Nonlinear Evolution of the Magnetohydrodynamic Rayleigh-Taylor Instability

We study the nonlinear evolution of the magnetic Rayleigh-Taylor instability using three-dimensional MHD simulations. We consider the idealized case of two inviscid, perfectly conducting fluids of constant density separated by a contact discontinuity perpendicular to the effective gravity g, with a uniform magnetic field B parallel to the interface. Modes parallel to the field with wavelengths smaller than l_c = [B B/(d_h - d_l) g] are suppressed (where d_h and d_l are the densities of the heavy and light fluids respectively), whereas modes perpendicular to B are unaffected. We study strong fields with l_c varying between 0.01 and 0.36 of the horizontal extent of the computational domain. Even a weak field produces tension forces on small scales that are significant enough to reduce shear (as measured by the distribution of the amplitude of vorticity), which in turn reduces the mixing between fluids, and increases the rate at which bubbles and finger are displaced from the interface compared to the purely hydrodynamic case. For strong fields, the highly anisotropic nature of unstable modes produces ropes and filaments. However, at late time flow along field lines produces large scale bubbles. The kinetic and magnetic energies transverse to gravity remain in rough equipartition and increase as t^4 at early times. The growth deviates from this form once the magnetic energy in the vertical field becomes larger than the energy in the initial field. We comment on the implications of our results to Z-pinch experiments, and a variety of astrophysical systems.Comment: 25 pages, accepted by Physics of Fluids, online version of journal has high resolution figure

Theory of the cold collision frequency shift in 1S--2S spectroscopy of Bose-Einstein-condensed and non-condensed hydrogen

We show that a correct formulation of the cold collision frequency shift for two photon spectroscopy of Bose-condensed and cold non-Bose-condensed hydrogen is consistent with experimental data. Our treatment includes transport and inhomogeneity into the theory of a non-condensed gas, which causes substantial changes in the cold collision frequency shift for the ordinary thermal gas, as a result of the very high frequency (3.9kHz) of transverse trap mode. For the condensed gas, we find substantial corrections arise from the inclusion of quasiparticles, whose number is very large because of the very low frequency (10.2Hz) of the longitudinal trap mode. These two effects together account for the apparent absence of a "factor of two" between the two possibilities. Our treatment considers only the Doppler-free measurements, but could be extended to Doppler-sensitive measurements. For Bose-condensed hydrogen, we predict a characteristic "foot" extending into higher detunings than can arise from the condensate alone, as a result of a correct treatment of the statistics of thermal quasiparticles.Comment: 16 page J Phys B format plus 6 postscript figure

The Quantum de Laval Nozzle: stability and quantum dynamics of sonic horizons in a toroidally trapped Bose gas containing a superflow

We study an experimentally realizable system containing stable black hole-white hole acoustic horizons in toroidally trapped Bose-Einstein condensates - the quantum de Laval nozzle. We numerically obtain stationary flow configurations and assess their stability using Bogoliubov theory, finding both in hydrodynamic and non-hydrodynamic regimes there exist dynamically unstable regions associated with the creation of positive and negative energy quasiparticle pairs in analogy with the gravitational Hawking effect. The dynamical instability takes the form of a two mode squeezing interaction between resonant pairs of Bogoliubov modes. We study the evolution of dynamically unstable flows using the truncated Wigner method, which confirms the two mode squeezed state picture of the analogue Hawking effect for low winding number.Comment: 12 pages, 10 figure

Quadripartite continuous-variable entanglement via quadruply concurrent downconversion

We investigate an intra-cavity coupled down-conversion scheme to generate quadripartite entanglement using concurrently resonant nonlinearities. We verify that quadripartite entanglement is present in this system by calculating the output fluctuation spectra and then considering violations of optimized inequalities of the van Loock-Furusawa type. The entanglement characteristics both above and below the oscillation threshold are considered. We also present analytic solutions for the quadrature operators and the van Loock-Furusawa correlations in the undepleted pump approximation.Comment: 9 pages, 5 figure

Theory of the Ramsey spectroscopy and anomalous segregation in ultra-cold rubidium

The recent anomalous segregation experiment of Lewandowski et al. (PRL, 88, 070403, 2002) shows dramatic, rapid internal state segregation for two hyperfine levels of rubidium. We simulate an effective one dimensional model of the system for experimental parameters and find reasonable agreement with the data. The Ramsey frequency is found to be insensitive to the decoherence of the superposition, and is only equivalent to the interaction energy shift for a pure superposition. A Quantum Boltzmann equation describing collisions is derived using Quantum Kinetic Theory, taking into account the different scattering lengths of the internal states. As spin-wave experiments are likely to be attempted at lower temperatures we examine the effect of degeneracy on decoherence by considering the recent experiment of Lewandowski et al. where degeneracy is around 10%. We also find that the segregation effect is only possible when transport terms are included in the equations of motion, and that the interactions only directly alter the momentum distributions of the states. The segregation or spin wave effect is thus entirely due to coherent atomic motion as foreseen in the experimental reportComment: 26 pages, 4 figures, to be published in J. Phys.

Properties of the stochastic Gross-Pitaevskii equation: Projected Ehrenfest relations and the optimal plane wave basis

We investigate the properties of the stochastic Gross-Pitaevskii equation describing a condensate interacting with a stationary thermal cloud derived by Gardiner and coworkers. We find the appropriate Ehrenfest relations for the SGPE, including the effect of growth noise and projector terms arising from the energy cutoff. This is carried out in the high temperature regime appropriate for the SGPE, which simplifies the action of the projectors. The validity condition for neglecting the projector terms in the Ehrenfest relations is found to be more stringent than the usual condition of validity of the truncated Wigner method or classical field method -- which is that all modes are highly occupied. In addition it is required that the overlap of the nonlinear term with the lowest energy eigenstate of the non-condensate band is small. We show how to use the Ehrenfest relations along with the corrections generated by the projector to monitor dynamical artifacts arising from the cutoff. We also investigate the effect of using different bases to describe a harmonically trapped BEC at finite temperature by comparing the condensate fraction found using the plane wave and single particle bases. We show that the equilibrium properties are strongly dependent on the choice of basis. There is thus an optimal choice of plane wave basis for a given cut-off energy and we show that this basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.Comment: 23 pages, 5 figure