Numerical procedure for simulating the large-signal quantum behaviour of superconducting tunnel-junction circuits

The authors describe a numerical procedure for simulating, in the frequency domain, the large-signal quantum behaviour of superconducting tunnel-junction circuits. It is shown that the steady-state dynamics of a circuit can be decomposed by using the method of harmonic balance, and that the resulting system of coupled nonlinear algebraic equations can be solved through the harmonic Newton method. The presentation is generalised in a number of ways: first, the scheme is described in terms of a generic circuit comprising a tunnel junction and a Thevenin voltage source; secondly, the circuit equations are normalised to the gap voltage and the gap current of the tunnel barrier; and thirdly, an imperfect junction is modelled by convolving an ideal BCS current/voltage characteristic with a Gaussian function