We observe interaction-induced broadening of the two-photon 5s-18s transition in 87 Rb atoms trapped in a 3D optical lattice. The measured linewidth increases by nearly two orders of magnitude with increasing atomic density and excitation strength, with corresponding suppression of resonant scattering and enhancement of off-resonant scattering. We attribute the increased linewidth to resonant dipole-dipole interactions of 18s atoms with blackbody induced population in nearby np states. Over a range of initial atomic densities and excitation strengths, the transition width is described by a single function of the steady-state density of Rydberg atoms, and the observed resonant excitation rate corresponds to that of a two-level system with the measured, rather than natural, linewidth. The broadening mechanism observed here is likely to have negative implications for many proposals with coherently interacting Rydberg atoms.

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, non-equilibrium setting of cavity-QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability---a foundational and patently non-equilibrium model of cavity-QED---the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model.Comment: 11 pages + appendices, 8 figure

In short-range interacting systems, the speed at which entanglement can be established between two separated points is limited by a constant Lieb-Robinson velocity. Long-range interacting systems are capable of faster entanglement generation, but the degree of the speed-up possible is an open question. In this paper, we present a protocol capable of transferring a quantum state across a distance L in d dimensions using long-range interactions with strength bounded by 1/r α . If α < d, the state transfer time is asymptotically independent of L; if α = d, the time scales logarithmically with the distance L; if d < α < d + 1, transfer occurs in time proportional to L α−d ; and if α ≥ d + 1, it occurs in time proportional to L. We then use this protocol to upper bound the time required to create a state specified by a MERA (multiscale entanglement renormalization ansatz) tensor network and show that if the linear size of the MERA state is L, then it can be created in time that scales with L identically to state transfer up to logarithmic corrections. This protocol realizes an exponential speed-up in cases of α = d, which could be useful in creating large entangled states for dipole-dipole (1/r 3 ) interactions in three dimensions.Entanglement generation in a quantum system is limited, even in a non-relativistic setting, by the available interactions. In a lattice system with short-range interactions, Lieb and Robinson showed that there exists a linear light cone defined by a speed proportional to both the interaction range and strength [1]. Suppose two operators A and B are supported on single sites separated by a distance r. Then the Lieb-Robinson bound states that, after time t, [A(t), B] ≤ c A B e vt−r where c is a constant, v is another constant known as the Lieb-Robinson velocity, and · represents the operator norm. If a system initially in a product state begins evolving under a short-range Hamiltonian, correlations decrease exponentially outside of the causal cone defined by r = vt [2-4]. However, in physical systems including polar molecules [5][6][7], Rydberg atoms [8,9], or trapped ions [10,11], the interactions fall off with distance r as a power law 1/r α . For these interactions, generalizations of the Lieb-Robinson bound are known, but they may not be tight [12][13][14]. In addition, for sufficiently longranged interactions the causal region may even encompass infinite space at finite time, signaling a breakdown of emergent locality [15][16][17][18].These bounds on entanglement have direct implications for quantum information processing. The LiebRobinson bound, even if time dependence is allowed [19,20], limits the speed at which operations can be performed or states created using local Hamiltonians, including states with important applications in quantum metrology and communication [21][22][23][24][25]. In this paper, we consider the task of using long-range interactions to speed up certain quantum information processes, such as quantum state transfer, GHZ (Greenberger-Horne-Zeilinger) state preparati...