Josephson Junction — Plasma Oscillations

The resistively shunted junction (RSJ) model: phase dynamics equivalent to a damped pendulum. Small oscillations = plasma frequency ω_p. Above critical current: voltage state (AC Josephson effect).

Bias current I/I_c 0.80

Damping β_c^½ 1.0

AC drive amplitude 0.00

AC frequency ω/ω_p 1.00

Phase φ: 0.00 Voltage V: 0.00 State: plasma

RSJ equation: (ℏ/2eR) φ̈ + (ℏ/2e·1/R) φ̇ + I_c sin(φ) = I_bias + I_ac cos(ωt). For I < I_c: plasma oscillations around locked phase. For I > I_c: running solution = AC Josephson voltage V = ℏω_J/2e. Shapiro steps appear at rational ω/ω_p with AC drive.