Flicker (1f) noise in Josephson tunnel junctions

We have measured the power spectrum of the voltage fluctuations in shunted Josephson junctions biased at a constant current $I$ greater than the critical current $I_c$. Over the frequency range ${5\times 10}^{-2\mathrm{}}$-50 Hz the power spectra vary approximately as $\frac{1}{f}$, where $f$ is the frequency. At any single frequency, the noise decreases as $I$ is increased. Experimental evidence is presented to show that the voltage noise arises from equilibrium fluctuations in the temperature $T$ of the junction, which in turn modulate $I_c$ and hence the voltage $V$ across the junction. The magnitude of the power spectra is consistently predicted to within a factor of 5 by an extension of the semiempirical formula of Clarke and Voss: $S_V\mathrm{}\left(f\right)=\frac{{\left(\frac{d{I}_c}{\mathrm{dT}}\right)}^2{\left(\frac{\partial V}{\partial I_c}\right)}_I^2{k}_B{T}^2}{3C_{V}f}$. In this formula, we postulate that $C_V$ is the heat capacity of an "effective" junction volume given by the product of the junction area and the sum of the coherence lengths of the two superconductors. The dependence of $S_V\mathrm{}\left(f\right)\mathrm{}$ on ${\left(\frac{\partial V}{\partial I_c}\right)}_I^2$ and ${\left(\frac{d{I}_c}{\mathrm{dT}}\right)}^2$ is experimentally established.