Circuit QED with fluxonium qubits: Theory of the dispersive regime

Guanyu Zhu*, David G. Ferguson, Vladimir E. Manucharyan, Jens Koch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

84 Scopus citations


In circuit QED, protocols for quantum gates and readout of superconducting qubits often rely on the dispersive regime, reached when the qubit-photon detuning Δ is large compared to the mutual coupling strength. For qubits including the Cooper-pair box and transmon, selection rules dramatically restrict the contributions to dispersive level shifts χ. By contrast, in the absence of selection rules many virtual transitions contribute to χ and can produce sizable dispersive shifts even at large detuning. We present theory for a generic multilevel qudit capacitively coupled to one or multiple harmonic modes and give general expressions for the effective Hamiltonian in second- and fourth-order perturbation theory. Applying our results to the fluxonium system, we show that the absence of strong selection rules explains the surprisingly large dispersive shifts observed in experiments and leads to the prediction of a two-photon vacuum Rabi splitting. Quantitative predictions from our theory are in good agreement with experimental data over a wide range of magnetic flux and reveal that fourth-order resonances are important for the phase modulation observed in fluxonium spectroscopy.

Original languageEnglish (US)
Article number024510
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number2
StatePublished - Jan 14 2013

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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