Quasiparticle effects in transmons with gap-asymmetric junctions*

Single-particle excitations, known as Bogoliubov quasiparticles, threaten the operation of superconducting qubits.  We model the qubit-quasiparticle coupling in terms of quasiparticle densities, accounting for the gap asymmetry in Josephson junctions, which naturally arise from the deposition of aluminum layers with different thicknesses.

We show how the subtle interplay of generation, tunneling, and relaxation mechanisms determines the steady state of nonequilibrium quasiparticles. Two substantially different regimes are identified: 1) small gap difference, where quasiparticles are mainly located at the larger gap energy in both leads and the excited state of the qubit is depleted 2) strong gap asymmetry, similar to or higher than qubit frequency, with quasiparticles trapped in the lower gap superconductor and reduced relaxation rate. Our results may be relevant to the design of qubits with improved suppression of quasiparticle poisoning.