Effects of Raman scattering and attenuation in silica fiber-based parametric frequency conversion

Four-wave mixing in the form of Bragg scattering (BS) has been predicted to enable quantum noise less frequency conversion by analytic quantum approaches. Using a semi-classical description of quantum noise that accounts for loss and stimulated and spontaneous Raman scattering, which are not currently described in existing quantum approaches, we quantify the impacts of these effects on the conversion efficiency and on the quantum noise properties of BS in terms of an induced noise figure (NF). We give an approximate closed-form expression for the BS conversion efficiency that includes loss and stimulated Raman scattering, and we derive explicit expressions for the Raman-induced NF from the semi-classical approach used here.Comment: 14 single col pages, 11 figure

Public Channel Cryptography: Chaos Synchronization and Hilbert's Tenth Problem

The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signal is concealed by two commutative private filters that are placed on each end of the communication channel. We demonstrate that when the transmitted signal is a convolution of the truncated time delayed output signals or some powers of the delayed output signals synchronization is still maintained. The task of a passive attacker is mapped onto Hilbert's tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-Complete problems. This bridge between two different disciplines, synchronization in nonlinear dynamical processes and the realm of the NPC problems, opens a horizon for a new type of secure public-channel protocols

Bounds on New Physics from B -> V1 V2 Decays

We consider the possibility that physics beyond the standard model contributes to the decays B -> V1 V2, where V1 and V2 are vector mesons. We show that a time-dependent angular analysis of B -> V1 V2 decays provides many tests for this new physics (NP). Furthermore, although one cannot solve for the NP parameters, we show that this angular analysis allows one to put bounds on these parameters. This can be useful in estimating the scale of NP, and can tell us whether any NP found directly at future high-energy colliders can be responsible for effects seen in B -> V1 V2 decays.Comment: 23 pages, plain LaTeX, 5 figures (included

Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations

In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves sought in experimental nonlinear model identification. We develop here a methodology to compute analytically both the shape of SSMs and their corresponding backbone curves from a data-assimilating model fitted to experimental vibration signals. Using examples of both synthetic and real experimental data, we demonstrate that this approach reproduces backbone curves with high accuracy.Comment: 32 pages, 4 figure