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Register a new userSolitons and soliton interactions in repulsive spinor Bose-Einstein condensates with non-zero background
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We characterize the soliton solutions and their interactions for a system of coupled evolution equations of nonlinear Schrodinger (NLS) type that models the dynamics in one-dimensional repulsive Bose-Einstein condensates with spin one, taking advantage of the representation of such model as a special reduction of a 2 x 2 matrix NLS system. Specifically, we study in detail the case in which solutions tend to a non-zero background at space infinities. First we derive a compact representation for the multi-soliton solutions in the system using the Inverse Scattering Transform (IST). We introduce the notion of canonical form of a solution, corresponding to the case when the background is proportional to the identity. We show that solutions for which the asymptotic behavior at infinity is not proportional to the identity, referred to as being in non-canonical form, can be reduced to canonical form by unitary transformations that preserve the symmetric nature of the solution (physically corresponding to complex rotations of the quantization axes). Then we give a complete characterization of the two families of one-soliton solutions arising in this problem, corresponding to ferromagnetic and to polar states of the system, and we discuss how the physical parameters of the solitons for each family are related to the spectral data in the IST. We also show that any ferromagnetic one-soliton solution in canonical form can be reduced to a single dark soliton of the scalar NLS equation, and any polar one-soliton solution in canonical form is unitarily equivalent to a pair of oppositely polarized displaced scalar dark solitons up to a rotation of the quantization axes. Finally, we discuss two-soliton interactions and we present a complete classification of the possible scenarios that can arise depending on whether either soliton is of ferromagnetic or polar type.
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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 modulation 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.
We investigate non-degenerate bound state solitons systematically in multi-component Bose-Einstein condensates, through developing Darboux transformation method to derive exact soliton solutions analytically. In particular, we show that bright solitons with nodes correspond to the excited bound eigen-states in the self-induced effective quantum wells, in sharp contrast to the bright soliton and dark soliton reported before (which usually correspond to ground state and free eigen-state respectively). We further demonstrate that the bound state solitons with nodes are induced by incoherent interactions between solitons in different components. Moreover, we reveal that the interactions between these bound state solitons are usually inelastic, caused by the incoherent interactions between solitons in different components and the coherent interactions between solitons in same component. The bound state solitons can be used to discuss many different physical problems, such as beating dynamics, spin-orbital coupling effects, quantum fluctuations, and even quantum entanglement states.
We introduce an effectively one-dimensional (1D) model of a bosonic gas of particles carrying collinear dipole moments which are induced by an external polarizing field with the strength periodically modulated along the coordinate, which gives rise to an effective nonlocal nonlinear lattice in the condensate. The existence, shape and stability of bright solitons, appearing in this model, are investigated by means of the variational approximation and numerical methods. The mobility of solitons and interactions between them are studied too.
We present experimental results and a systematic theoretical analysis of dark-br ight soliton interactions and multiple-dark-bright soliton complexes in atomic t wo-component Bose-Einstein condensates. We study analytically the interactions b etween two-dark-bright solitons in a homogeneous condensate and, then, extend ou r considerations to the presence of the trap. An effective equation of motion is derived for the dark-bright soliton center and the existence and stability of stationary two-dark-bright soliton states is illustrated (with the bright components being either in- or out-of-phase). The equation of motion provides the characteristic oscillation frequencies of the solitons, in good agreement with the eigenfrequencies of the anomalous modes of the system.
In this work we present a systematic study of the three-dimensional extension of the ring dark soliton examining its existence, stability, and dynamics in isotropic harmonically trapped Bose-Einstein condensates. Detuning the chemical potential from the linear limit, the ring dark soliton becomes unstable immediately, but can be fully stabilized by an external cylindrical potential. The ring has a large number of unstable modes which are analyzed through spectral stability analysis. Furthermore, a few typical destabilization dynamical scenarios are revealed with a number of interesting vortical structures emerging such as the two or four coaxial parallel vortex rings. In the process of considering the stability of the structure, we also develop a modified version of the degenerate perturbation theory method for characterizing the spectra of the coherent structure. This semi-analytical method can be reliably applied to any soliton with a linear limit to explore its spectral properties near this limit. The good agreement of the resulting spectrum is illustrated via a comparison with the full numerical Bogolyubov-de Gennes spectrum. The application of the method to the two-component ring dark-bright soliton is also discussed.
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