We develop a perturbation theory for bright solitons of the F=1 integrable spinor Bose-Einstein condensate (BEC) model. The formalism is based on using the Riemann-Hilbert problem and provides the means to analytically calculate evolution of the soliton parameters. Both rank-one and rank-two soliton solutions of the model are obtained. We prove equivalence of the rank-one soliton and the ferromagnetic rank-two soliton. Taking into account a splitting of a perturbed polar rank-two soliton into two ferromagnetic solitons, it is sufficient to elaborate a perturbation theory for the rank-one solitons only.
Treating a small deviation from the integrability condition as a perturbation, we describe the spinor BEC soliton dynamics in the adiabatic approximation. It is shown that the soliton is quite robust against such a perturbation and preserves its velocity, amplitude, and population of different spin components, only the soliton frequency acquires a small shift. Results of numerical simulations agree well with the analytical predictions, demonstrating only slight soliton profile deformation.
We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. An equation of nonlinear Schrödinger type is derived and exact magnetic soliton solutions are obtained analytically by means of Hirota method. Our results show that the critical external field is needed for creating the magnetic soliton in spinor Bose-Einstein condensates. The soliton size, velocity and shape frequency can be controlled in practical experiment by adjusting the magnetic field. Moreover, the elastic collision …
We consider a one-dimensional gas of half-solitons in a spinor Bose-Einstein condensate. We calculate the topological interaction potential between the half-solitons. Using a kinetic equation of the Vlasov-Boltzmann type, we model the coupled dynamics of the interacting solitons. We show that the dynamics of the system in the gaseous phase is marginally stable and spontaneously evolves towards a Wigner crystal.
We investigate the dynamics of bright matter wave solitons in spin-1 Bose-Einstein condensates with time modulated nonlinearities. We obtain soliton solutions of an integrable autonomous three-coupled Gross-Pitaevskii (3-GP) equations using Hirota's method involving a non-standard bilinearization. The similarity transformations are developed to construct the soliton solutions of non-autonomous 3-GP system. The non-autonomous solitons admit different density profiles. An interesting phenomenon of soliton compression is identified for kink-like nonlinearity coefficient with Hermite-Gaussian-like…
Adopting a mean-field Gross-Pitaevskii description for a spinor polariton Bose-Einstein condensates under non-resonant pumping, we investigate the static and dynamical properties of dark-bright solitons. We derive analytically the equation of motion for the center of mass of the dark-bright soliton center, using the Hamiltonian approach. The resulting equation captures how the combination of the open-dissipative character and the spin degrees of freedom of a polariton Bose-Einstein condensate affects the properties of a dark-bright soliton, i.e. the dark-bright soliton relaxes by blending with…
The existence of bright solitons in bulk superfluid He-4 is demonstrated by time-resolved shadowgraph i maging experiments and density functional theory (DFT) calculations. The initial liquid compression that leads to the creation of non-linear waves is produced by rapidly expanding plasma from laser ablation. Af ter the leading dissipative period, these waves transform into bright solitons, which exhibit three chara cteristic features: dispersionless propagation, negligible interaction in two-wave collision, and direct dependence between soliton amplitude and the propagation velocity. The exp…
Optical solitons are an ideal platform for the implementation of communication lines, since they can be packed extremely close one to another without risking partial loss of the encoded information due to their interaction. On the other hand, soliton-soliton interactions are needed to implement computations and achieve all-optical information processing. Here we study how bright dissipative polariton solitons interact and exploit their interaction to implement AND and OR gates with state of the art technology. Moreover, we show that soliton-soliton interaction can be used to determine the sign…
We study the interaction of dark-bright solitons in two component Bose-Einstein condensates by suitably tailoring the trap potential, atomic scattering length and atom gain or loss. We show that the coupled Gross-Pitaevskii (GP) equation can be mapped onto the Manakov model. An interesting class of matter wave solitons and their interaction are identified with time independent and periodically modulated trap potentials, which can be experimentally realized in two component condensates. These include periodic collapse and revival of solitons, and snake-like matter wave solitons as well as diffe…
Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose-Einstein condensate by temporal modulation of the scattering length
We revisit the collisional dynamics of bright solitons in the coupled Nonlinear Schrodinger equation. We observe that apart from the intensity redistribution in the interaction of bright solitons, one also witnesses a rotation of the trajectories of bright solitons . The angle of rotation can be varied by suitably manipulating the Self-Phase Modulation (SPM) or Cross Phase Modulation (XPM) parameters.The rotation of the trajectories of the bright solitons arises due to the excess energy that is injected into the dynamical system through SPM or XPM. This extra energy not only contributes to the…
