Josephson Junction — AC Effect & Washboard Potential

Phase dynamics: I = I_c sin(φ), V = (ℏ/2e) dφ/dt — RSJ model simulation

RSJ Model

State

Phase φ/π
Voltage V/V_0
Frequency ω_J/ω_0
State
RSJ: (ℏ/2eR)dφ/dt + I_c sinφ = I_b + ξ(t)
Washboard: U(φ) = −E_J cosφ − (ℏI/2e)φ
DC: ⟨V⟩ = 0 (pinned), ≠0 (running)
AC Josephson: ω_J = 2eV/ℏ (f≈484 GHz/mV)
SQUID: flux quantization Φ_0 = h/2e