We present the analysis of hysteresis for motion of soliton of Bose-Einstein condensate (i) between two oscillating atomic mirrors and (ii) above one oscillating mirror in presence of gravitation force.
We have proposed a mechanical model that corresponds to the Newton equation for describing the dynamics of an oscillon, viz., a soliton-like cluster of the Bose–Einstein condensate (with atomic attraction) placed above an oscillating atomic mirror in a uniform gravitational field. The model describes the stochastic Fermi acceleration and periodic, quasi-periodic, and chaotic motion of the oscillon center, as well as hysteresis phenomena in the case of a slow variation of mirror oscillation frequency, which are in good agreement with the results obtained using the Gross–Pitaevskii equation.
The dynamics of the soliton in a self-attractive Bose–Einstein condensate under the gravity are investigated. First, we apply the inverse scattering method, which gives rise to equation of motion for the center-of-mass coordinate of the soliton. We analyze the amplitude-frequency characteristic for nonlinear resonance. Applying the Krylov–Bogoliubov method for the small parameters the dynamics of soliton on the phase plane are considered. Hamiltonian chaos under the action of the gravity on the Poincaré map are studied.
We find a matter-wave solution of Bose-Einstein condensates trapped in a harmonic-oscillator potential and subjected to a homogeneous gravitational field, by means of the extended tanhfunction method. This solution has as special cases the bright and dark solitons. We investigate the dynamics and the kinematics of these solutions, and the role of gravity is sketched. It is shown that these solutions can be generated and manipulated by controlling the s-wave scattering length, without changing the strengths of the magnetic and gravitational fields.
The dynamics of matter-wave solitons in Bose-Einstein condensates (BEC) is considerably affected by the presence of a thermal cloud and the dynamical depletion of the condensate. Our numerical results, based on the time-dependent Hartree-Fock-Bogoliubov theory, demonstrate the collapse of the attractively interacting BEC via collisional emission of atom pairs into the thermal cloud, which splits the (quasi-one-dimensional) BEC soliton into two partially coherent solitonic structures of opposite momenta. These incoherent matter waves are analogous to optical random-phase solitons.
Abstract We present a possible way to control matter-wave solitons, which is through the collision between solitons and an accelerating atomic mirror. The acceleration of the mirror has a nontrivial effect on the dynamical characters of the reflected solitons. In the one-dimensional Bose–Einstein condensates, when the acceleration of the mirror has the identical direction with the initial soliton’s velocity, the soliton will diffuse after collision; in the contrasting case, the soliton will shrink and then diffuse. We quantitatively explain the above dynamical phenomena by analyzing the atoms’ movement in the soliton, and demonstrate that the method can generate a similar effect to the phase imprinting technology. Moreover, considering the dipolar effect between atoms, this approach can be used for the generation and control of breathing solitons.