Observation of the Schmid–Bulgadaev dissipative quantum phase transition

A classical particle moving in a periodic potential can localize inside a single potential minimum, but a quantum particle forms extended states by tunnelling to neighbouring minima. These two limits are separated by a quantum Schmid–Bulgadaev phase transition driven by a viscous friction force. This physics has implications for Josephson junction devices, which feature superconducting phase dynamics that can be modelled by a fictitious particle in a periodic potential. As a result, it has been anticipated that any junction of two superconductors connected to a resistor can undergo a Schmid–Bulgadaev transition when the value of the resistor exceeds a threshold. Here we observe this transition by implementing the ohmic environment as a massively multimode cavity and probing the effect of the junction on the standing-wave mode spectrum of the cavity. We find that, depending on the characteristic impedance of the cavity, sufficiently weak junctions scatter cavity photons as either inductors or capacitors. These regimes correspond to the superconducting and insulating phases, respectively, and the critical impedance matches the expected value. At the phase boundary, quantum fluctuations boost the junction nonlinearity so that the junction behaves as a resistor. This loss mechanism reconciles the superconducting and insulating phases and provides a possibly useful indication of quantum-critical dynamics.