we establish a universal connection between the qubit AC Stark shift and the longitudinal and dispersive coupling to photons. We find that the longitudinal coupling g∥ is controlled by the slope of the AC Stark shift as function of the driving strength Aq, while the dispersive shift χ depends on its curvature. The two quantities become proportional to each other in the weak drive limit (Aq→0). Our approach unifies the adiabatic limit (ωr→0) — where g∥ is generated by the static spectrum curvature (or quantum capacitance) — with the diabatic one, where the static spectrum plays no role. We derive analytical results supported by exact numerical simulations. We apply them to superconducting and spin-hybrid cQED systems, showcasing the flexibility of faster-than-dispersive longitudinal readout.
Unifying Floquet theory of longitudinal and dispersive readout
We devise a Floquet theory of longitudinal and dispersive readout in circuit QED. By studying qubits coupled to cavity photons and driven at the resonance frequency of the cavity ωr,