Quantum predator-prey cycles in dissipative Rydberg array

Abstract

The predator-prey cycle is a paradigmatic example of self-organized population oscillations in far-from-equilibrium systems, yet testing its underlying mechanism in natural ecosystems is often precluded by uncontrollable microscopic parameters. Here, we propose a quantum analogue of predator-prey dynamics using a tunable two-dimensional Rydberg atom array. Through mean-field analysis and large-scale numerical simulations based on the open-system discrete truncated Wigner approximation, we demonstrate stable predator-prey cycles of Rydberg excitations on microsecond timescales. We show that nonperturbative quantum coherence drives spontaneous time-translation symmetry breaking, leading to globally synchronized oscillations under short-range interactions. Even under desynchronization caused by quantum jumps, locally synchronized predator-prey cycles persist, with amplitude scaling inversely with the square root of the system size. Our work extends the study of predator-prey models to the quantum realm and advances quantum simulation strategies that leverage engineered many-body nonequilibrium effects.