Simulation of a stable dark soliton in a trapped Bose-Einstein condensate

Sadhan K. Adhikari

Sadhan K. Adhikari

Abstract We demonstrate robust, stable, mobile two-dimensional (2D) dipolar ring-dark-in-bright (RDB) Bose–Einstein condensate (BEC) solitons for repulsive contact interaction, subject to a harmonic trap along the y direction perpendicular to the polarisation direction z . Such a RDB soliton has a ring-shaped notch (zero in density) imprinted on a 2D bright soliton free to move in the x − z plane. At medium velocity the head-on collision of two such solitons is found to be quasi-elastic with practically no deformation. The possibility of creating the RDB soliton by phase imprinting is demonstrated. The findings are illustrated using numerical simulation employing realistic interaction parameters in a dipolar 164 Dy BEC.

P. G. Kevrekidis

U. Tanyeri, M. A. Gürkan, Ahmet Keleş +1 more

Solitons are striking manifestations of nonlinearity, encountered in diverse physical systems such as water waves, nonlinear optics, and Bose-Einstein condensates (BECs). In BECs, dark solitons emerge as exact stationary solutions of the one-dimensional Gross-Pitaevskii equation. While they can be long-lived in elongated traps, their stability is compromised in higher dimensions due to the snake instability, which leads to the decay of the soliton into vortex structures among other excitations. We investigate the dynamics of a dark soliton in a Bose-Einstein condensate confined in an anisotropic harmonic trap. Using a variational ansatz that incorporates both the transverse bending of the soliton plane and the emergence of vortices along the nodal line, we derive equations of motion governing the soliton's evolution. This approach allows us to identify stable oscillation modes as well as the growth rates of the unstable perturbations. In particular, we determine the critical trap anisotropy required to suppress the snake instability. Our analytical predictions are in good agreement with full numerical simulations of the Gross-Pitaevskii equation.

V. V. Konotop

Zhiqiang Zhang, Tie-Zhu Yang, Shusheng Meng +1 more

By using multiple-scale method, we analytically study the soliton dynamics of Bose–Einstein condensate (BEC) trapped in a double square well potential. It is shown that dark soliton can be stable, which is generated in BEC trapped in a double square well. The amplitude and the width of dark soliton are related to the initial position of the soliton. Within the double square well, because of the confinement of the potential, the amplitude of the dark soliton is larger, while the width of the dark soliton is smaller. Furthermore, we also find that the amplitude and the width of the soliton are closely related to the depth of the double square well. With the increase of the depth, the amplitude of the dark soliton increases remarkably, while the width of the dark soliton decreases slowly.