  We have measured noise in thin-film superconducting coplanar waveguide
resonators. This noise appears entirely as phase noise, equivalent to a jitter
of the resonance frequency. In contrast, amplitude fluctuations are not
observed at the sensitivity of our measurement. The ratio between the noise
power in the phase and amplitude directions is large, in excess of 30 dB. These
results have important implications for resonant readouts of various devices
such as detectors, amplifiers, and qubits. We suggest that the phase noise is
due to two-level systems in dielectric materials.
