Unifying Floquet theory of longitudinal and dispersive readout

TL;DR

This paper develops a unified Floquet theory for longitudinal and dispersive readout in circuit QED, linking the qubit AC Stark shift to coupling strengths and unifying adiabatic and diabatic regimes with analytical and numerical results.

Contribution

It introduces a universal Floquet framework connecting AC Stark shifts with coupling types, unifying different regimes of qubit-cavity interactions in circuit QED.

Findings

Longitudinal coupling controlled by AC Stark shift slope.

Dispersive shift depends on the curvature of the AC Stark shift.

Unified description applicable to superconducting and spin-hybrid systems.

Abstract

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 $\omega_{\rm r}$, 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 $g_\parallel$ is controlled by the slope of the AC Stark shift as function of the driving strength $A_{\rm q}$, while the dispersive shift $\chi$ depends on its curvature. The two quantities become proportional to each other in the weak drive limit ($A_{\rm q}\rightarrow 0$). Our approach unifies the adiabatic limit ($\omega_{\rm r}\rightarrow 0$) -- where $g_\parallel$ 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.