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].

The transmission spectrum for one atom strongly coupled to the field of a high finesse optical resonator is observed to exhibit a clearly resolved vacuum-Rabi splitting characteristic of the normal modes in the eigenvalue spectrum of the atom-cavity system. A new Raman scheme for cooling atomic motion along the cavity axis enables a complete spectrum to be recorded for an individual atom trapped within the cavity mode, in contrast to all previous measurements in cavity QED that have required averaging over many atoms.A cornerstone of optical physics is the interaction of a single two-level atom with the electromagnetic field of a high quality resonator. Of particular importance is the regime of strong coupling, for which the frequency scale g associated with reversible evolution for the atom-cavity system exceeds the rates (γ, κ) for irreversible decay of atom and cavity field, respectively [1]. In the domain of strong coupling, a photon emitted by the atom into the cavity mode is likely to be repeatedly absorbed and reemitted at the single-quantum Rabi frequency 2g before being irreversibly lost into the environment. This oscillatory exchange of excitation between atom and cavity field results from a normal mode splitting in the eigenvalue spectrum of the atom-cavity system [2] which is manifest in emission [3] and absorption [4] spectra, and has been dubbed the vacuum-Rabi splitting [3].Strong coupling in cavity QED as evidenced by the vacuum-Rabi splitting provides enabling capabilities for quantum information science, including for the implementation of scalable quantum computation [5,6], for the realization of distributed quantum networks [7,8], and more generally, for the study of open quantum systems [9]. Against this backdrop, experiments in cavity QED have made great strides over the past two decades to achieve strong coupling [10]. The vacuum-Rabi splitting for single intracavity atoms has been observed with atomic beams in both the optical [11,12,13] and microwave regimes [14]. The combination of laser cooled atoms and large coherent coupling has enabled single atomic trajectories to be monitored in real time with high signal-to-noise ratio, so that the vacuum-Rabi spectrum could be obtained from atomic transit signals produced by single atoms [15]. A significant advance has been the trapping of individual atoms in an optical cavity in a regime of strong coupling [16,17], with the vacuum-Rabi splitting first evidenced for single trapped atoms in Ref.[16] and the entire transmission spectra recorded in Ref. [18].Without exception these prior single atom experiments related to the vacuum-Rabi splitting in cavity QED [11,12,13,14,15,16,17,18] have required averaging over trials with many atoms to obtain quantitative spec- tral information, even if individual trials involved only single atoms (e.g., 10 5 atoms were required to obtain a spectrum in Ref. [14] and > 10 3 atoms were needed in Ref. [18]). By contrast, the implementation of complex algorithms in quantum information science requires the capabili...

We investigate the orthogonality of orbital angular momentum (OAM) with other multiplexing domains and present a free-space data link that uniquely combines OAM-, polarization-, and wavelength-division multiplexing. Specifically, we demonstrate the multiplexing/demultiplexing of 1008 data channels carried on 12 OAM beams, 2 polarizations, and 42 wavelengths. Each channel is encoded with 100 Gbit/s quadrature phase-shift keying data, providing an aggregate capacity of 100.8 Tbit/s (12×2×42×100 Gbit/s).

In our Letter [1], we employ a model of a two mode cavity coupled to an atom with multiple internal states. In this Supplement we make explicit the coupling used in the model Hamiltonian to determine the eigenvalues displayed in Figure 1(b) of Ref. [1]. This Hamiltonian was also incorporated into the master equation for the damped, driven system used to compute the theoretical results in Fig. 2(b) of Ref. [1]. We furthermore present an extension to this model which includes the effect of cavity birefringence and FORT induced ac-Stark shifts in the atomic states. The modified cavity transmission and intensity correlation function are presented for comparison.We approximate the atom-cavity coupling to be a dipole interaction. We define the atomic dipole transition operators for the 6S 1/2 , F = 4 → 6P 3/2 , F = 5 transition in atomic Caesium aswhere q = {−1, 0, 1} and µ q is the dipole operator for {σ − , π, σ + }-polarization, respectively, normalized such that for the cycling transition F = 4, m F = 4|µ 1 |F = 5 , m F = 5 = 1. The matrix element of the dipole operator F = 4, m F |µ q |F = 5 , m F is equivalent to the Clebsch-Gordan coefficient for adding spin 1 to spin 4 to reach total spin 5, namely j 1 = 4, j 2 = 1;The Hamiltonian of a single atom coupled to a cavity with two degenerate orthogonal linear modes is) is the dipole operator for linear polarization along the y-axis. We are using coordinates where the cavity supportsŷ andẑ polarizations andx is along the cavity axis. The annihilation operator for theẑ (ŷ) polarized cavity mode is a (b).Assuming ω A = ω C1 ≡ ω 0 , we find that the lowest eigenvalues of H 4→5 have a relatively simple structure. In the manifold of zero excitations all nine eigenvalues are zero. In manifolds with n excitations, the eigenvalues are of the form E n,k = n ω 0 + g 0 ε (n) k , where ε