Using cold atoms to simulate strongly interacting quantum systems is an exciting frontier of physics. However, because atoms are nominally neutral point particles, this limits the types of interaction that can be produced. We propose to use the powerful new platform of cold atoms trapped near nanophotonic systems to extend these limits, enabling a novel quantum material in which atomic spin degrees of freedom, motion and photons strongly couple over long distances. In this system, an atom trapped near a photonic crystal seeds a localized, tunable cavity mode around the atomic position. We find that this effective cavity facilitates interactions with other atoms within the cavity length, in a way that can be made robust against realistic imperfections. Finally, we show that such phenomena should be accessible using onedimensional photonic crystal waveguides in which coupling to atoms has already been experimentally demonstrated.T rapped ultracold atoms are a rich resource for physicists. Isolated from the environment and routinely manipulated, they can act as a quantum simulator for a wide variety of physical models 1 . However, although short-range interactions between atoms can be adjusted by Feshbach resonance, these systems typically lack the long-range interactions required to produce some of the most interesting condensed-matter phenomena. For example, exotic phases such as supersolids are predicted in systems with long-range interactions 2 , as well as Wigner crystallization 3 and topological states 4 . Long-range interactions can also lead to the breakdown of concepts such as additivity in statistical mechanics 5,6 and the violation of speed limits (Lieb-Robinson bounds) for the propagation of information [7][8][9] . As a result, there are active efforts to achieve long-range interactions using specific properties of the atoms 10 , such as their magnetic moment 11,12 , Rydberg excitation 13 or by using polar molecules 14 .In this Article we investigate another paradigm, where, instead of relying on atomic properties, we design the medium through which the atoms interact-specifically, by coupling the atoms via the photon modes of a photonic crystal. Our proposal is inspired by demonstrations of strong coupling of photons in nanophotonic systems with individual solid-state emitters 15 and, more recently, with cold atoms [16][17][18][19] . For example, systems of ∼10 3 atoms have been trapped by and coupled to the evanescent guided modes of nanofibres 16,17 , and single atoms have been coupled to photonic crystal cavities 18 and waveguides 19. One aim of these efforts is to utilize strong, controlled light-matter interactions for quantum information processing and networks 20. Here, we show that atoms interfaced with photonic crystals can also have remarkable consequences for the exploration of quantum many-body physics [21][22][23] .A photonic crystal is a periodic dielectric structure that controls the propagation of light 24 . By introducing a defect into this regular structure, it is possible to induce c...

The integration of nanophotonics and atomic physics has been a long-sought goal that would open new frontiers for optical physics, including novel quantum transport and many-body phenomena with photon-mediated atomic interactions. Reaching this goal requires surmounting diverse challenges in nanofabrication and atomic manipulation. Here we report the development of a novel integrated optical circuit with a photonic crystal capable of both localizing and interfacing atoms with guided photons. Optical bands of a photonic crystal waveguide are aligned with selected atomic transitions. From reflection spectra measured with average atom number N ¼ 1:1 AE 0:4, we infer that atoms are localized within the waveguide by optical dipole forces. The fraction of single-atom radiative decay into the waveguide is G 1D /G 0 C(0.32 ± 0.08), where G 1D is the rate of emission into the guided mode and G 0 is the decay rate into all other channels. G 1D /G 0 is unprecedented in all current atom-photon interfaces.