Strong interaction between two single photons is a long standing and important goal in quantum photonics. This would enable a new regime of nonlinear optics and unlock several applications in quantum information science, including photonic quantum gates and deterministic Bell-state measurements. In the context of quantum networks, it would be important to achieve interactions between single photons from independent photon pairs storable in quantum memories. So far, most experiments showing nonlinearities at the single-photon level have used weak classical input light. Here we demonstrate the storage and retrieval of a paired single photon emitted by an ensemble quantum memory in a strongly nonlinear medium based on highly excited Rydberg atoms. We show that nonclassical correlations between the two photons persist after retrieval from the Rydberg ensemble. Our result is an important step towards deterministic photon–photon interactions, and may enable deterministic Bell-state measurements with multimode quantum memories.

The combination of electromagnetically induced transparency (EIT) with the nonlinear interaction between Rydberg atoms provides an effective interaction between photons. In this paper, we investigate the storage of optical pulses as collective Rydberg atomic excitations in a cold atomic ensemble. By measuring the dynamics of the stored Rydberg polaritons, we experimentally demonstrate that storing a probe pulse as Rydberg polaritons strongly enhances the Rydberg mediated interaction compared to the slow propagation case. We show that the process is characterized by two time scales. At short storage times, we observe a strong enhancement of the interaction due to the reduction of the Rydberg polariton group velocity down to zero. For longer storage times, we observe a further, weaker enhancement dominated by Rydberg induced dephasing of the multiparticle components of the state. In this regime, we observe a non-linear dependence of the Rydberg polariton coherence time with the input photon number. Our results have direct consequences in Rydberg quantum optics and may enable the test of new theories of strongly interacting Rydberg systems.PACS numbers: 32.80. Ee,42.50.Nn,42.50.Gy The possibility to control the interaction between photons provided by highly nonlinear media is a key ingredient to the goal of quantum information processing (QIP) using photons and a unique tool to study the dynamics of many-body correlated systems [1]. Many different systems showing high nonlinear optical response at the single-photon level have been studied during the past years ranging from resonators coupled to single atoms [2-6], atomic ensembles [7], to artificial two-level atoms [8,9].A promising strategy to perform different QIP tasks using photons as carriers is the combination of electromagnetically induced transparency (EIT) [10][11][12][13] and Rydberg atoms [14] (see for example ). Using EIT one maps the state of the photons into atomic coherence in the form of Rydberg dark-state polaritons (DSPs) by means of an auxiliary coupling field. The strong Rydberg dipole-dipole (DD) interaction between neighboring excitations shifts the multiply-excited states from being resonantly coupled when these excitations are closer than a certain length called the blockade radius, r b [25]. This way, only a single excitation can be created inside of a blockaded volume of the atomic cloud (so-called superatom). This phenomenon, known as Rydberg blockade, has been used in combination with EIT to generate quantum states of light [27][28][29], single-photon switches and transistors [30,31,33,34] as well as a π phase shift controlled with single-photon level pulse [36]. These experiments typically require very high atomic densities and high-lying Rydberg states. By switching off and back on the coupling field, photons can be stored as Rydberg excitations and retrieved at later time [26,29]. In this case the DD interaction dephases the collective emission of the multiparticle components of the stored photonic states [37,38]. This feature was ...

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We study the photon statistics of weak coherent pulses propagating through a cold atomic ensemble in the regime of Rydberg electromagnetically induced transparency. We show experimentally that the value of the second-order autocorrelation function of the transmitted light strongly depends on the position within the pulse and heavily varies during the transients of the pulse. In particular, we show that the falling edge of the transmitted pulse displays much lower values than the rest of the pulse. We derive a theoretical model that quantitatively predicts our results and explains the physical behavior involved. Finally, we use this effect to generate single photons localized within a pulse. We show that by selecting only the last part of the transmitted pulse, the single photons show an antibunching parameter as low as 0.12 and a generation efficiency per trial larger than that possible with probabilistic generation schemes based on atomic ensembles.