Cross-Kerr coupling in the two-photon bosonic regime of a SQUID-coupled phase qubit never vanishes due to potential asymmetry and coupler nonlinearity, with explicit limits on the number of coherent states needed for the approximation.
Lisenfeld,Experiments on superconducting Josephson phase quantum bits, Ph.D
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Two-photon coupling via Josephson element II: Interaction dressing, cross-Kerr coupling, and limits of low-energy bosonic model
Cross-Kerr coupling in the two-photon bosonic regime of a SQUID-coupled phase qubit never vanishes due to potential asymmetry and coupler nonlinearity, with explicit limits on the number of coherent states needed for the approximation.