Quantum impurity physics meets circuit QED: observation of finite lifetime photons

We report a new regime of quantum electrodynamics (QED) where a single photon acquires a finite lifetime due to spontaneous decay to many lower-frequency photons. This phenomenon is a hallmark of ultra-strong coupling between a sufficiently non-linear quantum system (the quantum impurity) and a continuum of 1D bosonic modes. While this situation is impossible in atomic physics, it is ubiquitously in the bosonic description of strongly-correlated 1D electronic systems. We implemented bosonic versions of two key quantum impurity models: the boundary sine-Gordon model and the Kondo model. Physically our system is a long section of a high-impedance transmission line (the bosons) connected to a single small capacitance Josephson junction (the BSG impurity) or to a fluxonium qubit (the Kondo impurity). The many-body correlation functions of these two quantum impurity problems can be extracted from the measured inelastic spectrum of microwave photons, which implements a quantum simulation of a classically difficult computational problem.