8,994 research outputs found
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
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
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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
Heat transfer and Fourier's law in off-equilibrium systems
We study the most suitable procedure to measure the effective temperature in
off-equilibrium systems. We analyze the stationary current established between
an off-equilibrium system and a thermometer and the necessary conditions for
that current to vanish. We find that the thermometer must have a short
characteristic time-scale compared to the typical decorrelation time of the
glassy system to correctly measure the effective temperature. This general
conclusion is confirmed analyzing an ensemble of harmonic oscillators with
Monte Carlo dynamics as an illustrative example of a solvable model of a glass.
We also find that the current defined allows to extend Fourier's law to the
off-equilibrium regime by consistently defining effective transport
coefficients. Our results for the oscillator model explain why thermal
conductivities between thermalized and frozen degrees of freedom in structural
glasses are extremely small.Comment: 7 pages, REVTeX, 4 eps figure
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