Dissipate locally, couple globally: a sharp transition from decoupling to infinite range coupling in Josephson arrays with on-site dissipation

– We study the T = 0 normal to superconducting transition of Josephson arrays with on-site dissipation. A perturbative renormalization group solution is given. Like the previously studied case of bond dissipation (BD), this is a “floating” to coupled (FC) phase transition. Unlike the BD transition, at which only nearest-neighbor couplings become relevant, here all inter-grain couplings, out to infinitely large distances, do so simultaneously. We predict, for the first time in an FC transition, a diverging spatial correlation length. Our results show the robustness of floating phases in dissipative quantum systems. Coupling dissipation to quantum systems has interesting consequences. Quite generally, dissipation suppresses quantum fluctuations. This is evident at the level of a single macroscopic quantum ‘particle’ whose tunnelling probability out of a metastable state is suppressed by dissipation [1]. For the quantum particle in a double well [2, 3], or in a periodic [4, 5] potential, Ohmic (i.e., linear) dissipation can suppress quantum fluctuations enough to cause a dissipative ‘quantum to classical’ phase transition. In the classical phase, all quantum fluctuations are quenched and the system is spontaneously trapped into only one of the potential minima. From the point of view of understanding effects of dissipation on extended systems, a natural question to ask is what happens when such zero-dimensional dissipative systems are spatially coupled in a lattice. Understanding such effects has important practical applications. Such dissipative effects are thought to be at the heart of the physics of granular superconductivity [6]. They are also important in the context of decoherence in a qubit, which, it has been proposed [7], can be realized in a Josephson junction array . If the coupling of dissipation remains local, then it is natural to expect that quantum fluctuations can also be locally quenched by dissipation. At zero temperature, coupling such classical systems spatially should give rise to an ordered state of the extended system. This dissipative quantum phase transition (QPT), however, is expected to retain some of its local character.