Josephson energy and inductance
A junction stores nonlinear potential energy and acts as a tunable inductive element.
Physical intuition
A junction stores nonlinear potential energy and acts as a tunable inductive element. This is the starting point for understanding how superconducting circuit parameters determine quantum energy levels and dynamics.
Deep dive: how the mechanism works
Integrating the current-phase relation yields a cosine potential whose curvature controls small-signal inductance.
How the quantum phenomenon appears
The transmon uses the Josephson cosine to create unequally spaced levels. 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.