Numerical and variational solutions of the dipolar Gross-Pitaevskii equation in reduced dimensions

Abstract

We suggest a simple Gaussian Lagrangian variational scheme for the reduced time-dependent quasi-one- and quasi-two-dimensional Gross-Pitaevskii (GP) equations of a dipolar Bose-Einstein condensate (BEC) in cigar and disk configurations, respectively. The variational approximation for stationary states and breathing oscillation dynamics in reduced dimensions agrees well with the numerical solution of the GP equation even for moderately large short-range and dipolar nonlinearities. The Lagrangian variational scheme also provides much physical insight about soliton formation in dipolar BEC.

7 pages, 4 figures

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Cited by in corpus (25)

• Fortran and C programs for the time-dependent dipolar Gross-Pitaevskii equation in an anisotropic trap
• Vortex dynamics of rotating dipolar Bose-Einstein condensates
• Quasi-one-dimensional spin-orbit- and Rabi-coupled bright dipolar Bose-Einstein-condensate solitons
• All-optical production of a superfluid Bose-Fermi mixture of ${}^6$Li and ${}^7$Li
• Anisotropic sound and shock waves in dipolar Bose-Einstein condensate
• Effect of an oscillating Gaussian obstacle in a Dipolar Bose-Einstein condensate
• Self trapping of a dipolar Bose-Einstein condensate in a double well
• A self-bound matter-wave boson-fermion quantum ball
• Dynamics of the corotating vortices in dipolar Bose-Einstein condensates in the presence of dissipation
• Effective equations for matter-wave gap solitons in higher-order transversal states
• Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates
• Stabilization of trapless dipolar Bose-Einstein condensates by temporal modulation of the contact interaction
• Harmonically trapped attractive and repulsive spin-orbit and Rabi coupled Bose-Einstein condensates
• Effect of optical lattice potentials on the vortices in rotating dipolar Bose-Einstein condensates
• Matter-waves in Bose-Einstein condensates with spin-orbit and Rabi couplings
• Stable and mobile two-dimensional dipolar ring-dark-in-bright Bose-Einstein condensate soliton
• Bright solitons in a quasi-one-dimensional reduced model of a dipolar Bose-Einstein condensate with repulsive short-range interactions
• Stability of trapped degenerate dipolar Bose and Fermi gases
• Accurate one-dimensional effective description of realistic matter-wave gap solitons
• Stable and mobile excited two-dimensional dipolar Bose-Einstein condensate solitons
• Binary Mixture of quasi one dimensional dipolar Bose Einstein Condensates with tilted dipoles
• Study of a degenerate dipolar Fermi gas of 161Dy atoms
• Anharmonicity-Induced Criticality of Collective Excitation in a Trapped Bose-Einstein Condensate
• Characterization of the energy level-structure of a trapped dipolar Bose gas via mean-field parametric resonances
• Anisotropic merging and splitting of dipolar Bose-Einstein condensates