Flicker (1∕f) noise in the critical current of Josephson junctions at 0.09–4.2K

We have measured the low-frequency noise in the critical current $I_c$ of six dc superconducting quantum interference devices (SQUIDs) with resistively shunted $\mathrm{Nb}–\mathrm{Nb}{\mathrm{O}}_x–\mathrm{Pb}\mathrm{In}$ Josephson junctions in the temperature range $T=0.09–4.2\mathrm{K}$ . Each device is voltage biased, the applied flux is an integer number of flux quanta, and the current fluctuations are measured with a second dc SQUID. At low frequencies $f$ , there is a component of the power spectrum of the critical current fluctuations given approximately by $S_{I_c}\left(f\right)=C{I}_c^2{T}^2∕Af$ , where $A$ is the area of both junctions, and $C\approx (3.9\pm 0.4)\times {10}^{-23}{\mathrm{m}}^2∕{\mathrm{K}}^2$ . For quantum bits based on Josephson junctions, the scaling of $S_{I_c}\left(f\right)$ with $T^2$ implies that the dephasing time limited by critical current $\mathrm{l}∕f$ noise should scale as $1∕T$ for temperatures down to at least $0.09\mathrm{K}$ .