Transmon Relaxation Due to Non-Equilibrium Quasiparticles: Modelling Temperature Dependence

We have measured the relaxation time T₁ of Al/AlOx/Al transmon qubits mounted in 3D aluminum cavities and have found that T₁ can increase by as much as a factor of two (from 45 µs to 90 µs in one device) as the temperature increased from 15 mK to 100 mK. We present a model of this phenomenon that is based on the behavior of non-equilibrium quasiparticles in the transmon’s superconducting junction, which has two constituent layers with different volumes and slightly different superconducting energy gaps. At low temperatures, the non-equilibrium quasiparticles concentrate in the low-gap small-volume region producing a higher density near the junction. This higher quasiparticle density causes an increase in the relaxation rate of the transmon. As the temperature is increased, these quasiparticles are liberated from the low-gap region into the large-gap, large-volume region, leading to a reduction in the density of quasiparticles at the junction and an increase in the relaxation time.