Waves and Solitons

Carlo F. Barenghi, Thomas Bland, Nick G. Parker

Zhong-Zhou Lan

Abstract Spinor Bose–Einstein condensates (BECs) are formed when atoms in the multi-component BECs possess single hyperfine spin states but retain internal spin degrees of freedom. This study concentrates on a (1+1)-dimensional three-couple Gross–Pitaevskii system to depict the macroscopic spinor BEC waves within the mean-field approximation. Regarding the distribution of the atoms corresponding to the three vertical spin projections, a known binary Darboux transformation is utilized to derive the N matter-wave soliton solutions and triple-pole matter-wave soliton solutions on the zero background, where N is a positive integer. For those multiple matter-wave solitons, the asymptotic analysis is performed to obtain the algebraic expressions of the soliton components in the N matter-wave solitons and triple-pole matter-wave solitons. The asymptotic results indicate that the matter-wave solitons in the spinor BECs possess the property of maintaining their energy content and coherence during the propagation and interactions. Particularly, in the N matter-wave solitons, each soliton component contributes to the phase shifts of the other soliton components; and in the triple-pole matter-wave solitons, stable attractive forces exist between the different matter-wave soliton components. Those multiple matter-wave solitons are graphically illustrated through three-dimensional plots, density plot and contour plot, which are consistent with the asymptotic analysis results. The present analysis may provide the explanations for the complex natural mechanisms of the matter waves in the spinor BECs, and may have potential applications in designs of atom lasers, atom interferometry and coherent atom transport.

José Tito Mendonça, Hugo Terças

Dario Poletti, Tristram J. Alexander, Elena A. Ostrovskaya +2 more

We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realizes a flashing ratchet for matter-wave solitons. We find that the average velocity of a soliton and the soliton current induced by the ratchet depend on the number of atoms in the soliton. As a consequence, soliton transport can be induced through scattering of different solitons. In the regime when matter-wave solitons are narrow compared to the lattice period the dynamics is well described by the effective Hamiltonian theory.

Henry Luo

Solitons are non-dispersive wave packets that balance the wave dispersion with a focusing nonlinearity. They maintain their shape and velocity after collisions with other solitons, owing to the integrability of the underlying nonlinear partial differential equations. They appear in various physical systems, such as water waves, light waves in optical fiber, and matter waves. In our laboratory, we study solitons and their interactions in a Bose-Einstein condensate with an attractive nonlinearity, trapped in a quasi-one-dimensional waveguide. We investigate the collisions of a pair of solitons and explore the relative phase implications on the boundary of integrability. We study soliton train formation with the quench of the nonlinearity strength, and interactions between neighboring solitons in the train. We form a composite soliton, known as a breather, where multiple solitons overlap and the wavefunction ``breathes'' in time. We also explore the response of an elongated condensate to an external modulation of the nonlinearity. These experiments characterize the mean-field descriptions of solitons and Bose-Einstein condensates and explore the boundaries between the mean-field theory and quantum many-body theory.

S. M. Blinder