The motion of individual cesium atoms trapped inside an optical resonator is revealed with the atom-cavity microscope (ACM). A single atom moving within the resonator generates large variations in the transmission of a weak probe laser, which are recorded in real time. An inversion algorithm then allows individual atom trajectories to be reconstructed from the record of cavity transmission and reveals single atoms bound in orbit by the mechanical forces associated with single photons. In these initial experiments, the ACM yields 2-micrometer spatial resolution in a 10-microsecond time interval. Over the duration of the observation, the sensitivity is near the standard quantum limit for sensing the motion of a cesium atom.

The combination of cold atoms and large coherent coupling enables investigations in a new regime in cavity QED with single-atom trajectories monitored in real time with high signal-to-noise ratio. The underlying "vacuum-Rabi" splitting is clearly reflected in the frequency dependence of atomic transit signals recorded atom by atom, with evidence for mechanical light forces for intracavity photon number ,1. The nonlinear optical response of one atom in a cavity is observed to be in accord with the one-atom quantum theory but at variance with semiclassical predictions. [S0031-9007(98)06037-2] PACS numbers: 42.50. Ct, 42.50.Vk An important trend in modern physics has been the increasing ability to isolate and manipulate the dynamical processes of individual quantum systems, with interactions studied quantum by quantum. In optical physics, examples include cavity QED with single atoms and photons [1] and trapped ions cooled to the motional zero point [2], while in condensed matter physics, an example is the Coulomb blockade with discrete electron energies [3]. An essential ingredient in these endeavors is that the components of a complex quantum system should interact in a controlled fashion with minimal decoherence. More quantitatively, if the off-diagonal elements of the system's interaction Hamiltonian are characterized by ͗H int ͘ ϳhg, where g is the rate of coherent, reversible evolution, then a necessary requirement is to achieve strong coupling for which g . b ϵ max͓G, T 21 ͔ with T as the interaction time and G as the set of decoherence rates for the system.Although there are many facets to investigations of such open quantum systems, our primary motivation has been to exploit strong coupling in cavity QED to enable research in quantum measurement and more generally, in the emerging field of quantum information dynamics [4]. Several experiments in cavity QED have investigated the nonperturbative interaction of an atom with the electromagnetic field at the level of a single photon; for this system 2g 0 is the single-photon Rabi frequency and G ϵ ͕g Ќ , k͖, with g Ќ as the atomic dipole decay rate and k as the rate of decay of the cavity field [5][6][7][8]. However, without exception these experiments have employed atomic beams in settings for which the information per atomic transit (of duration T ) is I ϵ b ϳ 1, so that measurements over an ensemble of atoms are required. For example, the passage of a Rydberg atom through a microwave cavity and its subsequent measurement provides a single bit of information [5,7].By contrast, an exciting recent development in cavity QED has been the ability to observe single-atom trajectories in real time with I ¿ 1 [9]. In this method the transmitted power of a probe beam is monitored as cold atoms fall between the mirrors of a high-finesse optical resonator, with the probe transmission significantly altered by the position-dependent interaction between atom and cavity field [10,11].Similarly enabled by the use of cold atoms, the research reported in this Letter exploits...

Two recent experiments have reported the trapping of individual atoms inside optical resonators by the mechanical forces associated with single photons ͓Hood et al., Science 287, 1447 ͑2000͒; Pinkse et al., Nature ͑London͒ 404, 365 ͑2000͔͒. Here we analyze the trapping dynamics in these settings, focusing on two points of interest. First, we investigate the extent to which light-induced forces in these experiments are distinct from their free-space counterparts, and whether or not there are qualitatively different effects of optical forces at the single-photon level within the setting of cavity QED. Second, we explore the quantitative features of the resulting atomic motion, and how these dynamics are mapped onto experimentally observable variations of the intracavity field. Toward these ends, we present results from extensive numerical simulations of the relevant forces and their fluctuations, as well as a detailed derivation of our numerical simulation method, based on the full quantum-mechanical master equation. Not surprisingly, qualitatively distinct atomic dynamics arise as the coupling and dissipative rates are varied. For the experiment of Hood et al., we show that atomic motion is largely conservative and is predominantly in radial orbits transverse to the cavity axis. A comparison with the free-space theory demonstrates that the fluctuations of the dipole force are suppressed by an order of magnitude. This effect is based upon the Jaynes-Cummings eigenstates of the atom-cavity system and represents distinct physics for optical forces at the single-photon level within the context of cavity QED. By contrast, even in a regime of strong coupling in the experiment of Pinkse et al., there are only small quantitative distinctions between the potentials and heating rates in the free-space theory and the quantum theory, so it is not clear that a description of this experiment as a novel single-quantum trapping effect is necessary. The atomic motion is strongly diffusive, leading to an average localization time comparable to the time for an atom to transit freely through the cavity, and to a reduction in the ability to infer aspects of the atomic motion from the intracavity photon number.

Measuring an entangled state of two particles is crucial to many quantum communication protocols. Yet Bellstate distinguishability using a finite apparatus obeying linear evolution and local measurement is theoretically limited. We extend known bounds for Bell-state distinguishability in one and two variables to the general case of entanglement in n two-state variables. We show that at most 2 n+1 − 1 classes out of 4 n hyper-Bell states can be distinguished with one copy of the input state. With two copies, complete distinguishability is possible. We present optimal schemes in each case.

A roadmap is provided for building a quantum engineering education program to satisfy U.S. national and international workforce needs.Background: The rapidly growing quantum information science and engineering (QISE) industry will require both quantumaware and quantum-proficient engineers at the bachelor's level.Research Question: What is the best way to provide a flexible framework that can be tailored for the full academic ecosystem?Methodology: A workshop of 480 QISE researchers from across academia, government, industry, and national laboratories was convened to draw on best practices; representative authors developed this roadmap.Findings: 1) For quantum-aware engineers, design of a first quantum engineering course, accessible to all STEM students, is described; 2) for the education and training of quantumproficient engineers, both a quantum engineering minor accessible to all STEM majors, and a quantum track directly integrated into individual engineering majors are detailed, requiring only Manuscript