the junction provides a reasonable conjugate match to the fundamental antenna mode. We calculate the contribution to quasiparticle poisoning from resonant absorption of blackbody radiation. We extend our analysis to dissipation at the qubit frequency, where radiative losses provide an ultimate limit to qubit energy relaxation time. A clear understanding of the spurious antenna modes of qubits will allow designs that are insensitive to pair-breaking radiation and that display reduced radiative losses at the qubit frequency.