Noise, chaos, and the Josephson voltage standard

The design of zero-bias Josephson voltage standards is presented as a case study in nonlinear dynamics. Based on superconducting tunnel junctions, such standards rely on nonlinearity to create a phase lock between an internal junction variable and an applied rf bias. In the terminology of nonlinear dynamics, phase lock corresponds to motion on a periodic attractor. Not all attractors of the rf-biased junction are periodic, however, and both quasiperiodic and chaotic attractors must be avoided in voltage standards. Surprisingly, the optimum operating point for zero-bias standards is near a region of chaos. Thus, the Josephson coupling energy E(J), a measure of the junction's nonlinearity, must be chosen much larger than the thermal energy k(B)T to avoid disruption by intrinsic noise but not so large that chaos is evoked. The optimum E(J) maximizes the activation energy E(A) required for thermally induced escape from the phase-locked attractor. For nonequilibrium systems like the rf-biased junction, E(A) is a difference in quasipotential that can be calculated by finding the most probable path for escape from a basin of attraction in the limit of low temperature.