Complete methods set for scalable ion trap quantum information processing

Large-scale quantum information processors must be able to transport and maintain quantum information, and repeatedly perform logical operations. Here we demonstrate a combination of all the fundamental elements required to perform scalable quantum computing using qubits stored in the internal states of trapped atomic ions. We quantify the repeatability of a multi-qubit operation, observing no loss of performance despite qubit transport over macroscopic distances. Key to these results is the use of different pairs of beryllium ion hyperfine states for robust qubit storage, readout and gates, and simultaneous trapping of magnesium re-cooling ions along with the qubit ions.Comment: 9 pages, 4 figures. Accepted to Science, and thus subject to a press embarg

Hodge numbers for the cohomology of Calabi-Yau type local systems

We use Higgs cohomology to determine the Hodge numbers of the first intersection cohomology group of a local system V arising from the third direct image of a family of Calabi-Yau 3-folds over a smooth, quasi-projective curve. We give applications to Rhode's families of Calabi-Yau 3-folds without MUM.Comment: Some signs corrected. This article draws heavily from arXiv:0911.027

Detuning-dependent Properties and Dispersion-induced Instabilities of Temporal Dissipative Kerr Solitons in Optical Microresonators

Temporal-dissipative Kerr solitons are self-localized light pulses sustained in driven nonlinear optical resonators. Their realization in microresonators has enabled compact sources of coherent optical frequency combs as well as the study of dissipative solitons. A key parameter of their dynamics is the effective-detuning of the pump laser to the thermally- and Kerr-shifted cavity resonance. Together with the free spectral range and dispersion, it governs the soliton-pulse duration, as predicted by an approximate analytical solution of the Lugiato-Lefever equation. Yet, a precise experimental verification of this relation was lacking so far. Here, by measuring and controlling the effective-detuning, we establish a new way of stabilizing solitons in microresonators and demonstrate that the measured relation linking soliton width and detuning deviates by less than 1 % from the approximate expression, validating its excellent predictive power. Furthermore, a detuning-dependent enhancement of specific comb lines is revealed, due to linear couplings between mode-families. They cause deviations from the predicted comb power evolution, and induce a detuning-dependent soliton recoil that modifies the pulse repetition-rate, explaining its unexpected dependence on laser-detuning. Finally, we observe that detuning-dependent mode-crossings can destabilize the soliton, leading to an unpredicted soliton breathing regime (oscillations of the pulse) that occurs in a normally-stable regime. Our results test the approximate analytical solutions with an unprecedented degree of accuracy and provide new insights into dissipative-soliton dynamics.Comment: Updated funding acknowledgement

Normal modes of trapped ions in the presence of anharmonic trap potentials

We theoretically and experimentally examine the effects of anharmonic terms in the trapping potential for linear chains of trapped ions. We concentrate on two different effects that become significant at different levels of anharmonicity. The first is a modification of the oscillation frequencies and amplitudes of the ions' normal modes of vibration for multi-ion crystals, resulting from each ion experiencing a different curvature in the potential. In the second effect, which occurs with increased anharmonicity or higher excitation amplitude, amplitude-dependent shifts of the normal-mode frequencies become important. We evaluate normal-mode frequency and amplitude shifts, and comment on the implications for quantum information processing and quantum state engineering. Since the ratio of the anharmonic to harmonic terms typically increases as the ion--electrode distance decreases, anharmonic effects will become more significant as ion trap sizes are reduced. To avoid unwanted problems, anharmonicities should therefore be taken into account at the design stage of trap development.Comment: 26 pages, 7 figure