Concept 21 of 42 · Circuit QED and Decoherence

Dispersive regime

Off-resonant coupling produces qubit-state-dependent cavity frequencies.

01 / Mathematical framework

$$H_{\mathrm{disp}}/\hbar\approx(\omega_r+\chi\sigma_z)a^\dagger a+\frac{\omega_q}{2}\sigma_z$$

Physical intuition

Off-resonant coupling produces qubit-state-dependent cavity frequencies. This is the starting point for understanding how superconducting circuit parameters determine quantum energy levels and dynamics.

Deep dive: how the mechanism works

Virtual exchange shifts the resonator frequency without requiring real resonant swaps.

How the quantum phenomenon appears

A readout tone acquires a qubit-state-dependent phase shift. 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

The simple dispersive approximation requires sufficiently small coupling relative to detuning.

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

Circuit quantum electrodynamics Qubit relaxation T1

See the chapter guide and further reading.

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ΦDispersive regime