Noise driven fluctuations of Josephson junction series arrays

The shunted junction model is used to analyze the noise-driven fluctuations of series arrays of Josephson junctions. The total voltage across an array of coherently oscillating Josephson junctions is shown to exhibit two fundamentally different types of fluctuations, each of which makes its own characteristic type of contribution to the power spectrum. Phase fluctuations broaden the peaks in the power spectrum that correspond to the basic oscillations of the junctions and are primarily responsible for the linewidth of these oscillations. Transverse fluctuations contribute Lorentzian-shaped noise bumps to the power spectrum at the fundamental and harmonics of the basic Josephson oscillations. These noise bumps become larger and narrower at T/β_c increases, making a contribution to the linewidth for large β_c and large bias currents. The form of these fluctuations is calculated in the limit of small noise, and it is shown that the fluctuations increase as a dynamical instability is approached