Photons can carry angular momentum, not only due to their spin, but also due to their spatial structure. This extra twist has been used, for example, to drive circular motion of microscopic particles in optical tweezers as well as to create vortices in quantum gases. Here we excite an atomic transition with a vortex laser beam and demonstrate the transfer of optical orbital angular momentum to the valence electron of a single trapped ion. We observe strongly modified selection rules showing that an atom can absorb two quanta of angular momentum from a single photon: one from the spin and another from the spatial structure of the beam. Furthermore, we show that parasitic ac-Stark shifts from off-resonant transitions are suppressed in the dark centre of vortex beams. These results show how light's spatial structure can determine the characteristics of light–matter interaction and pave the way for its application and observation in other systems.

We realize fast transport of ions in a segmented micro-structured Paul trap. The ion is shuttled over a distance of more than 10 4 times its groundstate wavefunction size during only 5 motional cycles of the trap (280 µm in 3.6 µs). Starting from a ground-state-cooled ion, we find an optimized transport such that the energy increase is as low as 0.10±0.01 motional quanta. In addition, we demonstrate that quantum information stored in a spin-motion entangled state is preserved throughout the transport. Shuttling operations are concatenated, as a proof-of-principle for the shuttling-based architecture to scalable ion trap quantum computing. . Scalable information processing in a multiplexed ion trap can be accomplished by having fixed processing sites where logic operations are performed, and ion qubits will be moved in and out of these regions by shuttling operations. The duration of such shuttling has to be much faster than the relevant decoherence times [4]. Furthermore, it is desirable to reduce the total time consumption of all relevant operations, where shuttling will contribute a considerable amount [5], and aim for the performance of the naturally fast solid state architectures [6]. So far, ion shuttling in a multiplexed trap has been demonstrated together with additional sympathetic cooling [7], and in the adiabatic regime, where the transient displacement of the ion is smaller than the size of the its wavepacket [8,9]. Transport of neutral atoms have also been performed using magnetic [10] or optical [11] techniques.Because quantum gate operations require ions close to the motional ground state and fast transport inherently creates motional excitation, the challenge is to develop transport protocols that guarantee sufficiency small energy transfer. In this work we demonstrate shuttling operations that are highly non-adiabatic while the final state of the ion is close to the motional groundstate. We also show that quantum information stored in both the motional and the spin degree of freedom is preserved through the shuttling.During a shuttling operation, the ion motion in the harmonic trapping potential is excited when the acceleration is sufficiently strong. This motional excitation is a harmonic oscillation, characterized by a well defined phase, thus allowing it to be canceled out by proper management of the forces involved during or after the transport. We experimentally demonstrate two methods of canceling the acquired motional excitation. One method uses two shuttles, where the transport to the destination generates the same net momentum transfer as the transport back, but is applied 180 • out of phase with respect to the secular oscillation of the ion (Fig. 1b). We refer to this as the pairwise energy-neutral transport. For the second scheme, the self-neutral transport we apply a sharp counter-"kick" to the ion at the end of a single transport operation, stopping its motion (Fig. 1c). This case of single-sided transport allows even faster shuttling and can be sequentially repeated since it is ener...

Traversal of a symmetry-breaking phase transition at finite rates can lead to causally separated regions with incompatible symmetries and the formation of defects at their boundaries, which has a crucial role in quantum and statistical mechanics, cosmology and condensed matter physics. This mechanism is conjectured to follow universal scaling laws prescribed by the Kibble-Zurek mechanism. Here we determine the scaling law for defect formation in a crystal of 16 laser-cooled trapped ions, which are conducive to the precise control of structural phases and the detection of defects. The experiment reveals an exponential scaling of defect formation g b , where g is the rate of traversal of the critical point and b ¼ 2.68 ± 0.06. This supports the prediction of b ¼ 8/3E2.67 for finite inhomogeneous systems. Our result demonstrates that the scaling laws also apply in the mesoscopic regime and emphasizes the potential for further tests of non-equilibrium thermodynamics with ion crystals.

A quantitative assessment of the progress of small prototype quantum processors towards fault-tolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a necessary and fair criterion for quantum error correction (QEC), which must be achieved in the development of these quantum processors before their sizes are sufficiently big to consider the well-known QEC threshold. We apply this criterion to benchmark the ongoing effort in implementing QEC with topological color codes using trapped-ion quantum processors and, more importantly, to guide the future hardware developments that shall be required in order to demonstrate beneficial QEC with small topological quantum codes. In doing so, we present a thorough description of a realistic trapped-ion toolbox for QEC, and a physically-motivated error model that goes beyond standard simplifications in the QEC literature. We focus on laser-based quantum gates realised in two-species trapped-ion crystals in high-optical aperture segmented traps. Our large-scale numerical analysis shows that, with the foreseen technological improvements hereby described, this platform is a very promising candidate for fault-tolerant quantum computation.

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Trapped, laser-cooled atoms and ions are quantum systems which can be experimentally controlled with an as yet unmatched degree of precision. Due to the control of the motion and the internal degrees of freedom, these quantum systems can be adequately described by a well known Hamiltonian. In this colloquium, we present powerful numerical tools for the optimization of the external control of the motional and internal states of trapped neutral atoms, explicitly applied to the case of trapped laser-cooled ions in a segmented ion-trap. We then delve into solving inverse problems, when optimizing trapping potentials for ions. Our presentation is complemented by a quantum mechanical treatment of the wavepacket dynamics of a trapped ion. Efficient numerical solvers for both time-independent and time-dependent problems are provided. Shaping the motional wavefunctions and optimizing a quantum gate is realized by the application of quantum optimal control techniques. The numerical methods presented can also be used to gain an intuitive understanding of quantum experiments with trapped ions by performing virtual simulated experiments on a personal computer. Code and executables are supplied as supplementary online material 1 .

Miniaturized ion trap arrays with many trap segments present a promising architecture for scalable quantum information processing. The miniaturization of segmented linear Paul traps allows partitioning the microtrap in different storage and processing zones. The individual position control of many ions -each of them carrying qubit information in its long-lived electronic levels -by the external trap control voltages is important for the implementation of next generation large-scale quantum algorithms.We present a novel scalable microchip multi-segmented ion trap with two different adjacent zones, one for the storage and another dedicated for the processing of quantum information using single ions and linear ion crystals: A pair of radio-frequency driven electrodes and 62 independently controlled DC electrodes allows shuttling of single ions or linear ion crystals with numerically designed axial potentials at axial and radial trap frequencies of a few MHz. We characterize and optimize the microtrap using sideband spectroscopy on the narrow S 1/2 ↔ D 5/2 qubit transition of the 40 Ca + ion, demonstrate coherent single qubit Rabi rotations and optical cooling methods. We determine the heating rate using sideband cooling measurements to the vibrational ground state which is necessary for subsequent two-qubit quantum logic operations. The applicability for scalable quantum information processing is proven.

We demonstrate a coherence time of 2.1(1)~s for electron spin superposition states of a single trapped $^{40}$Ca$^+$ ion. The coherence time, measured with a spin-echo experiment, corresponds to residual rms magnetic field fluctuations $\leq$~2.7$\times$10$^{-12}$~T. The suppression of decoherence induced by fluctuating magnetic fields is achieved by combining a two-layer $\mu$-metal shield, which reduces external magnetic noise by 20 to 30~dB for frequencies of 50~Hz to 100~kHz, with Sm$_2$Co$_{17}$ permanent magnets for generating a quantizing magnetic field of 0.37~mT. Our results extend the coherence time of the simple-to-operate spin qubit to ultralong coherence times which so far have been observed only for magnetic insensitive transitions in atomic qubits with hyperfine structure