Probing the Phase Transition in the Spin-Boson Model With a Fluxonium Quantum Impurity

The spin-boson model predicts suppression of tunneling in a two-level system coupled to an Ohmic bath as the dissipation strength increases. We realize a tunable quantum-impurity platform using a superconducting fluxonium qubit (the two-level system) coupled to a high-impedance Josephson-junction transmission line that provides a dense bath of bosonic modes. By varying the external magnetic flux, we tune the effective dissipation in situ and perform spectroscopy of the bath modes to measure their frequency shifts and broadenings induced by the impurity. From these, we extract the dissipation strength, the renormalized tunneling rate, and impurity dynamic susceptibility across the predicted critical dissipation strength. Our approach provides a quantitative, circuit-QED route to testing the spin-boson model predictions around its critical point.