We demonstrate a cooperative optical non-linearity caused by dipolar interactions between Rydberg atoms in an ultra-cold atomic ensemble. By coupling a probe transition to the Rydberg state we map the strong dipoledipole interactions between Rydberg pairs onto the optical field. We characterize the non-linearity as a function of electric field and density, and demonstrate the enhancement of the optical non-linearity due to cooperativity. PACS numbers: 42.50.Nn, 32.80.Rm, 34.20.Cf, 42.50.Gy Photons are robust carriers of quantum information and consequently there is considerable interest in the development of photonic quantum technologies. As optical non-linearities are extremely small at the single photon level [1] attention has focussed on linear optical quantum computing [2,3]. In parallel, work has been carried out on materials with a large Kerr effect [4,5,6,7,8] potentially enabling non-linear photonic devices. Theoretical work has explored some of the difficulties in realizing a high fidelity quantum gate based on the Kerr effect [9]. An alternative mechanism for generating an optical non-linearity, for example a cooperative non-linearity due to dipolar interactions, could open new avenues for photonic quantum gates [10]. In a dipolar system the electric field is modified due to the local field of the neighbouring dipoles [11]. Such local field effects can give rise to cooperative behaviour such as superradiance [12,13] and optical bistability [14,15].In this paper we demonstrate a cooperative optical nonlinearity due to dipole-dipole interactions between Rydberg atoms. These strong interatomic interactions are sufficient to prevent excitation of neighbouring atoms to the Rydberg state [16] . This gives rise to a blockade mechanism which has been observed for a pair of trapped atoms [17,18] and an atomic ensemble [19]. In our work the effect of strong interactions between Rydberg pairs is mapped onto an optical transition using electromagnetically induced transparency (EIT) [20,21]. The resonant dark state responsible for EIT is modified by the dipole-dipole interactions, causing suppression of the transparency on resonance. The resulting optical non-linearity depends on interactions between pairs of atoms and is a cooperative effect where the optical response of a single atom is modified by the presence of its neighbours.To show how dipole-dipole interactions give rise to a cooperative non-linear effect, we consider the atom pair model [22] shown in fig. 1(a) for three level atoms with ground |g , excited |e , and Rydberg |r states. These states are coupled by a probe laser with Rabi frequency Ω p and a strong coupling laser with Rabi frequency Ω c . In the non-interacting case with probe and coupling lasers tuned to resonance the dark state is [23]: where tan θ = Ω p /Ω c and φ r is the relative phase between probe and coupling lasers. This state is not coupled to the probe field, leading to 100 % transparency independent of the mixing angle, θ. Dipole-dipole interactions modify this picture. The effe...

We use a microwave field to control the quantum state of optical photons stored in a cold atomic cloud. The photons are stored in highly excited collective states (Rydberg polaritons) enabling both fast qubit rotations and control of photon-photon interactions. Through the collective read-out of these pseudospin rotations it is shown that the microwave field modifies the long-range interactions between polaritons. This technique provides a powerful interface between the microwave and optical domains, with applications in quantum simulations of spin liquids, quantum metrology and quantum networks.

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This topical review addresses how Rydberg atoms can serve as building blocks for emerging quantum technologies. Whereas the fabrication of large numbers of artificial quantum systems with the uniformity required for the most attractive applications is difficult if not impossible, atoms provide stable quantum systems which, for the same species and isotope, are all identical. Whilst atomic ground-states provide scalable quantum objects, their applications are limited by the range over which their properties can be varied. In contrast, Rydberg atoms offer strong and controllable atomic interactions that can be tuned by selecting states with different principal quantum number or orbital angular momentum. In addition Rydberg atoms are comparatively long-lived, and the large number of available energy levels and their separations allow coupling to electromagnetic fields spanning over 6 orders of magnitude in frequency. These features make Rydberg atoms highly desirable for developing new quantum technologies. After giving a brief introduction to how the properties of Rydberg atoms can be tuned, we give several examples of current areas where the unique advantages of Rydberg atom systems are being exploited to enable new applications in quantum computing, electromagnetic field sensing, and quantum optics. arXiv:1907.09231v2 [physics.atom-ph]

The implementation of electromagnetically induced transparency (EIT) in a cold Rydberg gas provides an attractive route towards strong photon-photon interactions and fully deterministic all-optical quantum information processing. In this brief review we discuss the underlying principles of how large single photon non-linearities are achieved in this system and describe experimental progress to date. CONTENTS