Continuous variable tripartite entanglement and Einstein-Podolsky-Rosen correlations from triple nonlinearities

We compare theoretically the tripartite entanglement available from the use of three concurrent x(2) nonlinearities and three independent squeezed states mixed on beamsplitters, using an appropriate version of the van Loock-Furusawa inequalities. We also define three-mode generalizations of the Einstein-Podolsky-Rosen paradox which are an alternative for demonstrating the inseparability of the density matrix.

First-principles quantum dynamics in interacting Bose gases: I. The positive P representation

The performance of the positive P phase-space representation for exact many- body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made with other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.

BCS-BEC crossover in an asymmetric two-component Fermi gas

We discuss the superfluid phase transition of a strongly interacting Fermi gas with unequal ( asymmetric) chemical potentials in two pairing hyperfine states, and map out its phase diagram near the BCS-BEC crossover. Our approach includes the fluctuation contributions of preformed Cooper pairs to the thermodynamic potential at finite temperature. We show that, below a critical difference in chemical potentials between species, a normal gas is unstable towards the formation of either a finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov superconducting phase or a uniform superfluid, depending on the asymmetry and interaction strengths. We determine the value of critical chemical potential mismatch, and find that it is consistent with a recent measurement by Zwierlein et al. ( Science, 311 ( 2006) 492).

Optical turbulence and spectral condensate in long-fiber lasers

We study optical wave turbulence using as a particular example recently created ultralong-fiber laser. We show that the sign of the cavity dispersion has a critical impact on the spectral and temporal properties of generated radiation that are directly relevant to the fiber laser performance. For a normal dispersion, we observe an intermediate state with an extremely narrow spectrum condensate, which experiences an instability and a sharp transition to a strongly fluctuating regime with a wide spectrum and increased probability of spontaneous generation of large-amplitude pulses.

N'est-il de bon bec que de Paris?

Représentations littéraires de la langue non standard chez Arthur Masson (Wallonie), Fonson & Wicheler (Bruxelles) et Pagnol (Marseille)

Optical turbulence and spectral condensate in long fibre lasers

We study numerically optical turbulence using the particular example of a recently created, ultra-long fibre laser. For normal fibre dispersion, we observed an intermediate state with an extremely narrow spectrum (condensate), which experiences instability and a sharp transition to a fluctuating regime with a wider spectrum. We demonstrate that the number of modes has an impact on the condensate’s lifetime. The smaller the number of modes, the more resistant is the condensate to perturbations. Experimental results show a good agreement with numerical simulations.

Granular superconductors:from the nonlinear σ model to the Bose-Hubbard description

We modify a nonlinear σ model (NLσM) for the description of a granular disordered system in the presence of both the Coulomb repulsion and the Cooper pairing. We show that under certain controlled approximations the action of this model is reduced to the Ambegaokar-Eckern-Schön (AES) action, which is further reduced to the Bose-Hubbard (or “dirty-boson”) model with renormalized coupling constants. We obtain an effective action which is more general than the AES one but still simpler than the full NLσM action. This action can be applied in the region of parameters where the reduction to the AES or the Bose-Hubbard model is not justified. This action may lead to a different picture of the superconductor-insulator transition in two-dimensional systems.

Optical turbulence and spectral condensate in fibre lasers

We study optical wave turbulence in Raman fibre lasers using particular examples of 13 km and 22 km long Fabry-Perot resonators. We demonstrate that the sign of the cavity dispersion has a critical impact on the spectral and temporal properties of generated radiation that are directly relevant to the fibre laser performance. For a normal dispersion, we observe in numerical modelling an intermediate state with an extremely narrow spectrum (condensate), which experiences instability and a sharp transition to a strongly fluctuating regime with a wider spectrum. The experimental results for the generated spectra demonstrate a good match with numerical simulations. © 2011 IEEE.

Universal profile of the vortex condensate in two-dimensional turbulence

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate—a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of the type of small-scale dissipation, small-scale forcing, and boundary conditions. The theory predicts not only the vortex inner region profile, but also the amplitude, which both perfectly agree with the numerical data.

Dimensional dependence of the Stokes-Einstein relation and its violation

We generalize to higher spatial dimensions the Stokes-Einstein relation (SER) as well as the leading correction to diffusivity in finite systems with periodic boundary conditions, and validate these results with numerical simulations. We then investigate the evolution of the high-density SER violation with dimension in simple hard sphere glass formers. The analysis suggests that this SER violation disappears around dimension du = 8, above which it is not observed. The critical exponent associated with the violation appears to evolve linearly in 8 - d, below d = 8, as predicted by Biroli and Bouchaud [J. Phys.: Condens. Matter 19, 205101 (2007)], but the linear coefficient is not consistent with the prediction. The SER violation with d establishes a new benchmark for theory, and its complete description remains an open problem. © 2013 AIP Publishing LLC.