We analyze a class of multicomponent nonlinear Schrodinger equations (MNLS) related to the symmetric BD.I-type symmetric spaces and their reductions. We briefly outline the direct and the inverse scattering method for the relevant Lax operators and the soliton solutions. We use the Zakharov-Shabat dressing method to obtain the two-soliton solution and analyze the soliton interactions of the MNLS equations and some of their reductions.
A three- and five-component nonlinear Schrodinger-type models, which describe spinor Bose-Einstein condensates (BECs) with hyperfine structures F=1 and F=2 respectively, are studied. These models for particular values of the coupling constants are in
tegrable by the inverse scattering method. They are related to symmetric spaces of BD.I-type SO(2r+1)/(SO(2) x SO(2r-1)) for r=2 and r=3. Using conveniently modified Zakharov-Shabat dressing procedure we obtain different types of soliton solutions.
We experimentally investigate and analyze the rich dynamics in F=2 spinor Bose-Einstein condensates of Rb87. An interplay between mean-field driven spin dynamics and hyperfine-changing losses in addition to interactions with the thermal component is
observed. In particular we measure conversion rates in the range of 10^-12 cm^3/s for spin changing collisions within the F=2 manifold and spin-dependent loss rates in the range of 10^-13 cm^3/s for hyperfine-changing collisions. From our data we observe a polar behavior in the F=2 ground state of Rb87, while we measure the F=1 ground state to be ferromagnetic. Furthermore we see a magnetization for condensates prepared with non-zero total spin.
Extended Gross-Pitaevskii equations for the rotating F=2 condensate in a harmonic trap are solved both numerically and variationally using trial functions for each component of the wave function. Axially-symmetric vortex solutions are analyzed and en
ergies of polar and cyclic states are calculated. The equilibrium transitions between different phases with changing of the magnetization are studied. We show that at high magnetization the ground state of the system is determined by interaction in density channel, and at low magnetization spin interactions play a dominant role. Although there are five hyperfine states, all the particles are always condensed in one, two or three states. Two novel types of vortex structures are also discussed.
We consider the dynamics of dark matter solitons moving through non-uniform cigar-shaped Bose-Einstein condensates described by the mean field Gross-Pitaevskii equation with generalized nonlinearities, in the case when the condition for the modulatio
n stability of the Bose-Einstein condensate is fulfilled. The analytical expression for the frequency of the oscillations of a deep dark soliton is derived for nonlinearities which are arbitrary functions of the density, while specific results are discussed for the physically relevant case of a cubic-quintic nonlinearity modeling two- and three-body interactions, respectively. In contrast to the cubic Gross-Pitaevskii equation for which the frequencies of the oscillations are known to be independent of background density and interaction strengths, we find that in the presence of a cubic-quintic nonlinearity an explicit dependence of the oscillations frequency on the above quantities appears. This dependence gives rise to the possibility of measuring these quantities directly from the dark soliton dynamics, or to manage the oscillation via the changes of the scattering lengths by means of Feshbach resonance. A comparison between analytical results and direct numerical simulations of the cubic-quintic Gross-Pitaevskii equation shows good agreement which confirms the validity of our approach.
In this work, we explore systematically various SO(2)-rotation-induced multiple dark-dark soliton breathing patterns obtained from stationary and spectrally stable multiple dark-bright and dark-dark waveforms in trapped one-dimensional, two-component
atomic Bose-Einstein condensates (BECs). The stationary states stem from the associated linear limits (as the eigenfunctions of the quantum harmonic oscillator problem) and are parametrically continued to the nonlinear regimes by varying the respective chemical potentials, i.e., from the low-density linear limits to the high-density Thomas-Fermi regimes. We perform a Bogolyubov-de Gennes (BdG) spectral stability analysis to identify stable parametric regimes of these states. Upon SO(2)-rotation, the stable steady-states, one-, two-, three-, four-, and many dark-dark soliton breathing patterns are observed in the numerical simulations. Furthermore, analytic solutions up to three dark-bright solitons in the homogeneous setting, and three-component systems are also investigated.
V. S. Gerdjikov
,N. A. Kostov
,T. I. Valchev
.
(2009)
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"Bose-Einstein condensates with F=1 and F=2. Reductions and soliton interactions of multi-component NLS models"
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Vladimir S. Gerdjikov
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