Josephson voltage-phase relation
A voltage drives time evolution of the gauge-invariant phase difference.
Physical intuition
A voltage drives time evolution of the gauge-invariant phase difference. This is the starting point for understanding how superconducting circuit parameters determine quantum energy levels and dynamics.
Deep dive: how the mechanism works
A finite voltage advances the phase and produces AC Josephson oscillations.
How the quantum phenomenon appears
Microwave-frequency voltage oscillations follow from a DC junction bias. To establish the predicted quantum behavior, connect the circuit Hamiltonian to a measured transition, coherence experiment, gate benchmark or calibrated readout signal.
Assumptions and limitations
Research and simulation exercise
Identify the tunable parameters, predict the observable from the stated model, and sweep one parameter while holding the others fixed. Compare against a simpler reference model, quantify loss and uncertainty, and state which observations would falsify the hypothesis.
Connect the ideas
See the chapter guide and further reading.