Josephson Junction — Phase Qubit
RCSJ model: phase dynamics, IV characteristics & chaos
The RCSJ (Resistively-Capacitively Shunted Junction) model: (ℏ/2e)C φ̈ + (ℏ/2eR)φ̇ + Icsin(φ) = I + A cos(ωt).
For I < Ic the phase is locked (supercurrent). Above Ic the junction switches to the voltage state.
With AC driving, Shapiro steps appear at V = nℏω/2e and chaos emerges near the hysteretic boundary.