Unifying Floquet theory of longitudinal and dispersive readout

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

5 pages + supplementary material (14 pages)

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Cited by in corpus (5)

• Strong Intrinsic Longitudinal Coupling in Circuit Quantum Electrodynamics
• Parametric longitudinal coupling of a semiconductor charge qubit and a RF resonator
• Parametric Drive of a Double Quantum Dot in a Cavity
• Floquet-engineered fast SNAP gates in weakly coupled circuit-QED systems
• Switchable spin-photon coupling with hole spins in single-quantum dots