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 propose in this White Paper a concept for a space experiment using cold atoms to search for ultra-light dark matter, and to detect gravitational waves in the frequency range between the most sensitive ranges of LISA and the terrestrial LIGO/Virgo/KAGRA/INDIGO experiments. This interdisciplinary experiment, called Atomic Experiment for Dark Matter and Gravity Exploration (AEDGE), will also complement other planned searches for dark matter, and exploit synergies with other gravitational wave detectors. We give examples of the extended range of sensitivity to ultra-light dark matter offered by AEDGE, and how its gravitational-wave measurements could explore the assembly of super-massive black holes, first-order phase transitions in the early universe and cosmic strings. AEDGE will be based upon technologies now being developed for terrestrial experiments using cold atoms, and will benefit from the space experience obtained with, e.g., LISA and cold atom experiments in microgravity.KCL-PH-TH/2019-65, CERN-TH-2019-126

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.

We have developed an atom interferometer providing a full inertial base. This device uses two counter-propagating cold-atom clouds that are launched in strongly curved parabolic trajectories. Three single Raman beam pairs, pulsed in time, are successively applied in three orthogonal directions leading to the measurement of the three axis of rotation and acceleration. In this purpose, we introduce a new atom gyroscope using a butterfly geometry. We discuss the present sensitivity and the possible improvements.