Single atoms or atom-like emitters are the purest source of single photons, they are intrinsically incapable of multi-photon emission. To demonstrate this degree of photon number-state purity we have realized a single-photon source using a single ion trapped at the common focus of high numerical aperture lenses. Our trapped-ion source produces single-photon pulses with = ´g 0 1.9 0.2 10 2 3 ( ) ( ) without any background subtraction. After subtracting detector dark counts the residual g 0 2 ( ) is less than 3×10 −4 (95% confidence interval). The multi-photon component of the source light field is low enough that we measure violation of a quantum non-Gaussian state witness, by this characterization the source output is indistinguishable from ideal attenuated single photons. In combination with efforts to enhance collection efficiency from single emitters, our results suggest that single trapped ions are not only ideal stationary qubits for quantum information processing, but promising sources of light for scalable optical quantum networks.

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Far-field optical imaging techniques allow the determination of the position of point-like emitters and scatterers [ 1 – 3 ]. Although the optical wavelength sets a fundamental limit to the image resolution of unknown objects, the position of an individual emitter can in principle be estimated from the image with arbitrary precision. This is used for example in the determination of stars position [ 4 ] or in optical super-resolution microscopy [ 5 ]. Furthermore, precise position determination is an experimental prerequisite for the manipulation and measurement of individual quantum systems, such as atoms, ions, and solid-state-based quantum emitters [ 6 – 8 ]. Here we demonstrate that spin-orbit coupling of light in the emission of elliptically polarized emitters can lead to systematic, wavelength-scale errors in the estimation of the emitters position. Imaging a single trapped atom as well as a single sub-wavelength-diameter gold nanoparticle, we demonstrate a shift between the emitters measured and actual positions which is comparable to the optical wavelength. For certain settings, the expected shift can become arbitrarily large. Beyond optical imaging techniques, our findings could be relevant for the localization of objects using any type of wave that carries orbital angular momentum relative to the emitters position with a component orthogonal to the direction of observation.

The generation and manipulation of entanglement between isolated particles has precipitated rapid progress in quantum information processing. Entanglement is also known to play an essential role in the optical properties of atomic ensembles, but fundamental effects in the controlled emission and absorption from small, well-defined numbers of entangled emitters in free space have remained unobserved. Here we present the control of the emission rate of a single photon from a pair of distant, entangled atoms into a free-space optical mode. Changing the length of the optical path connecting the atoms modulates the single-photon emission rate in the selected mode with a visibility V=0.27±0.03 determined by the degree of entanglement shared between the atoms, corresponding directly to the concurrence C_{ρ}=0.31±0.10 of the prepared state. This scheme, together with population measurements, provides a fully optical determination of the amount of entanglement. Furthermore, large sensitivity of the interference phase evolution points to applications of the presented scheme in high-precision gradient sensing.

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