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

Representation of Markov chains by random maps: existence and regularity conditions

We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory also tells us how convexity properties of the supports of the measures translate into regularity properties of the maps via Legendre transforms. Thus, from this scheme, we cannot only deduce the representation by measurable random maps, but we can also obtain conditions for the representation by continuous random maps. Finally, we present conditions for the representation of Markov chain by random diffeomorphisms.Comment: 22 pages, several changes from the previous version including extended discussion of many detail

Temporal solitons in optical microresonators

Dissipative solitons can emerge in a wide variety of dissipative nonlinear systems throughout the fields of optics, medicine or biology. Dissipative solitons can also exist in Kerr-nonlinear optical resonators and rely on the double balance between parametric gain and resonator loss on the one hand and nonlinearity and diffraction or dispersion on the other hand. Mathematically these solitons are solution to the Lugiato-Lefever equation and exist on top of a continuous wave (cw) background. Here we report the observation of temporal dissipative solitons in a high-Q optical microresonator. The solitons are spontaneously generated when the pump laser is tuned through the effective zero detuning point of a high-Q resonance, leading to an effective red-detuned pumping. Red-detuned pumping marks a fundamentally new operating regime in nonlinear microresonators. While usually unstablethis regime acquires unique stability in the presence of solitons without any active feedback on the system. The number of solitons in the resonator can be controlled via the pump laser detuning and transitions to and between soliton states are associated with discontinuous steps in the resonator transmission. Beyond enabling to study soliton physics such as soliton crystals our observations open the route towards compact, high repetition-rate femto-second sources, where the operating wavelength is not bound to the availability of broadband laser gain media. The single soliton states correspond in the frequency domain to low-noise optical frequency combs with smooth spectral envelopes, critical to applications in broadband spectroscopy, telecommunications, astronomy and low phase-noise microwave generation.Comment: Includes Supplementary Informatio

Mode spectrum and temporal soliton formation in optical microresonators

The formation of temporal dissipative solitons in optical microresonators enables compact, high repetition rate sources of ultra-short pulses as well as low noise, broadband optical frequency combs with smooth spectral envelopes. Here we study the influence of the resonator mode spectrum on temporal soliton formation. Using frequency comb assisted diode laser spectroscopy, the measured mode structure of crystalline MgF2 resonators are correlated with temporal soliton formation. While an overal general anomalous dispersion is required, it is found that higher order dispersion can be tolerated as long as it does not dominate the resonator's mode structure. Mode coupling induced avoided crossings in the resonator mode spectrum are found to prevent soliton formation, when affecting resonator modes close to the pump laser. The experimental observations are in excellent agreement with numerical simulations based on the nonlinear coupled mode equations, which reveal the rich interplay of mode crossings and soliton formation

Spectral plots and the representation and interpretation of biological data

It is basic question in biology and other fields to identify the char- acteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein-protein interaction or neu- ral networks or foodwebs, and that on the other hand distinguish them from other structures. We introduce and apply a general method, based on the spectrum of the normalized graph Laplacian, that yields repre- sentations, the spectral plots, that allow us to find and visualize such properties systematically. We present such visualizations for a wide range of biological networks and compare them with those for networks derived from theoretical schemes. The differences that we find are quite striking and suggest that the search for universal properties of biological networks should be complemented by an understanding of more specific features of biological organization principles at different scales.Comment: 15 pages, 7 figure

Radion Induced Spontaneous Baryogenesis

We describe a possible scenario for the baryogenesis arising when matter is added on the branes of a Randall-Sundrum model with a radion stabilizing potential. We show that the radion field can naturally induce spontaneous baryogenesis when the cosmological evolution for the matter on the branes is taken into account.Comment: LaTeX 2e, 8 pages and no figures, minor corrections to match version to appear in MPL

Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies

In previous work, empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here that if the network of oscillators synchronizes for the static time-average of the topology, then the network will synchronize with the time-varying topology if the time-average is achieved sufficiently fast. Fast switching, fast on the time-scale of the coupled oscillators, overcomes the descychnronizing decoherence suggested by disconnected instantaneous networks. This result agrees in spirit with that of where empirical evidence suggested that a moving averaged graph Laplacian could be used in the master-stability function analysis. A new fast switching stability criterion here-in gives sufficiency of a fast-switching network leading to synchronization. Although this sufficient condition appears to be very conservative, it provides new insights about the requirements for synchronization when the network topology is time-varying. In particular, it can be shown that networks of oscillators can synchronize even if at every point in time the frozen-time network topology is insufficiently connected to achieve synchronization.Comment: Submitted to SIAD