The response of bright and dark solitons to rapid variations in an expulsive longitudinal trap is investigated. We concentrate on the effect of transient changes in the trap frequency in the form of temporal delta kicks and the hyperbolic cotangent functions. Exact expressions are obtained for the soliton profiles. This is accomplished using the fact that a suitable linear Schrodinger stationary state solution in time can be effectively combined with the solutions of non-linear Schrodinger equation, for obtaining solutions of the Gross-Pitaevskii equation with time dependent scattering length in a harmonic trap. Interestingly, there is rapid pulse amplification in certain scenarios.
Experimentally observed grey solitons are analytically extracted from a physically viable \GP equation. Associated Lieb and Bogoliubov modes are calculated for these class of solitons. It is observed that, these nonlinear excitations have strong coupling with the trap at low momenta and hence can be effectively isolated from the Bogoliubov sound modes, which responds weakly to harmonic confinement. This strong coupling with the trap also makes the grey soliton amenable for control and manipulation through both trap modulation and temporal variation of the two-body interaction.
We derive exact solitonic solutions of a class of Gross-Pitaevskii equations with time-dependent harmonic trapping potential and interatomic interaction. We find families of exact single-solitonic, multi-solitonic, and solitary wave solutions. We show that, with the special case of an oscillating trapping potential and interatomic interaction, a soliton can be localized indefinitely at an arbitrary position. The localization is shown to be experimentally possible for sufficiently long time even with only an oscillating trapping potential and a constant interatomic interaction.
We investigate the dynamics of a spin-orbit (SO) coupled BECs in a time dependent harmonic trap and show the dynamical system to be completely integrable by constructing the Lax pair. We then employ gauge transformation approach to witness the rapid oscillations of the condensates for a relatively smaller value of SO coupling in a time independent harmonic trap compared to their counterparts in a transient trap. Keeping track of the evolution of the condensates in a transient trap during its transition from confining to expulsive trap, we notice that they collapse in the expulsive trap. We fur…
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…
We investigate the exact bright and dark solitary wave solutions of an effective one dimensional (1D) Bose-Einstein condensate (BEC) by assuming that the interaction energy is much less than the kinetic energy in the transverse direction. In particular, following the earlier works in the literature Pérez-García et al. [Physica D 221 (2006) 31], Serkin et al. [Phys. Rev. Lett. 98 (2007) 074102], Gürses [arXiv:0704.2435] and Kundu [Phys. Rev. E 79 (2009) 015601], we point out that the effective 1D equation res ulting from the Gross-Pitaevskii (GP) equation can be transformed into the stand ard s…
