In our recent paper [1], we reported observations of photon blockade by one atom strongly coupled to an optical cavity. In support of these measurements, here we provide an expanded discussion of the general phenomenology of photon blockade as well as of the theoretical model and results that were presented in Ref. [1]. We describe the general condition for photon blockade in terms of the transmission coefficients for photon number states. For the atom-cavity system of Ref.[1], we present the model Hamiltonian and examine the relationship of the eigenvalues to the predicted intensity correlation function. We explore the effect of different driving mechanisms on the photon statistics. We also present additional corrections to the model to describe cavity birefringence and ac-Stark shifts.

On the occasion of the hundredth anniversary of Albert Einstein's annus mirabilis, we reflect on the development and current state of research in cavity quantum electrodynamics in the optical domain. Cavity QED is a field which undeniably traces its origins to Einstein's seminal work on the statistical theory of light and the nature of its quantized interaction with matter. In this paper, we emphasize the development of techniques for the confinement of atoms strongly coupled to high-finesse resonators and the experiments which these techniques enable.(Some figures in this article are in colour only in the electronic version) From Einstein to cavity QEDIn the years prior to his seminal 1905 papers, Albert Einstein had given much thought to the statistical properties of electromagnetic fields [1], especially with regard to the theory of black-body radiation developed by Max Planck [2]. Einstein realized that the quantization of light-particularly the creation and annihilation of 'light quanta'-is something more fundamental than a tacit consequence of the assumption that the total energy of a black-body is discretely distributed between a set of microstates. Beginning in 1905 with On a heuristic point of view about the creation and conversion of light [3] and in four subsequent papers on quantization [4][5][6][7], he laid the foundations of the 'old quantum theory ' [8], summarized in what is commonly referred to as the 'light quantization hypothesis':. . . the energy of a light ray emitted from a point [is] not continuously distributed over an ever increasing space, but consists of a finite number of energy quanta which are localized at points in space, which move without dividing, and which can only be produced and absorbed as complete units [3].

Optical communication channels have redefined the purview and applications of classical computing; similarly, photonic transfer of quantum information promises to open new horizons for quantum computing. The implementation of light-matter interfaces that preserve quantum information is technologically challenging, but key building blocks for such devices have recently been demonstrated in several research groups. Here, we outline the theoretical framework for information transfer between nodes of a quantum network, review the current experimental state of the art, and discuss the prospects for hybrid systems currently in development.

We demonstrate the reversible mapping of a coherent state of light with a mean photon number n ' 1:1 to and from the hyperfine states of an atom trapped within the mode of a high-finesse optical cavity. The coherence of the basic processes is verified by mapping the atomic state back onto a field state in a way that depends on the phase of the original coherent state. Our experiment represents an important step toward the realization of cavity QED-based quantum networks, wherein coherent transfer of quantum states enables the distribution of quantum information across the network. DOI: 10.1103/PhysRevLett.98.193601 PACS numbers: 42.50.Pq, 03.67.ÿa, 32.80.Pj An important goal in quantum information science is the realization of quantum networks for the distribution and processing of quantum information [1], including for quantum computation, communication, and metrology [2 -5]. In the initial proposal for the implementation of quantum networks [6], atomic internal states with long coherence times serve as ''stationary'' qubits, stored and locally manipulated at the nodes of the network. Quantum channels between different nodes are provided by optical fibers, which transport photons (''flying'' qubits) over long distances [7]. A crucial requirement for such network protocols is the reversible mapping of quantum states between light and matter. Cavity quantum electrodynamics (QED) provides a promising avenue for achieving this capability by using strong coupling for the interaction of single atoms and photons [8].Within this setting, reversible emission and absorption of one photon can be achieved by way of a dark-state process involving an atom and the field of a high-finesse optical cavity. For classical fields, this adiabatic passage process was first considered 20 years ago [9,10], before being adapted to quantum fields [11] and specifically to the coherent transfer of quantum states between remote locations [6], with many extensions since then [12]. The basic scheme, illustrated in Fig.

Proposed quantum networks require both a quantum interface between light and matter and the coherent control of quantum states1,2. A quantum interface can be realized by entangling the state of a single photon with the state of an atomic or solid-state quantum memory, as demonstrated in recent experiments with trapped ions3,4, neutral atoms5,6, atomic ensembles7,8, and nitrogen-vacancy spins9. The entangling interaction couples an initial quantum memory state to two possible light–matter states, and the atomic level structure of the memory determines the available coupling paths. In previous work, these paths’ transition parameters determine the phase and amplitude of the final entangled state, unless the memory is initially prepared in a superposition state4, a step that requires coherent control. Here we report the fully tunable entanglement of a single 40Ca+ ion and the polarization state of a single photon within an optical resonator. Our method, based on a bichromatic, cavity-mediated Raman transition, allows us to select two coupling paths and adjust their relative phase and amplitude. The cavity setting enables intrinsically deterministic, high-fidelity generation of any two-qubit entangled state. This approach is applicable to a broad range of candidate systems and thus presents itself as a promising method for distributing information within quantum networks.

Quantum computing hardware technologies have advanced during the past two decades, with the goal of building systems that can solve problems that are intractable on classical computers. The ability to realize large-scale systems depends on major advances in materials science, materials engineering, and new fabrication techniques. We identify key materials challenges that currently limit progress in five quantum computing hardware platforms, propose how to tackle these problems, and discuss some new areas for exploration. Addressing these materials challenges will require scientists and engineers to work together to create new, interdisciplinary approaches beyond the current boundaries of the quantum computing field.

We realize a deterministic single-photon source from one and the same calcium ion interacting with a high-finesse optical cavity. Photons are created in the cavity with efficiency (88 ± 17)%, a tenfold improvement over previous cavity-ion sources. Results of the second-order correlation function are presented, demonstrating a high suppression of two-photon events limited only by background counts. The cavity photon pulse shape is obtained, with good agreement between experiment and simulation. Moreover, theoretical analysis of the temporal evolution of the atomic populations provides relevant information about the dynamics of the process and opens the way to future investigations of a coherent atom-photon interface.

Localization to the ground state of axial motion is demonstrated for a single, trapped atom strongly coupled to the field of a high finesse optical resonator. The axial atomic motion is cooled by way of coherent Raman transitions on the red vibrational sideband. An efficient state detection scheme enabled by strong coupling in cavity QED is used to record the Raman spectrum, from which the state of atomic motion is inferred. We find that the lowest vibrational level of the axial potential with zero-point energy @! a =2k B 13 K is occupied with probability P 0 ' 0:95. DOI: 10.1103/PhysRevLett.97.083602 PACS numbers: 42.50.Pq, 03.67.ÿa, 32.80.Pj Single atoms strongly coupled to the fields of high quality optical resonators are of fundamental importance in quantum optics and, more generally, can be used for many tasks in quantum information science, including the implementation of scalable quantum computation [1,2] and the realization of distributed quantum networks [3,4]. In recent years, significant experimental progress to develop tools suitable for these tasks has been made by employing optical forces to localize individual atoms within optical cavities in a regime of strong coupling [5][6][7][8][9][10][11], as well as by combining trapped ions with optical cavities [12]. Scientific advances thereby enabled include the observation of the vacuum-Rabi spectrum for an individual atom [9] and vacuum-stimulated cooling [10].Although great strides are being made with atoms localized and strongly coupled to the fields of optical cavities, it has not previously been possible to access the quantum regime for the atomic center-of-mass motion in cavity QED. Qualitatively new phenomena have been predicted in this regime for which a quantized treatment is required for both the internal (i.e., the atomic dipole and cavity field) and external (i.e., atomic motion) degrees of freedom, as was first recognized in the seminal work of Refs. [13][14][15] and in the years since [16 -22]. Examples include the transfer of quantized states of atomic motion to quantum states of light, and conversely [22], as well as for measurements that surpass the standard quantum limit for sensing atomic position [16].Our effort towards quantum control of atomic motion in cavity QED follows the remarkable set of achievements for trapped ions [23] and atoms in optical lattices [24], for which such control has led to the creation of manifestly quantum states of motion and to the manipulation of quantum information. A first step in many of these investigations has been the capability to cool to the ground state of motion for single trapped atoms or ions.In this Letter, we report localization to the ground state of motion for one atom trapped in an optical cavity in a regime of strong coupling [11]. Resolved sideband cooling to the ground state is accomplished with a coherent pair of intracavity Raman fields. To deduce the resulting state of atomic motion, we introduce a scheme for recording Raman spectra by way of the interaction of the atom with a ...