Two-photon coupling via Josephson element II: Interaction dressing, cross-Kerr coupling, and limits of low-energy bosonic model

TL;DR

This paper investigates the interactions mediated by a SQUID in superconducting qubits, analyzing their renormalizations, the limits of the bosonic approximation, and potential applications in quantum measurement.

Contribution

It provides a detailed analysis of two-photon coupling, the persistence of cross-Kerr effects, and criteria for the validity of the bosonic model in superconducting qubits.

Findings

Cross-Kerr coupling never vanishes in the two-photon regime due to asymmetry and nonlinearity.

Quantitative limits of the bosonic approximation are established based on the minimum number of energy states needed.

Predictions for coupling rates and potential applications in quantum nondemolition readout are provided.

Abstract

We study the interactions mediated by a symmetric superconducting quantum interference device (SQUID), their renormalizations, and the applicability of the anharmonic oscillator (bosonic) model for a coupled phase qubit. The latter dwells in its metastable well holding a number of anharmonic energy states. The coupling SQUID can switch between the single- and two-photon interactions in situ. We find that, in the bosonic two-photon regime, the cross-Kerr coupling never vanishes as it dresses due to asymmetry in the qubit potential and nonlinearity of the coupler. Our quantitative results also depend on the bosonic approximation. We approach determining its limits by finding the minimum number of coherent energy states required for a dressing. For that, we lay out diagrams of the dressing virtual processes that climb the qubit ladder as high as possible. Near the two-photon resonance with a coupled resonator, we systematically calculate other relevant renormalizations due to nonresonant interactions. We provide verifiable predictions for the coupling rates. Modified systems can be applied for two-photon detection and for quantum-nondemolition readout of a qubit with an asymmetrical potential.