Unifying Floquet Theory of Longitudinal and Dispersive Readout
Alessandro Chessari, Esteban A. Rodríguez-Mena, J. C. Abadillo-Uriel, V. Champain, Simon Zihlmann, Romain Maurand, Yann‐Michel Niquet, Michele Filippone · Physical Review Letters · 2025
We devise a Floquet theory of longitudinal and dispersive readout in circuit quantum electrodynamics (cQED). By studying qubits coupled to cavity photons and driven at the resonance frequency of the cavity ${\ensuremath{\omega}}_{\mathrm{r}}$, 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 ${g}_{\ensuremath{\parallel}}$ is controlled by the slope of the ac Stark shift as function of the driving strength ${A}_{\mathrm{q}}$, while the dispersive shift $\ensuremath{\chi}$ depends on its curvature. The two quantities become proportional to each other in the weak drive limit (${A}_{\mathrm{q}}\ensuremath{\rightarrow}0$). Our approach unifies the adiabatic limit (${\ensuremath{\omega}}_{\mathrm{r}}\ensuremath{\rightarrow}0$)---where ${g}_{\ensuremath{\parallel}}$ is generated by the static spectrum curvature (or quantum capacitance)---with the diabatic limit, where ${\ensuremath{\omega}}_{\mathrm{r}}$ is large and 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.