TY - JOUR
T1 - Circuit QED with fluxonium qubits
T2 - Theory of the dispersive regime
AU - Zhu, Guanyu
AU - Ferguson, David G.
AU - Manucharyan, Vladimir E.
AU - Koch, Jens
PY - 2013/1/14
Y1 - 2013/1/14
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevB.87.024510
DO - 10.1103/PhysRevB.87.024510
M3 - Article
AN - SCOPUS:84872976076
VL - 87
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
SN - 1098-0121
IS - 2
M1 - 024510
ER -