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

Quasistatic Scale-free Networks

A network is formed using the $N$ sites of an one-dimensional lattice in the shape of a ring as nodes and each node with the initial degree $k_{in}=2$. $N$ links are then introduced to this network, each link starts from a distinct node, the other end being connected to any other node with degree $k$ randomly selected with an attachment probability proportional to $k^{\alpha}$. Tuning the control parameter $\alpha$ we observe a transition where the average degree of the largest node $$ changes its variation from $N^0$ to $N$ at a specific transition point of $\alpha_c$. The network is scale-free i.e., the nodal degree distribution has a power law decay for $\alpha \ge \alpha_c$.Comment: 4 pages, 5 figure

Randomized Benchmarking of Multi-Qubit Gates

As experimental platforms for quantum information processing continue to mature, characterization of the quality of unitary gates that can be applied to their quantum bits (qubits) becomes essential. Eventually, the quality must be sufficiently high to support arbitrarily long quantum computations. Randomized benchmarking already provides a platform-independent method for assessing the quality of one-qubit rotations. Here we describe an extension of this method to multi-qubit gates. We provide a platform-independent protocol for evaluating the performance of experimental Clifford unitaries, which form the basis of fault-tolerant quantum computing. We implemented the benchmarking protocol with trapped-ion two-qubit phase gates and one-qubit gates and found an error per random two-qubit Clifford unitary of $0.162 \pm 0.008$, thus setting the first benchmark for such unitaries. By implementing a second set of sequences with an extra two-qubit phase gate at each step, we extracted an error per phase gate of $0.069 \pm 0.017$. We conducted these experiments with movable, sympathetically cooled ions in a multi-zone Paul trap - a system that can in principle be scaled to larger numbers of ions.Comment: Corrected description of parallel single-qubit benchmark experiment. Results unchange

Axiomatic formulations of nonlocal and noncommutative field theories

We analyze functional analytic aspects of axiomatic formulations of nonlocal and noncommutative quantum field theories. In particular, we completely clarify the relation between the asymptotic commutativity condition, which ensures the CPT symmetry and the standard spin-statistics relation for nonlocal fields, and the regularity properties of the retarded Green's functions in momentum space that are required for constructing a scattering theory and deriving reduction formulas. This result is based on a relevant Paley-Wiener-Schwartz-type theorem for analytic functionals. We also discuss the possibility of using analytic test functions to extend the Wightman axioms to noncommutative field theory, where the causal structure with the light cone is replaced by that with the light wedge. We explain some essential peculiarities of deriving the CPT and spin-statistics theorems in this enlarged framework.Comment: LaTeX, 13 pages, no figure

Reconstruction in quantum field theory with a fundamental length

In this paper, we establish an analog of Wightman's reconstruction theorem for nonlocal quantum field theory with a fundamental length. In our setting, the Wightman generalized functions are defined on test functions analytic in a complex l-neighborhood of the real space and are localizable at scales large compared to l. The causality condition is formulated as continuity of the field commutator in an appropriate topology associated with the light cone. We prove that the relevant function spaces are nuclear and derive the kernel theorems for the corresponding classes of multilinear functionals, which provides the basis for the reconstruction procedure. Special attention is given to the accurate determination of the domain of the reconstructed quantum fields in the Hilbert space of states. We show that the primitive common invariant domain must be suitably extended to implement the (quasi)localizability and causality conditions.Comment: LaTeX, 23 pages, no figure

Measuring surface-area-to-volume ratios in soft porous materials using laser-polarized xenon interphase exchange NMR

We demonstrate a minimally invasive nuclear magnetic resonance (NMR) technique that enables determination of the surface-area-to-volume ratio (S/V) of soft porous materials from measurements of the diffusive exchange of laser-polarized 129Xe between gas in the pore space and 129Xe dissolved in the solid phase. We apply this NMR technique to porous polymer samples and find approximate agreement with destructive stereological measurements of S/V obtained with optical confocal microscopy. Potential applications of laser-polarized xenon interphase exchange NMR include measurements of in vivo lung function in humans and characterization of gas chromatography columns.Comment: 14 pages of text, 4 figure

The massive analytic invariant charge in QCD

The low energy behavior of a recently proposed model for the massive analytic running coupling of QCD is studied. This running coupling has no unphysical singularities, and in the absence of masses displays infrared enhancement. The inclusion of the effects due to the mass of the lightest hadron is accomplished by employing the dispersion relation for the Adler D function. The presence of the nonvanishing pion mass tames the aforementioned enhancement, giving rise to a finite value for the running coupling at the origin. In addition, the effective charge acquires a "plateau-like" behavior in the low energy region of the timelike domain. This plateau is found to be in agreement with a number of phenomenological models for the strong running coupling. The developed invariant charge is applied in the processing of experimental data on the inclusive $\tau$ lepton decay. The effects due to the pion mass play an essential role here as well, affecting the value of the QCD scale parameter $\Lambda$ extracted from these data. Finally, the massive analytic running coupling is compared with the effective coupling arising from the study of Schwinger-Dyson equations, whose infrared finiteness is due to a dynamically generated gluon mass. A qualitative picture of the possible impact of the former coupling on the chiral symmetry breaking is presented.Comment: 13 pages, 7 figures, revtex

Cellular automata approach to three-phase traffic theory

The cellular automata (CA) approach to traffic modeling is extended to allow for spatially homogeneous steady state solutions that cover a two dimensional region in the flow-density plane. Hence these models fulfill a basic postulate of a three-phase traffic theory proposed by Kerner. This is achieved by a synchronization distance, within which a vehicle always tries to adjust its speed to the one of the vehicle in front. In the CA models presented, the modelling of the free and safe speeds, the slow-to-start rules as well as some contributions to noise are based on the ideas of the Nagel-Schreckenberg type modelling. It is shown that the proposed CA models can be very transparent and still reproduce the two main types of congested patterns (the general pattern and the synchronized flow pattern) as well as their dependence on the flows near an on-ramp, in qualitative agreement with the recently developed continuum version of the three-phase traffic theory [B. S. Kerner and S. L. Klenov. 2002. J. Phys. A: Math. Gen. 35, L31]. These features are qualitatively different than in previously considered CA traffic models. The probability of the breakdown phenomenon (i.e., of the phase transition from free flow to synchronized flow) as function of the flow rate to the on-ramp and of the flow rate on the road upstream of the on-ramp is investigated. The capacity drops at the on-ramp which occur due to the formation of different congested patterns are calculated.Comment: 55 pages, 24 figure

Ten years of the Analytic Perturbation Theory in QCD

The renormalization group method enables one to improve the properties of the QCD perturbative power series in the ultraviolet region. However, it ultimately leads to the unphysical singularities of observables in the infrared domain. The Analytic Perturbation Theory constitutes the next step of the improvement of perturbative expansions. Specifically, it involves additional analyticity requirement which is based on the causality principle and implemented in the K\"allen--Lehmann and Jost--Lehmann representations. Eventually, this approach eliminates spurious singularities of the perturbative power series and enhances the stability of the latter with respect to both higher loop corrections and the choice of the renormalization scheme. The paper contains an overview of the basic stages of the development of the Analytic Perturbation Theory in QCD, including its recent applications to the description of hadronic processes.Comment: 26 pages, 9 figures, to be published in Theor. Math. Phys. (2007