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We measure the hyperfine structure of the $5{p}^{6}5d\phantom{\rule{4pt}{0ex}}{}^{2}{D}_{3/2}$, $5{p}^{6}5d\phantom{\rule{4pt}{0ex}}{}^{2}{D}_{5/2}$, $5{p}^{6}4f\phantom{\rule{4pt}{0ex}}{}^{2}{F}_{5/2}^{o}$, and $5{p}^{6}4f\phantom{\rule{4pt}{0ex}}{}^{2}{F}_{7/2}^{o}$ levels in doubly ionized lanthanum (La iii; ${\mathrm{La}}^{2+}$) in a hollow-cathode lamp using optogalvanic spectroscopy. Analysis of the observed spectra allows us to determine the hyperfine $A$ coefficients for these levels to be ${A}_{D3/2}=412(4)$ MHz, ${A}_{D5/2}=20(5)$ MHz, ${A}_{F5/2}=319(2)$ MHz, and ${A}_{F7/2}=155(4)$ MHz, and provide estimates for the hyperfine $B$ coefficients as ${B}_{D3/2}=105(29)$ MHz, ${B}_{D5/2}=157(40)$ MHz, ${B}_{F5/2}=\ensuremath{-}2(53)$ MHz, and ${B}_{F7/2}=171(51)$ MHz.

We use a pulsed nitrogen laser to produce atomic ions by laser ablation, measuring the relative ion yield for several elements, including some that have only recently been proposed for use in cold trapped ion experiments. For barium, we monitor the ion yield as a function of the number of applied ablation pulses for different substrates. We also investigate the ion production as a function of the pulse energy, and the efficiency of loading an ion trap as a function of radiofrequency voltage., 6 pages, 6 figures

Quantum networks based on atomic qubits and scattered photons provide a promising way to build a large-scale quantum information processor. We review quantum protocols for generating entanglement and operating gates between two distant atomic qubits, which can be used for constructing scalable atom--photon quantum networks. We emphasize the crucial role of collecting light from atomic qubits for large-scale networking and describe two techniques to enhance light collection using reflective optics or optical cavities. A brief survey of some applications for scalable and efficient atom--photon networks is also provided.

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 collect the fluorescence from two trapped atomic ions, and measure quantum interference between photons emitted from the ions. The interference of two photons is a crucial component of schemes to entangle atomic qubits based on a photonic coupling. The ability to preserve the generated entanglement and to repeat the experiment with the same ions is necessary to implement entangling quantum gates between atomic qubits, and allows the implementation of protocols to efficiently scale to larger numbers of atomic qubits., Comment: 4 pages, 4 figures

We present two complementary designs of pneumatically actuated and kinematically positioned optics mounts: one designed for vertical mounting and translation, the other designed for horizontal mounting and translation. The design and measured stability make these mounts well-suited to experiments with laser-cooled atoms.

We theoretically evaluate establishing remote entanglement between distinguishable matter qubits through interference and detection of two emitted photons. The fidelity of the entanglement operation is analyzed as a function of the temporal and frequency mode-matching between the photons emitted from each quantum memory. With a general analysis, we define limits on the absolute magnitudes of temporal and frequency mode-mismatches in order to maintain entanglement fidelities greater than 99% with two-photon detection efficiencies greater than 90%. We apply our analysis to several selected systems of quantum memories. Results indicate that high fidelities may be achieved in each system using current experimental techniques, while maintaining acceptable rates of entanglement. Thus, it might be possible to use two-photon-mediated entanglement operations between distinguishable quantum memories to establish a network for quantum communication and distributed quantum computation., 13 pages, 10 figures

Random number generation is vital for a wide range of applications, including numerical simulation, gambling, and cryptography. However, verifying the randomness of a bit stream generated by a device is exceedingly difficult. Even if a sequence of numbers passes all of the standard statistical tests, it is often impossible to certify the authenticity of the device and rule out the possibility that an adversary has loaded a predetermined sequence into an internal memory. Recently, it has been shown that the non-local correlations between entangled quantum systems can be used to verify the generation of true random numbers [1, 2]. This insight enables the construction of a private random number generator whose output can be verified as random through the violation of a Bell inequality, without requiring any assumptions about the internal mechanisms of the device.

We perform randomized benchmarking on neutral atomic quantum bits (qubits) confined in an optical lattice. Single qubit gates are implemented using microwaves, resulting in a measured error per randomized computational gate of 1.4(1) x 10^-4 that is dominated by the system T2 relaxation time. The results demonstrate the robustness of the system, and its viability for more advanced quantum information protocols., 11 pages, 4 figures

We demonstrate near-complete cancellation of the differential light shift of a two-photon magnetic-field-insensitive microwave hyperfine (clock) transition in $^{87}$Rb atoms trapped in an optical lattice. Up to $95(2)%$ of the differential light shift is canceled while maintaining magnetic-field insensitivity. This technique should have applications in quantum information and frequency metrology., Comment: 5 pages, 4 figures

We demonstrate the use of an optical frequency comb to coherently control and entangle atomic qubits. A train of off-resonant ultrafast laser pulses is used to efficiently and coherently transfer population between electronic and vibrational states of trapped atomic ions and implement an entangling quantum logic gate with high fidelity. This technique can be extended to the high field regime where operations can be performed faster than the trap frequency. This general approach can be applied to more complex quantum systems, such as large collections of interacting atoms or molecules., Comment: 4 pages, 5 figures

We present a precise measurement of the lifetime of the $6p\text{ }{^{2}P}_{1/2}^{o}$ excited state of a single trapped ytterbium ion $({\text{Yb}}^{+})$. A time-correlated single-photon counting technique is used, where ultrafast pulses excite the ion and the emitted photons are coupled into a single-mode optical fiber. By performing the measurement on a single atom with fast excitation and excellent spatial filtering, we are able to eliminate common systematics. The lifetime of the $6p\text{ }{^{2}P}_{1/2}^{o}$ state is measured to be $8.12\ifmmode\pm\else\textpm\fi{}0.02\text{ }\text{ns}$, in good agreement with previous experimental measurements and some theoretical values.

Trapped atomic ions have proven to be one of the most promising candidates for the realization of quantum computation due to their long trapping times, excellent coherence properties, and exquisite control of the internal atomic states. Integrating ions (quantum memory) with photons (distance link) offers a unique path to large-scale quantum computation and long-distance quantum communication. In this article, we present a detailed review of the experimental implementation of a heralded photon-mediated quantum gate between remote ions, and the employment of this gate to perform a teleportation protocol between two ions separated by a distance of about one meter., 59 pages, 19 figures

Randomness is a fundamental feature in nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on nonlocality based and device independent quantum information processing, we show that the nonlocal correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design of a new type of cryptographically secure random number generator which does not require any assumption on the internal working of the devices. This strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately 1 meter. The observed Bell inequality violation, featuring near-perfect detection efficiency, guarantees that 42 new random numbers are generated with 99% confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory., Comment: 10 pages, 3 figures, 16 page appendix. Version as close as possible to the published version following the terms of the journal

Quantum teleportation is the faithful transfer of quantum states between systems, relying on the prior establishment of entanglement and using only classical communication during the transmission. We report teleportation of quantum information between atomic quantum memories separated by about 1 meter. A quantum bit stored in a single trapped ytterbium ion (Yb+) is teleported to a second Yb+ atom with an average fidelity of 90% over a replete set of states. The teleportation protocol is based on the heralded entanglement of the atoms through interference and detection of photons emitted from each atom and guided through optical fibers. This scheme may be used for scalable quantum computation and quantum communication., Comment: 5 pages, 4 figures

We demonstrate a probabilistic entangling quantum gate between two distant trapped ytterbium ions. The gate is implemented between the hyperfine "clock" state atomic qubits and mediated by the interference of two emitted photons carrying frequency encoded qubits. Heralded by the coincidence detection of these two photons, the gate has an average output state fidelity of 89+/-2%. This entangling gate together with single qubit operations is sufficient to generate large entangled cluster states for scalable quantum computing.

We teleport quantum information between two distant ytterbium ions trapped in different vacuum chambers separated by one meter. Full state tomography shows that the heralded probabilistic process employed has a fidelity of 90%.

We implement a probabilistic entangling gate between two remote trapped ytterbium ions and measure an average gate fidelity of 89%. The entangled state of the ions violates a Bell inequality.

We implement a probabilistic entangling gate between two distant trapped ytterbium ions and measure an average gate fidelity of 90%.

We observe violation of a Bell inequality between the quantum states of two remote Yb ions separated by a distance of about one meter with the detection loophole closed. The heralded entanglement of two ions is established via interference and joint detection of two emitted photons, whose polarization is entangled with each ion. The entanglement of remote qubits is also characterized by full quantum state tomography., 4 pages, 4 figures

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 171Yb+, 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., Comment: 10 pages, 9 figures, 1 table

Atomic cadmium ions are loaded into radiofrequency ion traps by photoionization of atoms in a cadmium vapor with ultrafast laser pulses. The photoionization is driven through an intermediate atomic resonance with a frequency-quadrupled mode-locked Ti:sapphire laser that produces pulses of either 100-fs or 1-ps duration at a central wavelength of 229 nm. The large bandwidth of the pulses photoionizes all velocity classes of the Cd vapor, resulting in a high loading efficiency compared to previous ion trap loading techniques. Measured loading rates are compared with a simple theoretical model, and we conclude that this technique can potentially ionize every atom traversing the laser beam within the trapping volume. This may allow the operation of ion traps with lower levels of background pressures and less trap electrode surface contamination. The technique and laser system reported here should be applicable to loading most laser-cooled ion species.

We measure and characterize anomalous motional heating of an atomic ion confined in the lowest quantum levels of a novel rf ion trap that features moveable electrodes. The scaling of heating with electrode proximity is measured, and when the electrodes are cooled from 300 to 150 K, the heating rate is suppressed by an order of magnitude. This provides direct evidence that anomalous motional heating of trapped ions stems from microscopic noisy potentials on the electrodes that are thermally driven. These observations are relevant to decoherence in quantum information processing schemes based on trapped ions and perhaps other charge-based quantum systems.

We demonstrate a two-dimensional 11-zone ion trap array, where individual laser-cooled atomic ions are stored, separated, shuttled, and swapped. The trap geometry consists of two linear rf ion trap sections that are joined at a 90 degree angle to form a T-shaped structure. We shuttle a single ion around the corners of the T-junction and swap the positions of two crystallized ions using voltage sequences designed to accommodate the nontrivial electrical potential near the junction. Full two-dimensional control of multiple ions demonstrated in this system may be crucial for the realization of scalable ion trap quantum computation and the implementation of quantum networks., 3 pages, 5 figures

Linking distant quantum memories with light has been a goal of the quantum information community for many years. A team at the University of Geneva has now demonstrated that memories made from rare-earth-ion-doped crystals can be connected using a single photon.