The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The well-established conce
pt at or near equilibrium, universality, can also characterize the physics of systems out of equilibrium. The most fundamental instance of a genuine non-equilibrium phase transition is the directed percolation universality class, where a system switches from an absorbing inactive to a fluctuating active phase. Despite being known for several decades it has been challenging to find experimental systems that manifest this transition. Here we show theoretically that signatures of the directed percolation universality class can be observed in an atomic system with long range interactions. Moreover, we demonstrate that even mesoscopic ensembles --- which are currently studied experimentally --- are sufficient to observe traces of this non-equilibrium phase transition in one, two and three dimensions.
The steady state of a driven dense ensemble of two-level atoms is determined from the competition of coherent laser excitation and decay that acts in a correlated way on several atoms simultaneously. We show that the presence of this non-local dissip
ation lifts the direct link between the density of excited atoms and the photon emission rate which is typically present when atoms decay independently. The non-locality disconnects these static and dynamic observables so that a dynamical transition in one does not necessarily imply a transition in the other. Furthermore, the collective nature of the quantum jump operators governing the non-local decay results in the formation of spatial coherence in the steady state which can be measured by analyzing solely global quantities - the photon emission rate and the density of excited atoms. The experimental realization of the system with strontium atoms in a lattice is discussed.
Alkaline-earth-metal atoms exhibit long-range dipolar interactions, which are generated via the coherent exchange of photons on the 3P_0-3D_1-transition of the triplet manifold. In case of bosonic strontium, which we discuss here, this transition has
a wavelength of 2.7 mu m and a dipole moment of 2.46 Debye, and there exists a magic wavelength permitting the creation of optical lattices that are identical for the states 3P_0 and 3D_1. This interaction enables the realization and study of mixtures of hard-core lattice bosons featuring long-range hopping, with tuneable disorder and anisotropy. We derive the many-body Master equation, investigate the dynamics of excitation transport and analyze spectroscopic signatures stemming from coherent long-range interactions and collective dissipation. Our results show that lattice gases of alkaline-earth-metal atoms permit the creation of long-lived collective atomic states and constitute a simple and versatile platform for the exploration of many-body systems with long-range interactions. As such, they represent an alternative to current related efforts employing Rydberg gases, atoms with large magnetic moment, or polar molecules.
