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This system features different interactions that act on disparate length scales, from zero-range defect scattering of atomic excitations and finite-range dipole exchange processes to long-range Rydberg-state interactions, which span the entire array and can block multiple Rydberg excitations. Analyzing their interplay, we identify conditions that yield a nonlinear quantum mirror which coherently splits incident fields into correlated photon-pairs in a single transverse mode, while transmitting single photons unaffected. In particular, we find strong anti-bunching of the transmitted light with equal-time pair correlations that decrease exponentially with an increasing range of the Rydberg blockade. Such strong photon-photon interactions in the absence of photon losses open up promising avenues for the generation and manipulation of quantum light, and the exploration of many-body phenomena with interacting photons.<\/jats:p>","DOI":"10.22331\/q-2022-03-30-674","type":"journal-article","created":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T13:11:19Z","timestamp":1648645879000},"page":"674","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":36,"title":["Photon-photon interactions in Rydberg-atom arrays"],"prefix":"10.22331","volume":"6","author":[{"given":"Lida","family":"Zhang","sequence":"first","affiliation":[{"name":"Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark"}]},{"given":"Valentin","family":"Walther","sequence":"additional","affiliation":[{"name":"Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark"},{"name":"ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA"}]},{"given":"Klaus","family":"M\u00f8lmer","sequence":"additional","affiliation":[{"name":"Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark"}]},{"given":"Thomas","family":"Pohl","sequence":"additional","affiliation":[{"name":"Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark"}]}],"member":"9598","published-online":{"date-parts":[[2022,3,30]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"D. 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