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Recent breakthroughs in the experimental manipulation of strongly interactingatomic Rydberg gases in lattice potentials have opened a new avenue for thestudy of many-body phenomena. Considerable efforts are currently beingundertaken to achieve clean experimental settings that show a minimal amount ofnoise and disorder and are close to zero temperature. A complementary directioninvestigates the interplay between coherent and dissipative processes. Recentexperiments have revealed a first glimpse into the emergence of a richnon-equilibrium behavior stemming from the competition of laser excitation,strong interactions and radiative decay of Rydberg atoms. The aim of thepresent theoretical work is to show that local incoherent loss and gain ofatoms can in fact be the source of interesting out-of-equilibrium dynamics.This perspective opens new paths for the exploration of non-equilibriumcritical phenomena and, more generally, phase transitions, some of which so farhave been rather difficult to study. To demonstrate the richness of theencountered dynamical behavior we consider here three examples. The first twofeature local atom loss and gain together with an incoherent excitation ofRydberg states. In this setting either a continuous or a discontinuous phasetransition emerges with the former being reminiscent of genuine non-equilibriumtransitions of stochastic processes with multiple absorbing states. The thirdexample considers the regime of coherent laser excitation. Here the many-bodydynamics is dominated by an equilibrium transition of the "model A"universality class.

Atomic loss and gain as a resource for non-equilibrium phase transitions in optical lattices