  We directly observe low-temperature non-equilibrium quasiparticle tunneling
in a pair of charge qubits based on the single Cooper-pair box. We measure
even- and odd-state dwell time distributions as a function of temperature, and
interpret these results using a kinetic theory. While the even-state lifetime
is exponentially distributed, the odd-state distribution is more heavily
weighted to short times, implying that odd-to-even tunnel events are not
described by a homogenous Poisson process. The mean odd-state dwell time
increases sharply at low temperature, which is consistent with quasiparticles
tunneling out of the island before reaching thermal equilibrium.
