Quantum information science involves the storage, manipulation and communication of information encoded in quantum systems, where the phenomena of superposition and entanglement can provide enhancements over what is possible classically. Large-scale quantum information processors require stable and addressable quantum memories, usually in the form of fixed quantum bits (qubits), and a means of transferring and entangling the quantum information between memories that may be separated by macroscopic or even geographic distances. Atomic systems are excellent quantum memories, because appropriate internal electronic states can coherently store qubits over very long timescales. Photons, on the other hand, are the natural platform for the distribution of quantum information between remote qubits, given their ability to traverse large distances with little perturbation. Recently, there has been considerable progress in coupling small samples of atomic gases through photonic channels, including the entanglement between light and atoms and the observation of entanglement signatures between remotely located atomic ensembles. In contrast to atomic ensembles, single-atom quantum memories allow the implementation of conditional quantum gates through photonic channels, a key requirement for quantum computing. Along these lines, individual atoms have been coupled to photons in cavities, and trapped atoms have been linked to emitted photons in free space. Here we demonstrate the entanglement of two fixed single-atom quantum memories separated by one metre. Two remotely located trapped atomic ions each emit a single photon, and the interference and detection of these photons signals the entanglement of the atomic qubits. We characterize the entangled pair by directly measuring qubit correlations with near-perfect detection efficiency. Although this entanglement method is probabilistic, it is still in principle useful for subsequent quantum operations and scalable quantum information applications.

We demonstrate the use of trapped ytterbium ions as quantum bits for quantum information processing. We implement fast, efficient state preparation and state detection of the first-order magnetic field-insensitive hyperfine levels of 171 Yb + , with a measured coherence time of 2.5 seconds. The high efficiency and high fidelity of these operations is accomplished through the stabilization and frequency modulation of relevant laser sources.

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Trapped atomic ions are among the most attractive implementations of quantum bits for applications in quantuminformation processing, owing to their long trapping lifetimes and long coherence times. Although nearby trapped ions can be entangled through their Coulomb-coupled motion 1-6 , it seems more natural to entangle remotely located ions through a coupling mediated by photons, eliminating the need to control the ion motion. A promising way to entangle ions via a photonic channel is to interfere two photons emitted from the ions and then detect appropriate photon coincidence events 7-9 . Here, we report the pivotal element of this scheme in the observation of quantum interference between pairs of single photons emitted from two atomic ions residing in independent traps.Remote entanglement of two ions or atoms can be achieved by subjecting two photons emitted by the particles to a Bellstate measurement and is heralded by an appropriate coincidence detection of the photons 7 . The essence of this Bell-state measurement is the quantum interference of two photons, which has been observed previously with photons generated in a variety of physical processes and systems, including nonlinear optical down-conversion 10,11 , quantum dots 12 , atoms in cavity quantum electrodynamics 13 , atomic ensembles 14-16 and two nearby trapped neutral atoms 17 . We report the first observation of interference between two single photons emitted from two remote trapped atomic ions. The two Yb ions are stored in independent traps in two vacuum chambers separated by about one metre. The interference of two single photons emitted by remote ions is the only element of remote-entanglement schemes that has not previously been demonstrated. Hence, this demonstration is an essential step towards future remote-ion-entanglement experiments, which may ultimately lead to large-scale quantum networks [18][19][20][21][22][23] . In the experiment, single 174 Yb + ions are trapped in two congeneric Paul traps located in separate vacuum chambers as described in detail in the Methods section. Laser cooling localizes the ions to within the resolution of the diffraction-limited imaging optics but well outside the Lamb-Dicke limit. The ions are excited with ultrafast laser pulses generated by a picosecond mode-locked Ti:sapphire laser with a centre frequency of 739 nm. Each pulse is then frequency doubled to 369.5 nm through a phase-matched lithium triborate nonlinear crystal. An electro-optic pulse picker is used to reduce the pulse repetition rate from 81 MHz to 8.1 MHz with an extinction ratio of better than 10 4 :1. The second harmonic is filtered from the fundamental with a prism, split between the two traps using a beam splitter and aligned to arrive at the two ions within 100 ps of each other. Each pulse has a neartransform-limited pulse duration of 2 ps and excites the ions on a timescale much faster than the excited-state lifetime of 8 ns. The 174 Yb + ion is collected using a triplet lens with a numerical aperture of 0.23 and a working distanc...

Rubidium Rydberg atoms are laser excited and subsequently trapped in a one-dimensional optical lattice (wavelength 1064 nm). Efficient trapping is achieved by a lattice inversion immediately after laser excitation using an electro-optic technique. The trapping efficiency is probed via analysis of the trap-induced shift of the two-photon microwave transition 50S→51S. The inversion technique allows us to reach a trapping efficiency of 90%. The dependence of the efficiency on the timing of the lattice inversion and on the trap laser power is studied. The dwell time of 50D(5/2) Rydberg atoms in the lattice is analyzed using lattice-induced photoionization.