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

Quantum communication relies on the availability of light pulses with strong quantum correlations among photons. An example of such an optical source is a single-photon pulse with a vanishing probability for detecting two or more photons. Using pulsed laser excitation of a single quantum dot, a single-photon turnstile device that generates a train of single-photon pulses was demonstrated. For a spectrally isolated quantum dot, nearly 100% of the excitation pulses lead to emission of a single photon, yielding an ideal single-photon source.

Cavity quantum electrodynamics (QED) studies the interaction between a quantum emitter and a single radiation-field mode. When an atom is strongly coupled to a cavity mode, it is possible to realize important quantum information processing tasks, such as controlled coherent coupling and entanglement of distinguishable quantum systems. Realizing these tasks in the solid state is clearly desirable, and coupling semiconductor self-assembled quantum dots to monolithic optical cavities is a promising route to this end. However, validating the efficacy of quantum dots in quantum information applications requires confirmation of the quantum nature of the quantum-dot-cavity system in the strong-coupling regime. Here we find such confirmation by observing quantum correlations in photoluminescence from a photonic crystal nanocavity interacting with one, and only one, quantum dot located precisely at the cavity electric field maximum. When off-resonance, photon emission from the cavity mode and quantum-dot excitons is anticorrelated at the level of single quanta, proving that the mode is driven solely by the quantum dot despite an energy mismatch between cavity and excitons. When tuned to resonance, the exciton and cavity enter the strong-coupling regime of cavity QED and the quantum-dot exciton lifetime reduces by a factor of 145. The generated photon stream becomes antibunched, proving that the strongly coupled exciton/photon system is in the quantum regime. Our observations unequivocally show that quantum information tasks are achievable in solid-state cavity QED.

The electronic spin degrees of freedom in semiconductors typically have decoherence times that are several orders of magnitude longer than other relevant timescales. A solid-state quantum computer based on localized electron spins as qubits is therefore of potential interest. Here, a scheme that realizes controlled interactions between two distant quantum dot spins is proposed. The effective long-range interaction is mediated by the vacuum field of a high finesse microcavity. By using conduction-band-hole Raman transitions induced by classical laser fields and the cavity-mode, parallel controlled-not operations and arbitrary single qubit rotations can be realized. Optical techniques can also be used to measure the spin-state of each quantum dot. 03.67.Lx, 42.50.Dv, 03.65.Bz Within the last few years, quantum computation (QC) has developed into a truly interdisciplinary field involving the contributions of physicists, engineers, and computer scientists [1]. The seminal discoveries of Shor and others, both in developing quantum algorithms for important problems like prime factorization [2], and in developing protocols for quantum error correction (QEC) [3] and fault-tolerant quantum computation [4], have indicated the desirability and the ultimate feasibility of the experimental realization of QC in various quantum systems.The elementary unit in most QC schemes is a twostate system referred to as a quantum bit (qubit). Since QEC can only work if the decoherence rate is small, it is crucial to identify schemes where the qubits are well isolated from their environment. Ingenious schemes based on Raman-coupled low-energy states of trapped ions [5] and nuclear spins in chemical solutions [6] satisfy this criterion, in addition to providing methods of fast quantum manipulation of qubits that do not introduce significant decoherence. Even though these schemes are likely to provide the first examples of quantum information processing at 5-10 qubit level, they do not appear to be scalable to larger systems containing more than 100 qubits.Here, we propose a new scheme for quantum information processing based on quantum dot (QD) electron spins coupled through a microcavity mode. The motivation for this scheme is threefold: (1) a QC scheme based on semiconductor quantum dot arrays should be scalable to ≥ 100 coupled qubits; (2) recent experiments demonstrated very long spin decoherence times for conduction band electrons in III-V and II-VI semiconductors [7], making electron spin a likely candidate for a qubit; and (3) cavity-QED techniques can provide longdistance, fast interactions between qubits [8]. The QC scheme detailed below relies on the use of a single cavity mode and laser fields to mediate coherent interactions between distant QD spins. As we will show shortly, the proposed scheme does not require that QDs be identical and can be used to carry out parallel quantum logic operations [9].We note that a QC scheme based on electron spins in QDs have been previously proposed [10]: this scheme is based on local exchan...

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*Semiconductor quantum dots have emerged as promising candidates for the implementation of quantum information processing, because they allow for a quantum interface between stationary spin qubits and propagating single photons [1][2][3] . In the meantime, transition-metal dichalcogenide monolayers have moved to the forefront of solid-state research due to their unique band structure featuring a large bandgap with degenerate valleys and non-zero Berry curvature 4 . Here, we report the observation of zero-dimensional anharmonic quantum emitters, which we refer to as quantum dots, in monolayer tungsten diselenide, with an energy that is 20-100 meV lower than that of two-dimensional excitons. Photon antibunching in second-order photon correlations unequivocally demonstrates the zero-dimensional anharmonic nature of these quantum emitters. The strong anisotropic magnetic response of the spatially localized emission peaks strongly indicates that radiative recombination stems from localized excitons that inherit their electronic properties from the host transition-metal dichalcogenide. The large ∼1 meV zero-field splitting shows that the quantum dots have singlet ground states and an anisotropic confinement that is most probably induced by impurities or defects. The possibility of achieving electrical control in van der Waals heterostructures 5 and to exploit the spin-valley degree of freedom 6 renders transitionmetal-dichalcogenide quantum dots interesting for quantum information processing.Advances in semiconductor-based quantum information processing have been made on two disjoint fronts. While optically active self-assembled quantum dots with deep electron and hole confinement allow for the realization of highly efficient single-photon sources 7 , all-optical manipulation of confined spins 8,9 and a spinphoton quantum interface 3,10 , the random nature of their growth seems to be the biggest hindrance to their use in scalable quantum information processing. In contrast, electrically defined single 11 or double quantum dots 12 hosting one or two excess electrons have been shown to exhibit long spin coherence times together with a clear path towards integrated scalable devices. However, weaker confinement has precluded the possibility to reliably transfer quantum information from spins to photons in these systems. Quantum dots in monolayer transition-metal dichalcogenides (TMDs) have the potential to combine the desirable features of both optically active and electrically defined quantum dots. Although we report tungsten diselenide (WSe 2 ) quantum dots that appear due to uncontrolled impurity-or defect-induced traps, the two-dimensional nature of these materials makes it easier to electrically control the local potentials on a scale of a few tens of nanometres. More importantly, strong electron-hole binding in TMDs suggests that it would be possible to obtain a quantized optical excitation spectrum due to trapping of excitons or trions in large electric field gradients induced by external gates 13 .The samples we s...

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We analyze a cross-phase modulation (XPM) scheme that exhibits a giant, resonantly enhanced nonlinearity, along with vanishing linear susceptibilities. The proposed atomic system uses an electromagnetically induced transparency and is limited only by two-photon absorption. We predict dramatic improvement by several orders of magnitude for conditional phase shifts in XPM, and the system has possible applications in quantum nondemolition measurements and for quantum logic gates.