The realization of strong nonlinear interactions between individual light quanta (photons) is a long-standing goal in optical science and engineering 1, 2 that is both of fundamental and technological significance. In conventional optical materials, the nonlinearity at light powers corresponding to single photons is negligibly weak. Here we demonstrate a medium that is nonlinear at the level of individual quanta, exhibiting strong absorption of photon pairs while remaining transparent to single photons. The quantum nonlinearity is obtained by coherently coupling slowly propagating photons [3][4][5] to strongly interacting atomic Rydberg states [6][7][8][9][10][11][12] in a cold, dense atomic gas 13 . Our approach opens the door for quantum-byquantum control of light fields, including single-photon switching 14 , all-optical deterministic 1 quantum logic 15 , and the realization of strongly correlated many-body states of light 16 .Recently, remarkable advances have been made towards optical systems that are nonlinear at the level of individual photons. The most promising approaches have used high-finesse optical cavities to enhance the atom-photon interaction probability 2,[17][18][19][20][21] . In contrast, our present method is cavity-free and is based on mapping photons onto atomic states with strong interactions in an extended atomic ensemble 13,14,22,23 . The central idea is illustrated in Fig. 1, where a quantum probe field incident onto a cold atomic gas is coupled to high-lying atomic states (Rydberg levels 24 ) by means of a second, stronger laser field (control field). For a single incident probe photon, the control field induces a transparency window in the otherwise opaque medium via Electromagnetically Induced Transparency (EIT), and the probe photon travels at much reduced speed in the form of a coupled excitation of light and matter (Rydberg polariton). However, in stark contrast to conventional EIT 5 , if two probe photons are incident onto the Rydberg EIT medium, the strong interaction between two Rydberg atoms tunes the EIT transition out of resonance, thereby destroying the EIT and leading to absorption 14,22,23, 25, 26 . The experimental demonstration of an extraordinary optical material exhibiting strong two-photon attenuation in combination with single-photon transmission is the central result of this work.The quantum nonlinearity can be viewed as a photon-photon blockade mechanism that prevents the transmission of any multi-photon state. It arises from the Rydberg excitation blockade 27 , which precludes the simultaneous excitation of two Rydberg atoms that are separated by less than a blockade radius r b (see Figure 1). During the optical excitation, an incident single photon is 2 converted, under the EIT conditions, into a Rydberg polariton inside the medium. However, due to the Rydberg blockade, a second polariton cannot travel within a blockade radius from the first one, and EIT is destroyed. Accordingly if the second photon approaches the single Rydberg polariton, it will be signific...

* These authors contributed equally to this workThe fundamental properties of light derive from its constituent particles (photons) that are massless and do not interact with one another 1 . At the same time, it has been long known that the realization of coherent interactions between individual photons, akin to those associated with conventional massive particles, could enable a wide variety of unique scientific and engineering applications 2,3 . Here, by coupling light to strongly interacting atomic Rydberg states in a dispersive regime, we demonstrate a quantum nonlinear medium inside which individual photons travel as massive particles with strong mutual attraction, such that the propagation of photon pairs is dominated by a two-photon bound state 4-7 . We measure the dynamical evolution of the two-photon wavefunction using time-resolved quantum state tomography, and demonstrate a conditional phase shift 8 exceeding one radian, resulting in polarization-entangled photon pairs. Unique applications include all-optical switching, deterministic photonic quantum logic, and the generation of strongly correlated states of light 9 .Interactions between individual photons are being explored in cavity quantum electrodynamics, where a single, confined electromagnetic mode is coupled to an atomic system 10-12 . Our approach is to couple a light field propagating in a dispersive medium to highly excited atomic states with strong mutual interactions (Rydberg states) 13,14 . Similar to previous studies of quantum nonlinearities via Rydberg states that were based on dissipation 15-19 rather than dispersion 20 , we make use of electromagnetically induced transparency (EIT) to slow down the propagation of light 21 in a cold atomic gas. By operating in a dispersive regime away from the intermediate atomic resonance (Fig. 1b), where atomic absorption is low and only weakly nonlinear 22 , we realize a situation where Rydberg-atom-mediated coherent interactions between individual photons dominate the propagation dynamics of weak light pulses. Previous theoretical studies have proposed various scenarios for inducing strong interactions between individual photons 2,3,23 and for creating bound states of a few quanta 4,5,7,24 , a feature generic to strongly interacting quantum field theories. The first experimental realization of a photonic system with strong attractive interactions, including evidence for a predicted two-photon bound state, represents the main result of this work.Our experiment (outlined in Fig. 1a) makes use of an ultracold rubidium gas loaded into a dipole trap, as described previously 19 . The probe light of interest is σ + polarized, coupling the ground state |g to the Rydberg state |r via an intermediate state |e of linewidth Γ/(2π) = 6.1 MHz by means of a control field that is detuned by ∆ below the resonance frequency of the upper transition |e → |r (Fig. 1b). Under these conditions, for a very weak probe field with mean incident photon rate R i = 0.5 µs −1 , EIT is established when the probe detuning matches...

We demonstrate a fiber-optical switch that is activated at tiny energies corresponding to few hundred optical photons per pulse. This is achieved by simultaneously confining both photons and a small laser-cooled ensemble of atoms inside the microscopic hollow core of a single-mode photoniccrystal fiber and using quantum optical techniques for generating slow light propagation and large nonlinear interaction between light beams.

We describe the loading of laser-cooled rubidium atoms into a single-mode hollow-core photoniccrystal fiber. Inside the fiber, the atoms are confined by a far-detuned optical trap and probed by a weak resonant beam. We describe different loading methods and compare their trade-offs in terms of implementation complexity and atom-loading efficiency. The most efficient procedure results in loading of ∼30,000 rubidium atoms, which creates a medium with optical depth ∼180 inside the fiber. Compared to our earlier study [1] this represents a six-fold increase in maximum achieved optical depth in this system.