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.

Quantum information science attempts to exploit capabilities from the quantum realm to accomplish tasks that are otherwise impossible in the classical domain. Although sufficient conditions have been formulated for the physical resources required to achieve quantum computation and communication, there is a growing understanding of the power of quantum measurement combined with the conditional evolution of quantum states for accomplishing diverse tasks in quantum information science. For example, a protocol has recently been developed for the realization of scalable long-distance quantum communication and the distribution of entanglement over quantum networks. Here we report the first enabling step in the realization of this protocol, namely the observation of quantum correlations for photon pairs generated in the collective emission from an atomic ensemble. The nonclassical character of the fields is demonstrated by the violation of an inequality involving their normalized correlation functions. Compared to previous investigations of non-classical correlations for photon pairs produced in atomic cascades and in parametric down-conversion, our experiment is distinct in that the correlated photons are separated by a programmable time interval (of about 400 nanoseconds in our initial experiments).

EXPERIMENTAL DETAILSOur experimental setup is depicted by the simple drawing in Fig. 1A of the manuscript, with many of the technical aspects described in more detail in Refs.[S1, S2]. After releasing a cloud of atoms from a magnetooptical trap (MOT) above the cavity, transverse cooling beams illuminate the cavity region, at which point an atom can be loaded into the intracavity far-off resonance trap (FORT), which is matched to a standingwave, TEM 00 mode along the cavity axis. The trap depth is U 0 /k B = 2.3 mK (47 MHz), and because its wavelength is λ F = 935.6 nm, the potential for the atomic center-of-mass motion is only weakly dependent on the atom's internal state [S2]. The cavity length is actively stabilized with an auxiliary laser at wavelength λ C = 835.8 nm that does not interfere with the trapping or the cQED interactions. Relevant cavity parameters are length l 0 = 42.2 µm, waist w 0 = 23.6 µm, and finesse F = 4.2 × 10 5 at 852 nm. For our system, the Rabi frequency 2g 0 for a single quantum of excitation is given by g 0 /2π = 16 MHz, where g 0 is based upon the reduced dipole moment for the 6S 1/2 , F = 4 ↔ 6P 3/2 , F = 3 transition in atomic Cs (Fig 1B). The amplitude decay rates (κ, γ) due to cavity losses and atomic spontaneous emission are κ/2π = 4.2 MHz, and γ/2π = 2.6 MHz. Since g 0 (κ, γ), strong coupling is achieved, resulting in critical photon and atom numbers n 0 ≡ γ 2 /(2gWith an atom loaded into the intracavity FORT, our protocol for the generation of single-photon pulses consists in illuminating the atom with a sequence of laser pulses according to the timing diagram shown in Fig. 1(c) of the manuscript. Within each trial, the first pulse Ω 3 (t) contains light tuned 10 MHz blue of F = 3 → F = 3 , which initiates the adiabatic transfer F = 3 → 4 between the ground hyperfine levels, with the emission of a photon into the cavity mode. This transformation is principally accomplished via "dark" eigenstates of the atom-cavity system, with no contribution from the excited level F = 3 , and hence with a concomitant reduction of fluorescent loss [S3, S4, S5]. The second pulse Ω 4 (t) is tuned 17 MHz blue of F = 4 → F = 4 and recycles the atom back to the F = 3 ground state through spontaneous decay F = 4 → F = 3. Each Ω 3,4 field consists of two orthogonal pairs of counter-propagating beams in a σ + −σ − configuration. The detuning between the 3 → 4 transition at ω 43 and the cavity resonance ω C is ∆ CA ≡ ω C − ω 43 = 2π × 9 MHz [S6].We now provide some additional details on the optical path from the cavity to the detectors. After emerging from the vacuum chamber window, the path includes a polarizing beam splitter (PBS), several dichroic mirrors and two interference filters. The light is next coupled into a single-mode fiber, and then split using a 50/50 fiber coupler. The two output fibers of the coupler are connected to fiber-coupled avalanche photodiodes (APD), labelled D A and D B . LOSSES AND EFFICIENCIESPhotons generated in the cavity are subject to various types of loss along thei...

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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 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.

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 ...