Tunable Coupler for Mediating Interactions between a Two-Level System and a Waveguide from a Decoupled State to the Ultra-Strong Coupling Regime

Two-level systems (TLS) coupled to waveguides are a fundamental paradigm for light-matter interactions and quantum networks. We introduce and experimentally demonstrate a method to tune the interaction between a TLS, implemented as a flux qubit, and a transmission line waveguide from a decoupled state to a coupling strength that is a significant fraction of the TLS transition frequency, near the ultra-strong coupling regime. The coupling, controlled via magnetic flux, is described by a normalized coupling strength $\alpha$ that is measured to range between $6.2\times {10}^{-5}$ and $2.19\times {10}^{-2}$, with larger attainable maximum values predicted by a circuit model of the device. This system enables future investigations in the dynamics of the spin-boson model, microwave photonics, and relativistic quantum information.