  We have directly measured quasiparticle number fluctuations in a thin film
superconducting Al resonator in thermal equilibrium. The spectrum of these
fluctuations provides a measure of both the density and the lifetime of the
quasiparticles. We observe that the quasiparticle density decreases
exponentially with decreasing temperature, as theoretically predicted, but
saturates below 160 mK to 25-55 per cubic micron. We show that this saturation
is consistent with the measured saturation in the quasiparticle lifetime, which
also explains similar observations in qubit decoherence times.
