[en] A study of ‘high temperature’ entangled states in a system of two parametrically coupled quantum oscillators placed into independent thermal baths is performed taking into account partially coherent parametric pump. Processes in an open system are considered based on the Heisenberg–Langevin formalism. We obtain a closed system of equations for the averaged quadratic correlation functions in quantum stochastic problem as a result of Markov processes approximation. On the basis of numerical calculations the dynamics of the logarithmic negativity, which is the measure of entanglement in the system, is investigated. It is shown that the partial coherence of the parametric pump makes the lifetime of the entangled states finite. The threshold characteristics of the formation and existence of these states are specified. (paper)

[en] The problem of excitation of a homogeneous Bose-Einstein condensate by axially symmetric potential barriers moving with respect to the condensate with both supersonic and subsonic velocities is considered in terms of the Gross-Pitaevskii equation. The specific features of the structure of the vortex shedding past the barriers are analyzed for both regimes of motion.

[en] We analyze the scattering of vortex pairs (the particular case of 2D dark solitons) by a single quantum vortex in a Bose–Einstein condensate with repulsive interaction between atoms. For this purpose, an asymptotic theory describing the dynamics of such 2D soliton-like formations in an arbitrary smoothly nonuniform flow of a ultracold Bose gas is developed. Disregarding the radiation loss associated with acoustic wave emission, we demonstrate that vortex–antivortex pairs can be put in correspondence with quasiparticles, and their behavior can be described by canonical Hamilton equations. For these equations, we determine the integrals of motion that can be used to classify various regimes of scattering of vortex pairs by a single quantum vortex. Theoretical constructions are confirmed by numerical calculations performed directly in terms of the Gross–Pitaevskii equation. We propose a method for estimating the radiation loss in a collision of a soliton-like formation with a phase singularity. It is shown by direct numerical simulation that under certain conditions, the interaction of vortex pairs with a core of a single quantum vortex is accompanied by quite intense acoustic wave emission; as a result, the conditions for applicability of the asymptotic theory developed here are violated. In particular, it is visually demonstrated by a specific example how radiation losses lead to a transformation of a vortex–antivortex pair into a vortex-free 2D dark soliton (i.e., to the annihilation of phase singularities).

[en] The nonlinear stage of modulation instability of dark solitons is studied analytically and numerically. We propose an asymptotic description of the dynamics of these solitons in terms of their local velocity and the curvature of the lines at which solitons are concentrated. The features of the destruction of dark solitons (in particular, the formation of vortex structures from them) are analyzed.

[en] Based on a discrete nonlinear Schrödinger equation (DNSE), we studied analytically and numerically the peculiarities of the self-action of one-dimensional quasi-optic wave beams injected into a spatially inhomogeneous medium consisting of a set of equidistant mutually coupled optical fibers. A variational approach allowing the prediction of the global evolution of localized fields with the initially plane phase front was developed. The self-consistent equations are obtained for the main parameters of such beams (the position of the center of mass, the effective width, and linear and quadratic phase-front corrections) in the aberrationless approximation. The case of radiation incident on a periodic system of nonlinear optical fibers at an angle to the axis oriented along them is analyzed in detail. It is shown that for the radiation power exceeding a critical value, the self-focusing of the wave field is observed, which is accompanied by the shift of the intensity maximum followed by the concentration of the main part of radiation only in one of the structural elements of the array under study. In this case, the beams propagate along paths considerably different from linear and the direction of their propagation changes compared to the initial direction. Asymptotic expressions are found that allow us to estimate the self-focusing length and to determine quite accurately the final position of a point with the maximum field amplitude after radiation trapping a channel. The results of the qualitative study of the possible self-channeling regimes for wave beams in a system of weakly coupled optical fibers in the aberrationless approximation are compared with the results of direct numerical simulations within the DNSE framework.

[en] We propose a method of laser pulse self-compression in an array of equidistant, identical, weakly-coupled active light guides. It is shown that laser pulse self-focusing in such one-dimensional arrays decreases the compression length significantly (by more than 15 times) in comparison with the case of laser pulse self-compression in a single active light guide. Analytical estimates for the minimal pulse duration and the length of self-compression of laser pulses in a system of weakly-coupled active light guides are derived, and they agree well with the numerical simulation results. (paper)

[en] The theory of stationary linear wave patterns generated in a supersonic flow of a Bose-Einstein condensate past a point-like obstacle is developed. It is shown that they are located mainly outside the Mach cone corresponding to infinitely long wavelengths. The shape of wave crests and dependence of amplitude on coordinates far enough from the obstacle are calculated. The results are in good agreement with the results of numerical simulations. The theory gives a qualitative description of experiments with Bose-Einstein condensate flow past an obstacle after the condensate's release from a trap