Cooperative Atom-Light Interaction in a Blockaded Rydberg Ensemble

Abstract

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...

Quantum nonlinear optics with single photons enabled by strongly interacting atoms

“…To maintain strong two-photon suppression in the presence of diffusion, the loss term must exceed the diffusion on the length scale of the blockade radius, requiring r b > l a . Large optical depth OD b = r b /l a of the blockaded region is therefore the key experimental feature that allows us to extend earlier studies 13 into the quantum nonlinear regime.…”

“…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.…”

“…The interactions between cold Rydberg atoms have been explored in ensembles [6][7][8][9][10] and have been used to realize quantum logic gates between two Rydberg atoms 11,12,24 . Giant optical nonlinearities using Rydberg EIT 14,22,23 have been observed in a classical, multi-photon regime 13 . Very recently, the Rydberg blockade in a dense, mesoscopic atomic ensemble has been used to implement a deterministic single-photon source 30 .…”

Attractive photons in a quantum nonlinear medium

“…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][16][17][18][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.…”

Interaction of independent single photons based on integrated nonlinear optics

“…It has recently been shown that even weak optical nonlinearities between single photons can be used to perform important quantum communication tasks more efficiently than methods based on linear optics 2 , which have fundamental limitations 3 . Nonlinear optical effects at single-photon levels in atomic media have been studied 4,5 and demonstrated [6][7][8][9] , but these are neither flexible nor compatible with quantum communication, as they impose restrictions on photons' wavelengths and bandwidths. Here we use a high-efficiency nonlinear waveguide (WG) 10,11 to observe the sum-frequency generation (SFG) between a single photon and a single-photon level coherent state from two independent sources.…”