Two-photon interaction in a superconducting circuit with SQUID-mediated coupling

Abstract

In this work, we study interactions between a resonator and an rf SQUID (Superconducting QUantum Interference Device) coupled via a Josephson element. The latter is a symmetrical dc SQUID, which induces two-photon and other inductive interactions. By changing the SQUID magnetic bias, one can control two- and single-photon interaction rates [1]. In addition to the twophoton interaction mediated by the SQUID coupler, we consider cross-Kerr, linear, and optomechanical interactions. The rf SQUID in the circuit acts as an artificial atom—a phase qubit [2]. We focus on the regime of resonant two-photon interaction. We calculate the rates of relevant interactions, including renormalizations near the two-photon resonance. Our theory provides interpretations for these renormalizations and establishes conditions under which particular interactions can be neglected. Finally, we discuss the range of its validity.