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

Sadhan K. Adhikari

Oct 19, 20050 citations

Dark Soliton of a Growing Bose–Einstein Condensate in an External Trap

Hong Li, Wang D N.

The dynamics of dark soliton in a growing Bose–Einstein condensate with an external magnetic trap are investigated by the variational approach based on the renormalized integrals of motion. The stationary states as physical solutions to the describing equation are obtained, and the evolution of the dark soliton is numerically simulated. The numerical results confirm the theoretical analysis and show that the dynamics depend strictly on the initial condition, the gain coefficient and the external potential.The dynamics of dark soliton in a growing Bose–Einstein condensate with an external magnetic trap are investigated by the variational approach based on the renormalized integrals of motion. The stationary states as physical solutions to the describing equation are obtained, and the evolution of the dark soliton is numerically simulated. The numerical results confirm the theoretical analysis and show that the dynamics depend strictly on the initial condition, the gain coefficient and the external potential.

Chinese Physics LettersOct 30, 20083 citations

Variational approach to the snake instability of a Bose-Einstein condensate soliton

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.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.

arXiv:2507.04926Physical Review ADec 23, 20250 citations

Dark Soliton Dynamics In Bose-Einstein Condensates

P. G. Kevrekidis

Bulletin of the American Physical SocietyMar 15, 20100 citations

Stable and mobile two-dimensional dipolar ring-dark-in-bright Bose–Einstein condensate soliton

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.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.

arXiv:1601.01519Laser Physics LettersFeb 8, 20165 citations

Interacting multiple zero mode formulation for a dark soliton in a Bose-Einstein condensate

Junichi Takahashi, Yusuke Nakamura, Y. Yamanaka

Bulletin of the American Physical SocietyMar 14, 20160 citations

Simulation of a Stationary Dark Soliton in a Trapped Zero-Temperature Bose-Einstein Condensate

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