In conventional nonlinear optics, linear quantum optics 1,2 , and cavity quantum electrodynamics 3,4 to create e ective photonphoton interactions photons must have, at one time, interacted with matter inside a common medium. In contrast, in Rydberg quantum optics [5][6][7][8][9][10] , optical photons are coherently and reversibly mapped onto collective atomic Rydberg excitations 11 , giving rise to dipole-mediated e ective photon-photon interactions that are long range 12,13 . Consequently, a spatial overlap between the light modes is no longer required. We demonstrate such a contactless coupling between photons stored as collective Rydberg excitations in spatially separate optical media. The potential induced by each photon modifies the retrieval mode of its neighbour 7,9,14,15 , leading to correlations between them. We measure these correlations as a function of interaction strength, distance and storage time, demonstrating an e ective interaction between photons separated by 15 times their wavelength. Contactless e ective photon-photon interactions 16 are relevant for scalable multichannel photonic devices 15,17 and the study of strongly correlated many-body dynamics using light 18 . In vacuum, photon-photon interactions are so weak that they are discernible only at cosmological scales 19 . This is a remarkable asset for astronomy, imaging and communications, but a serious obstacle for all-optical processing. In linear quantum optics, one can engineer an effective interaction via measurement 1 which enables entanglement swapping between remote photons 2 ; however, this relies on probabilistic post-selective measurements. Inside a medium, interactions between light fields are possible if the lightmatter coupling is nonlinear. For sufficiently strong nonlinearities, such as in cavity quantum electrodynamics (cQED) 3 or Rydberg quantum optics 5 , one enters a quantum nonlinear regime 20 , allowing deterministic effective interactions at the single-photon level 4,[7][8][9][10] . This has paved the way towards prototypical single-photon transistors 21,22 , phase-shifters 23 , and photon gates 24 . A unique feature of Rydberg-mediated quantum nonlinear optics 5 is that the interaction is long range 12,13 , and can be mediated through free space by virtual microwave photons. This adds new geometric degrees of freedom to the nonlinear optics tool box which could facilitate scalable photonic networks, quantum simulation with photons, and circumvent 'no-go' theorems that limit the scope for all-optical quantum information processing (QIP) [15][16][17]25 . To directly demonstrate the long-range character of Rydberg-mediated nonlinear optics, we realize two strongly interacting photonic channels in independent optical media separated by an adjustable distance d of more than 10 µm. While stored as collective Rydberg excitations, van der Waals (vdW) interactions imprint non-uniform phase shifts 14,15 that lead to reduced retrieval in the photons' initial modes (Fig. 1). By counting photons in the unperturbed modes, the red...

Abstract. Using electromagnetically induced transparency and photon storage, the strong dipolar interactions between Rydberg atoms and the resulting dipole blockade can be mapped onto light fields to realise optical non-linearities and interactions at the single photon level. We report on the realisation of an experimental apparatus designed to study interactions between single photons stored as Rydberg excitations in optically trapped microscopic ensembles of ultracold 87 Rb atoms. A pair of in-vacuum high numerical aperture lenses focus excitation and trapping beams down to 1 μm, well below the Rydberg blockade. Thanks to efficient magneto-optical trap (MOT) loading from an atomic beam generated by a 2D MOT and the ability to recycle the microscopic ensembles more than 20000 times without significant atom loss, we achieve effective repetition rates exceeding 110 kHz to obtain good photon counting statistics on reasonable time scales. To demonstrate the functionality of the setup, we present evidence of strong photon interactions including saturation of photon storage and the retrieval of non-classical light. Using in-vacuum antennae operating at up to 40 GHz, we perform microwave spectroscopy on photons stored as Rydberg excitations and observe an interaction induced change in lineshape depending on the number of stored photons.

No abstract