Unifying Floquet theory of longitudinal and dispersive readout

  1. Alessandro Chessari,
  2. Esteban A. Rodríguez-Mena,
  3. José Carlos Abadillo-Uriel,
  4. Victor Champain,
  5. Simon Zihlmann,
  6. Romain Maurand,
  7. Yann-Michel Niquet,
  8. and Michele Filippone
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, 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.
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