Epidemic Dynamics in Open Quantum Spin Systems

We explore the nonequilibrium evolution and stationary states of an open many-body system that displays epidemic spreading dynamics in a classical and a quantum regime. Our study is motivated by recent experiments conducted in strongly interacting gases of highly excited Rydberg atoms where the facilitated excitation of Rydberg states competes with radiative decay. These systems approximately implement open quantum versions of models for population dynamics or disease spreading where species can be in a healthy, infected or immune state. We show that in a two-dimensional lattice, depending on the dominance of either classical or quantum effects, the system may display a different kind of nonequilibrium phase transition. We moreover discuss the observability of our findings in laser driven Rydberg gases with particular focus on the role of long-range interactions.The research leading to these results has received fund- ing from the European Research Council under the Euro- pean Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement No. 335266 (ESC-QUMA), the EPSRC Grant No. EP/M014266/1 and the H2020-FETPROACT-2014 Grant No. 640378 (RYSQ). RG acknowledges the funding received from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 703683. We are also grateful for access to the University of Nottingham High Performance Computing Facility