  Quasiparticles are an important decoherence mechanism in superconducting
qubits, and can be described with a complex admittance that is a generalization
of the Mattis-Bardeen theory. By injecting non-equilibrium quasiparticles with
a tunnel junction, we verify qualitatively the expected change of the decay
rate and frequency in a phase qubit. With their relative change in agreement to
within 4% of prediction, the theory can be reliably used to infer quasiparticle
density. We describe how settling of the decay rate may allow determination of
whether qubit energy relaxation is limited by non-equilibrium quasiparticles.
