Quasiparticle Poisoning in a Cooper-Pair Box

We have used a single-electron transistor (SET) to measure the Coulomb staircase of a single Cooper-pair box (CPB) from a temperature of 30 mK to 300 mK. At the lowest temperature, the data shows that the CPB, which is fabricated from Al/AlO$_{\mbox{x}}$/Al tunnel junctions, is poisoned by nonequilibrium quasiparticles. As the temperature is increased from 30 to 150 mK, the width of the odd step in the staircase, which corresponds to a quasiparticle on the island of the box, decreases linearly with temperature. Above 180 mK, the width of the odd step increases, eventually producing a staircase with 1\textit{e} steps. The low-temperature poisoning is consistent with the assumptions of Aumentado \textit{et al.} that quasiparticles are spontaneously generated in the leads.\footnote{J. Aumentado, M. Keller, J. Martinis, \& M. Devoret, Phys. Rev. Lett. \textbf{92}, 066802 (2004).} For particular gate voltages it is energetically favorable to have a nonequilbrium quasiparticle occupy a state on the island; hence poisoning the pure 2\textit{e} staircase. The data above 180 mK is consistent with the quasiparticle states of the island being thermally populated.