Additive Entropies of degree-q and the Tsallis Entropy

The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are derived. Notions of additivity, extensivity and homogeneity are clarified. The relation between mean code lengths in coding theory and various expressions for average entropies is discussed.Comment: 13 page

Towards Zeptosecond-Scale Pulses from X-Ray Free-Electron Lasers

The short wavelength and high peak power of the present generation of free-electron lasers (FELs) opens the possibility of ultra-short pulses even surpassing the present (tens to hundreds of attoseconds) capabilities of other light sources - but only if x-ray FELs can be made to generate pulses consisting of just a few optical cycles. For hard x-ray operation (~0.1nm), this corresponds to durations of approximately a single attosecond, and below into the zeptosecond scale. This talk will describe a novel method to generate trains of few-cycle pulses, at GW peak powers, from existing x-ray FEL facilities by using a relatively short 'afterburner'. Such pulses would enhance research opportunity in atomic dynamics and push capability towards the investigation of electronic-nuclear and nuclear dynamics. The corresponding multi-colour spectral output, with a bandwidth envelope increased by up to two orders of magnitudes over SASE, also has potential applications.Comment: Submitted to 35th International Free Electron Laser Conference, New York, 201

Distribution of E/N and N sub e in a cross-flow electric discharge laser

The spatial distribution of the ratio of electric field to neutral gas density on a flowing gas, multiple pin-to-plane discharge was measured in a high-power, closed loop laser. The laser was operated at a pressure of 140 torr (1:7:20, CO2, N2, He) with typically a 100 meter/second velocity in the 5 x 8 x 135 centimeter discharge volume. E/N ratios ranged from 2.7 x 10 to the minus 16th power to 1.4 x 10 to the minus 16th power volts/cu cm along the discharge while the electron density ranged from 2.8 x 10 to the 10th power to 1.2 x 10 to the 10th power cm/3

A wide bandwidth free-electron laser with mode locking using current modulation

A new scheme for mode locking a free-electron laser (FEL) amplifier is proposed based on electron beam current modulation. It is found that certain properties of the original concept (Thompson and McNeil 2008 Phys. Rev. Lett. 100 203901), based on the energy modulation of electrons, are improved, including the spectral brightness of the source and the purity of the series of short pulses. Numerical comparisons are made between the new and old schemes and between a mode-locked FEL and a self-amplified spontaneous emission FEL. Illustrative examples using a hypothetical mode-locked FEL amplifier are provided. The ability to generate intense coherent radiation with a large bandwidth is demonstrated

Ultralong-Range Rydberg Molecules in a Divalent-Atomic System

We report the creation of ultralong-range Sr$_2$ molecules comprising one ground-state $5s^2$ $^1S_0$ atom and one atom in a $5sns$ $^3S_1$ Rydberg state for $n$ ranging from 29 to 36. Molecules are created in a trapped ultracold atomic gas using two-photon excitation near resonant with the $5s5p$ $^3P_1$ intermediate state, and their formation is detected through ground-state atom loss from the trap. The observed molecular binding energies are fit with the aid of first-order perturbation theory that utilizes a Fermi pseudopotential with effective $s$-wave and $p$-wave scattering lengths to describe the interaction between an excited Rydberg electron and a ground-state Sr atom.Comment: 5 pages, 2 figure

Lifetimes of ultralong-range strontium Rydberg molecules in a dense BEC

The lifetimes and decay channels of ultralong-range Rydberg molecules created in a dense BEC are examined by monitoring the time evolution of the Rydberg population using field ionization. Studies of molecules with values of principal quantum number, $n$, in the range $n=49$ to $n=72$ that contain tens to hundreds of ground state atoms within the Rydberg electron orbit show that their presence leads to marked changes in the field ionization characteristics. The Rydberg molecules have lifetimes of $\sim1-5\,\mu$s, their destruction being attributed to two main processes: formation of Sr$^+_2$ ions through associative ionization, and dissociation induced through $L$-changing collisions. The observed loss rates are consistent with a reaction model that emphasizes the interaction between the Rydberg core ion and its nearest neighbor ground-state atom. The measured lifetimes place strict limits on the time scales over which studies involving Rydberg species in cold, dense atomic gases can be undertaken and limit the coherence times for such measurements.Comment: 9 pages, 8 figure

Complex WKB Analysis of a PT Symmetric Eigenvalue Problem

The spectra of a particular class of PT symmetric eigenvalue problems has previously been studied, and found to have an extremely rich structure. In this paper we present an explanation for these spectral properties in terms of quantisation conditions obtained from the complex WKB method. In particular, we consider the relation of the quantisation conditions to the reality and positivity properties of the eigenvalues. The methods are also used to examine further the pattern of eigenvalue degeneracies observed by Dorey et al. in [1,2].Comment: 22 pages, 13 figures. Added references, minor revision