Flicker (1 / f) 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 × 10^-2-50 Hz the power spectra vary approximately as 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(f)=(dI_c / dT)²(∂V / ∂I_c)_I²k_BT² / 3C_Vf. 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(f) on (∂V / ∂I_c)_I² and (dI_c / dT)² is experimentally established.