Attractive photons in a quantum nonlinear medium

The fundamental properties of light derive from its constituent particles—massless quanta (photons) that do not interact with one another\(^1\). However, it has long been known that the realization of coherent interactions between individual photons, akin to those associated with conventional massive particles, could enable a wide variety of novel scientific and engineering applications\(^{2,3}\). Here 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 achieve this through dispersive coupling of light to strongly interacting atoms in highly excited Rydberg states. We measure the dynamical evolution of the two-photon wavefunction using time-resolved quantum state tomography, and demonstrate a conditional phase shift8 exceeding one radian, resulting in polarization-entangled photon pairs. Particular applications of this technique include all-optical switching, deterministic photonic quantum logic and the generation of strongly correlated states of light\(^9\).Physic