Steady-state thermodynamics of nonequilibrium quasiparticles in a Cooper-pair box

A superconducting Coulomb-blockade electrometer was used to measure the Coulomb staircase of an Al∕AlOₓ∕Al Cooper-pair box from a temperature of 300.3em0exto0.3em0ex3000.3em0exmK. At the lowest temperature, the Coulomb staircase displays effects from nonequilibrium quasiparticles. As the temperature is increased, an initial decrease is found in the width of the odd steps in the staircase, which corresponds to a reduction in the probability of having a quasiparticle on the island of the box. Above 1800.3em0exmK, the width of the odd steps increases, eventually producing a staircase with $1e$ features. We develop a steady-state model of the system and find that the presence of quasiparticles at low temperature is consistent with the assumption of Aumentado et al. [Phys. Rev. Lett. 92, 066802 (2004)] that nonequilibrium quasiparticles are generated in the leads. Above 1800.3em0exmK, our results are consistent with the quasiparticle states of the island being thermally populated.