Faraday waves in binary non-miscible Bose-Einstein condensates

We show by extensive numerical simulations and analytical variational calculations that elongated binary non-miscible Bose-Einstein condensates subject to periodic modulations of the radial confinement exhibit a Faraday instability similar to that seen in one-component condensates. Considering the hyperfine states of $^{87}$Rb condensates, we show that there are two experimentally relevant stationary state configurations: the one in which the components form a dark-bright symbiotic pair (the ground state of the system), and the one in which the components are segregated (first excited state). For each of these two configurations, we show numerically that far from resonances the Faraday waves excited in the two components are of similar periods, emerge simultaneously, and do not impact the dynamics of the bulk of the condensate. We derive analytically the period of the Faraday waves using a variational treatment of the coupled Gross-Pitaevskii equations combined with a Mathieu-type analysis for the selection mechanism of the excited waves. Finally, we show that for a modulation frequency close to twice that of the radial trapping, the emergent surface waves fade out in favor of a forceful collective mode that turns the two condensate components miscible.Comment: 13 pages, 10 figure

FARADAY WAVES IN BOSE-EINSTEIN CONDENSATES SUBJECT TO ANISOTROPIC TRANSVERSE CONFINEMENT

Abstract. In this study we introduce a variational model for the dynamics of Faraday waves in longitudinally-inhomogeneous Bose-Einstein condensates subject to anisotropic transverse confinement and periodic modulations of the scattering length. We derive a set of variational equations under the assumption that the period of the Faraday wave is smaller than the longitudinal width of the condensate and determine analytically the dispersion relation for large condensates through a Mathieu-type analysis of the variational equations. Finally, we show the emergence of Faraday waves in a realistic anisotropic 87 Rb Bose-Einstein condensate and discuss possible extensions of the variational treatment to binary condensates

Nonlinear dynamics of Bose-condensed gases by means of a low- to high-density variational approach

We propose a versatile variational method to investigate the spatio-temporal dynamics of one-dimensional magnetically-trapped Bose-condensed gases. To this end we employ a \emph{q}-Gaussian trial wave-function that interpolates between the low- and the high-density limit of the ground state of a Bose-condensed gas. Our main result consists of reducing the Gross-Pitaevskii equation, a nonlinear partial differential equation describing the T=0 dynamics of the condensate, to a set of only three equations: \emph{two coupled nonlinear ordinary differential equations} describing the phase and the curvature of the wave-function and \emph{a separate algebraic equation} yielding the generalized width. Our equations recover those of the usual Gaussian variational approach (in the low-density regime), and the hydrodynamic equations that describe the high-density regime. Finally, we show a detailed comparison between the numerical results of our equations and those of the original Gross-Pitaevskii equation.Comment: 11 pages, 12 figures, submitted to Phys. Rev. A, January 200

Measurements of the Total and Differential Higgs Boson Production Cross Sections Combining the H??????? and H???ZZ*???4??? Decay Channels at s\sqrt{s}=8??????TeV with the ATLAS Detector

Measurements of the total and differential cross sections of Higgs boson production are performed using 20.3~fb$^{-1}$ of $pp$ collisions produced by the Large Hadron Collider at a center-of-mass energy of $\sqrt{s} = 8$ TeV and recorded by the ATLAS detector. Cross sections are obtained from measured $H \rightarrow \gamma \gamma$ and $H \rightarrow ZZ ^{*}\rightarrow 4\ell$ event yields, which are combined accounting for detector efficiencies, fiducial acceptances and branching fractions. Differential cross sections are reported as a function of Higgs boson transverse momentum, Higgs boson rapidity, number of jets in the event, and transverse momentum of the leading jet. The total production cross section is determined to be $\sigma_{pp \to H} = 33.0 \pm 5.3 \, ({\rm stat}) \pm 1.6 \, ({\rm sys}) \mathrm{pb}$. The measurements are compared to state-of-the-art predictions.Measurements of the total and differential cross sections of Higgs boson production are performed using 20.3  fb-1 of pp collisions produced by the Large Hadron Collider at a center-of-mass energy of s=8  TeV and recorded by the ATLAS detector. Cross sections are obtained from measured H→γγ and H→ZZ*→4ℓ event yields, which are combined accounting for detector efficiencies, fiducial acceptances, and branching fractions. Differential cross sections are reported as a function of Higgs boson transverse momentum, Higgs boson rapidity, number of jets in the event, and transverse momentum of the leading jet. The total production cross section is determined to be σpp→H=33.0±5.3 (stat)±1.6 (syst)  pb. The measurements are compared to state-of-the-art predictions.Measurements of the total and differential cross sections of Higgs boson production are performed using 20.3 fb$^{-1}$ of $pp$ collisions produced by the Large Hadron Collider at a center-of-mass energy of $\sqrt{s} = 8$ TeV and recorded by the ATLAS detector. Cross sections are obtained from measured $H \rightarrow \gamma \gamma$ and $H \rightarrow ZZ ^{*}\rightarrow 4\ell$ event yields, which are combined accounting for detector efficiencies, fiducial acceptances and branching fractions. Differential cross sections are reported as a function of Higgs boson transverse momentum, Higgs boson rapidity, number of jets in the event, and transverse momentum of the leading jet. The total production cross section is determined to be $\sigma_{pp \to H} = 33.0 \pm 5.3 \, ({\rm stat}) \pm 1.6 \, ({\rm sys}) \mathrm{pb}$. The measurements are compared to state-of-the-art predictions