Chaos and Related Nonlinear Noise Phenomena in Josephson Tunnel Junctions.
Abstract
The nonlinear dynamics of Josephson tunnel junctions shunted by a resistance with substantial selfinductance have been thoroughly investigated. The currentvoltage characteristics of these devices exhibit stable regions of negative differential resistance. Very large increases in the lowfrequency voltage noise with equivalent noise temperatures of 10('6) K or more, observed in the vicinity of these regions, arise from switching, or hopping, between subharmonic modes. Moderate increases in the noise, with temperatures of about 10('3) K, arise from chaotic behavior. Both of these conclusions are substantiated by analog simulations. Measurements of the lowfrequency spectrum of the hopping noise in one type of junction show a 1/f('2)dependence, independent of both bias current and temperature. A simple amplifier utilizing the negative differential resistance is found to exhibit a "noise rise.". Analog and digital simulations indicate that under somewhat rarer circumstances the same junction system can sustain a purely deterministic hopping between to unstable subharmonic modes, accompanied by excess lowfrequency noise. Unlike the noiseinduced case, this chaotic process occurs over a much narrower range in bias current and is destroyed by the addition of thermal noise. The differential equation describing the junction system can be reduced to a onedimensional mapping in the vicinity of one of the unstable modes. A general analytical calculation of switching processes for a class of mappings yields the frequency dependence of the noise spectrum in terms of the parameters of the mapping. Finally, the concepts of noiseinduced hopping near bifurcation thresholds are applied to the problem of the threephoton Josephson parametric amplifier. Analog simulations indicate that the noise rise observed in experimental devices arises from occasional hopping between a mode at the pump frequency (omega)(,p) and a mode at the half harmonic (omega)(,p)/2. The hopping is induced by thermal noise associated with the shunt resistance.
 Publication:

Ph.D. Thesis
 Pub Date:
 1984
 Bibcode:
 1984PhDT.......121M
 Keywords:

 Physics: Condensed Matter