Impact of charge dispersion on lifetime of transmon with different electrode gaps*

Non-equilibrium quasiparticles tunneling across the Al/AlO_x/Al Josephson junction is a source of energy relaxation for transmon qubits. To suppress the quasiparticle tunneling, the superconducting gaps across the junction should be different. We fabricated a 3D transmon qubit where the bottom oxygen doped Al base electrode has the largest superconducting gap, a less doped counter-electrode with a smaller gap, and finally a third pure Al capping electrode. At a base temperature of 20 mK, the T₁ for the qubit transition temporally varied from 80 to 150 μs. The charge dispersion of g-f transition from the spectrum is around 1MHz. By adding a time delay to this standard spectroscopy sequence, we measured the lifetime of |f> state as a function of g-f transition frequency as well as the life time of |e> state from the subsequent |e> to |g> decay.