Noise, chaos, and the Josephson voltage standard

Physics

Scientific paper

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Scientific paper

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 0034-4885/59/8/001/img1, a measure of the junction's nonlinearity, must be chosen much larger than the thermal energy 0034-4885/59/8/001/img2 to avoid disruption by intrinsic noise but not so large that chaos is evoked. The optimum 0034-4885/59/8/001/img1 maximizes the activation energy 0034-4885/59/8/001/img4 required for thermally induced escape from the phase-locked attractor. For nonequilibrium systems like the rf-biased junction, 0034-4885/59/8/001/img4 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.

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