1/f noise of Josephson-junction-embedded microwave resonators at single   photon energies and millikelvin temperatures
  We present measurements of 1/f frequency noise in both linear and Josephson-junction-embedded superconducting aluminum resonators in the low power, low temperature regime - typical operating conditions for superconducting qubits. The addition of the Josephson junction does not result in additional frequency noise, thereby placing an upper limit for fractional critical current fluctuations of $10^{-8}$ (Hz$^{-1/2}$) at 1 Hz for sub-micron, shadow evaporated junctions. These values imply a minimum dephasing time for a superconducting qubit due to critical current noise of 40 -- 1400 $\mu$s depending on qubit architecture. Occasionally, at temperatures above 50 mK, we observe the activation of individual fluctuators which increase the level of noise significantly and exhibit Lorentzian spectra. 
K. W. Murch, S. J. Weber, E. M. Levenson-Falk, R. Vijay and I. Siddiqi
cond-mat.supr-con cond-mat.mes-hall quant-ph