We study collective 'free-space' radiation properties of two distant single-layer arrays of quantum emitters as two-level atoms. We show that this system can support a long-lived Bell superposition state of atomic excitations exhibiting strong subradiance, which corresponds to a non-local excitation of the two arrays. We describe the preparation of these states and their application in quantum information as resource of non-local entanglement, including deterministic quantum state transfer with high fidelity between the arrays representing quantum memories. We discuss experimental realizations using cold atoms in optical trap arrays with subwavelength spacing, and analyze the role of imperfections.Introduction. -Recent advances in preparing regular arrays of atoms with optical traps [1-4] offer new opportunities to engineer strong collective coupling between atoms and light, with applications in quantum information science. In particular, a single layer of atoms loaded into a regular 2D array with sub-wavelength spacing has been proposed as an atomic mirror with high reflectivity [5][6][7][8][9], as quantum memory with efficient storage and retrieval [10], and to implement topological quantum optics [11,12]; in addition, emission of single photons from bilayer atomic arrays can be engineered to be highly directional in free-space [13]. Moreover, single-layered atomic arrays have been shown to support subradiant collective excitations [14][15][16], which consist of excited superposition states of atoms decaying much slower than a single isolated excited atom, due to interference in spontaneous emission [17][18][19][20][21][22][23].Here we show that the composite quantum system consisting of two distant single-layered arrays of atoms [cf. Figs. 1(a-c)] can support an atomic Bell superposition state exhibiting strong subradiance. Remarkably, this non-radiating 'dark' state is a non-local entangled state, i.e. a superposition state of a collective excitation living in the first or second array, where the two arrays can be separated by a distance L much larger than the transverse size L ⊥ of each individual array. This phenomenon relies on two ingredients. First, spontaneous emission from a collective atomic excitation in a single layer can be directional, with a proper phasing of the atomic dipoles, corresponding to light emission in both directions perpendicular to the atomic array, as in Fig. 1(a) [5]. Second, radiation from two distant atomic arrays can -provided the separation length L is commensurate with half the optical wavelength [upper panel in Fig. 1(c)] -lead to destructive interference of light emitted to the left and to the right of the two arrays, corresponding to a subradiant state, i.e. this 'dark' state will show strongly suppressed radiative loss to the outside world. In contrast, the lower panel in Fig. 1(c) displays a 'bright' (i.e., radiating) state due to constructive interference.Below we will show that these non-local subradiant

We describe a quantum state transfer protocol, where a quantum state of photons stored in a first cavity can be faithfully transferred to a second distant cavity via an infinite 1D waveguide, while being immune to arbitrary noise (e.g., thermal noise) injected into the waveguide. We extend the model and protocol to a cavity QED setup, where atomic ensembles, or single atoms representing quantum memory, are coupled to a cavity mode. We present a detailed study of sensitivity to imperfections, and apply a quantum error correction protocol to account for random losses (or additions) of photons in the waveguide. Our numerical analysis is enabled by matrix product state techniques to simulate the complete quantum circuit, which we generalize to include thermal input fields. Our discussion applies both to photonic and phononic quantum networks.

We present the design of a chiral photonic quantum link, where distant atoms interact by exchanging photons propagating in a single direction in free-space. This is achieved by coupling each atom in a laser-assisted process to an atomic array acting as a quantum phased-array antenna. This provides a basic building block for quantum networks in free space, i.e. without requiring cavities or nanostructures, which we illustrate with high-fidelity quantum state transfer protocols. Our setup can be implemented with neutral atoms using Rydberg-dressed interactions. arXiv:1802.05592v2 [quant-ph]