Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications. CONTENTS

We identify form-stable coupled excitations of light and matter ("dark-state polaritons") associated with the propagation of quantum fields in electromagnetically induced transparency. The properties of dark-state polaritons such as the group velocity are determined by the mixing angle between light and matter components and can be controlled by an external coherent field as the pulse propagates. In particular, light pulses can be decelerated and "trapped" in which case their shape and quantum state are mapped onto metastable collective states of matter. Possible applications of this reversible coherent-control technique are discussed.

We describe a technique for manipulating quantum information stored in collective states of mesoscopic ensembles. Quantum processing is accomplished by optical excitation into states with strong dipole-dipole interactions. The resulting "dipole blockade" can be used to inhibit transitions into all but singly excited collective states. This can be employed for a controlled generation of collective atomic spin states as well as nonclassical photonic states and for scalable quantum logic gates. An example involving a cold Rydberg gas is analyzed.

In atomic physics, the coherent coupling of a broad and a narrow resonance leads to quantum interference and provides the general recipe for electromagnetically induced transparency (EIT). A sharp resonance of nearly perfect transmission can arise within a broad absorption profile. These features show remarkable potential for slow light, novel sensors and low-loss metamaterials. In nanophotonics, plasmonic structures enable large field strengths within small mode volumes. Therefore, combining EIT with nanoplasmonics would pave the way towards ultracompact sensors with extremely high sensitivity. Here, we experimentally demonstrate a nanoplasmonic analogue of EIT using a stacked optical metamaterial. A dipole antenna with a large radiatively broadened linewidth is coupled to an underlying quadrupole antenna, of which the narrow linewidth is solely limited by the fundamental non-radiative Drude damping. In accordance with EIT theory, we achieve a very narrow transparency window with high modulation depth owing to nearly complete suppression of radiative losses.

An ideal and reversible transfer technique for the quantum state between light and metastable collective states of matter is presented and analyzed in detail. The method is based on the control of photon propagation in coherently driven 3-level atomic media, in which the group velocity is adiabatically reduced to zero. Form-stable coupled excitations of light and matter ("dark-state polaritons") associated with the propagation of quantum fields in Electromagnetically Induced Transparency are identified, their basic properties discussed and their application for quantum memories for light analyzed.

Techniques to facilitate controlled interactions between single photons and atoms are now being actively explored. These techniques are important for the practical realization of quantum networks, in which multiple memory nodes that utilize atoms for generation, storage and processing of quantum states are connected by single-photon transmission in optical fibres. One promising avenue for the realization of quantum networks involves the manipulation of quantum pulses of light in optically dense atomic ensembles using electromagnetically induced transparency (EIT, refs 8, 9). EIT is a coherent control technique that is widely used for controlling the propagation of classical, multi-photon light pulses in applications such as efficient nonlinear optics. Here we demonstrate the use of EIT for the controllable generation, transmission and storage of single photons with tunable frequency, timing and bandwidth. We study the interaction of single photons produced in a 'source' ensemble of 87Rb atoms at room temperature with another 'target' ensemble. This allows us to simultaneously probe the spectral and quantum statistical properties of narrow-bandwidth single-photon pulses, revealing that their quantum nature is preserved under EIT propagation and storage. We measure the time delay associated with the reduced group velocity of the single-photon pulses and report observations of their storage and retrieval.

We show that the adiabatic motion of ultra-cold, multi-level atoms in spatially varying laser fields can give rise to effective non-Abelian gauge fields if degenerate adiabatic eigenstates of the atomlaser interaction exist. A pair of such degenerate dark states emerges e.g. if laser fields couple three internal states of an atom to a fourth common one under pairwise two-photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component.

We develop the theory of light propagation under the conditions of electromagnetically induced transparency (EIT) in systems involving strongly interacting Rydberg states. Taking into account the quantum nature and the spatial propagation of light, we analyze interactions involving fewphoton pulses. We demonstrate that this system can be used for the generation of nonclassical states of light including trains of single photons with an avoided volume between them, for implementing photon-photon quantum gates, as well as for studying many-body phenomena with strongly correlated photons.PACS numbers: 42.50. Nn, 32.80.Ee, 42.50.Gy, 34.20.Cf The phenomenon of electromagnetically induced transparency (EIT) [1] in systems involving Rydberg states [2] has recently attracted significant experimental [3][4][5][6][7][8][9][10] and theoretical [11][12][13][14][15][16][17][18][19][20][21] attention. While EIT allows for strong atom-light interactions without absorption, Rydberg states provide strong long-range atom-atom interactions. Therefore, the resulting combination of EIT with Rydberg atoms is ideal for implementing mesoscopic quantum gates [2,16] and for inducing strong photonphoton interactions, with applications to photonic quantum information processing [2,[11][12][13][14][19][20][21][22] and to the realization of many-body phenomena with strongly interacting photons [23]. At the same time, the many-body theoretical description of EIT with arbitrarily strongly interacting Rydberg atoms, taking into account the full quantum dynamics and the spatial propagation of light, has not been reported previously.In this Letter, we develop such a theory by analyzing the problem for at most two incident photons, which, in turn, provides intuition for understanding the full multiphoton problem. We show that Rydberg atom interactions give rise to photon-photon interactions, which, below a critical inter-photonic distance, turn the EIT medium into an effective two-level medium. This can be used to implement photon-atom and photon-photon phase gates and to enable deterministic single-photon sources.The basic physics is illustrated by considering a simple case [ Fig. 1(b)], in which a single-photon wavepacket E propagates in an EIT medium [level scheme in Fig. 1(a)] with a central control atom at z = 0 prepared in a Rydberg state |r . Atoms in another Rydberg state |r , coupled by the EIT control laser [ Fig. 1(a)], experience a van der Waals potential V (z) = C 6 /z 6 due to the interaction with the control atom, which is decoupled from the applied fields. Alternatively, one could apply an electric field to induce dipole moments in states |r and |r ,Sufficiently far away from z = 0, the incident photon propagates in a standard EIT medium featuring a twophoton-resonant control field with Rabi frequency Ω. In the vicinity of the control atom, however, the state |r is shifted so strongly out of resonance that the photon sees only a two-level (|g , |e ) medium with transition linewidth 2γ. The critical z, at which the interaction is ...