Variational separable expansion scheme for two-body Coulomb-scattering problems

We present a separable expansion approximation method for Coulomb-like potentials which is based on Schwinger variational principle and uses Coulomb-Sturmian functions as basis states. The new scheme provides faster convergence with respect to our formerly used non-variational approach.Comment: some typos correcte

Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states

If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Green's operator can be constructed in terms of a continued fraction. As an illustrative example we discuss the Coulomb Green's operator in Coulomb-Sturmian basis representation. Based on this representation, a quantum mechanical approximation method for solving Lippmann-Schwinger integral equations can be established, which is equally applicable for bound-, resonant- and scattering-state problems with free and Coulombic asymptotics as well. The performance of this technique is illustrated with a detailed investigation of a nuclear potential describing the interaction of two $\alpha$ particles.Comment: 7 pages, 4 ps figures, revised versio

Electron-hydrogen scattering in Faddeev-Merkuriev integral equation approach

Electron-hydrogen scattering is studied in the Faddeev-Merkuriev integral equation approach. The equations are solved by using the Coulomb-Sturmian separable expansion technique. We present $S$- and $P$-wave scattering and reactions cross sections up to the $H(n=4)$ threshold.Comment: 2 eps figure

Observation of Heteronuclear Feshbach Molecules from a 85^{85}Rb - 87^{87}Rb gas

We report on the observation of ultracold heteronuclear Feshbach molecules. Starting with a $^{87}$Rb BEC and a cold atomic gas of $^{85}$Rb, we utilize previously unobserved interspecies Feshbach resonances to create up to 25,000 molecules. Even though the $^{85}$Rb gas is non-degenerate we observe a large molecular conversion efficiency due to the presence of a quantum degenerate $^{87}$Rb gas; this represents a key feature of our system. We compare the molecule creation at two different Feshbach resonances with different magnetic-field widths. The two Feshbach resonances are located at $265.44\pm0.15$ G and $372.4\pm1.3$ G. We also directly measure the small binding energy of the molecules through resonant magnetic-field association.Comment: v2 - minor change

Resonant-state solution of the Faddeev-Merkuriev integral equations for three-body systems with Coulomb potentials

A novel method for calculating resonances in three-body Coulombic systems is proposed. The Faddeev-Merkuriev integral equations are solved by applying the Coulomb-Sturmian separable expansion method. The $e^- e^+ e^-$ S-state resonances up to $n=5$ threshold are calculated.Comment: 6 pages, 2 ps figure

Hybrid Electro-Optically Modulated Microcombs

Optical frequency combs based on mode-locked lasers have proven to be invaluable tools for a wide range of applications in precision spectroscopy and metrology. A novel principle of optical frequency comb generation in whispering-gallery mode microresonators ("microcombs") has been developed recently, which represents a promising route towards chip-level integration and out-of-the-lab use of these devices. Presently, two families of microcombs have been demonstrated: combs with electronically detectable mode spacing that can be directly stabilized, and broadband combs with up to octave-spanning spectra but mode spacings beyond electronic detection limits. However, it has not yet been possible to achieve these two key requirements simultaneously, as will be critical for most microcomb applications. Here we present a key step to overcome this problem by interleaving an electro-optic comb with the spectrum from a parametric microcomb. This allows, for the first time, direct control and stabilization of a microcomb spectrum with large mode spacing (>140 GHz) with no need for an additional mode-locked laser frequency comb. The attained residual 1-second-instability of the microcomb comb spacing is 10^-15, with a microwave reference limited absolute instability of 10^-12 at a 140 GHz mode spacing.Comment: 8 pages, 4 figures; accepted for publication in Physical Review Letter

Parametric seeding of a microresonator optical frequency comb

We have investigated parametric seeding of a microresonator frequency comb (microcomb) by way of a pump laser with two electro-optic-modulation sidebands. We show that the pump-sideband spacing is precisely replicated throughout the microcomb's optical spectrum, and we demonstrate a record absolute line-spacing stability for microcombs of $1.6\times10^{-13}$ at 1 s. The spectrum of a parametric comb is complex, and often non-equidistant subcombs are observed. Our results demonstrate that parametric seeding can not only control the subcombs, but can lead to the generation of a strictly equidistant microcomb spectrum.Comment: 10 pages, 5 figure