Gap solitons in elongated geometries: the one-dimensional Gross-Pitaevskii equation and beyond

Abstract

We report results of a systematic analysis of matter-wave gap solitons (GSs) in three-dimensional self-repulsive Bose-Einstein condensates (BECs) loaded into a combination of a cigar-shaped trap and axial optical-lattice (OL) potential. Basic cases of the strong, intermediate, and weak radial (transverse) confinement are considered, as well as settings with shallow and deep OL potentials. Only in the case of the shallow lattice combined with tight radial confinement, which actually has little relevance to realistic experimental conditions, does the usual one-dimensional (1D) cubic Gross-Pitaevskii equation (GPE) furnish a sufficiently accurate description of GSs. However, the effective 1D equation with the nonpolynomial nonlinearity, derived in Ref. [Phys. Rev. A \textbf{77}, 013617 (2008)], provides for quite an accurate approximation for the GSs in all cases, including the situation with weak transverse confinement, when the soliton's shape includes a considerable contribution from higher-order transverse modes, in addition to the usual ground-state wave function of the respective harmonic oscillator. Both fundamental GSs and their multipeak bound states are considered. The stability is analyzed by means of systematic simulations. It is concluded that almost all the fundamental GSs are stable, while their bound states may be stable if the underlying OL potential is deep enough.

14 pages, 12 figures; v2: matches published version

References in corpus (10)

• Solitons in nonlinear lattices
• Effective mean-field equations for cigar-shaped and disk-shaped Bose-Einstein condensates
• Quasi-1D Bose-Einstein condensates in the dimensional crossover regime
• Dynamics of Dark-Bright Solitons in Cigar-Shaped Bose-Einstein Condensates
• Splitting times of doubly quantized vortices in dilute Bose-Einstein condensates
• Tightly bound gap solitons in a Fermi gas
• Matter-wave vortices in cigar-shaped and toroidal waveguides
• Effective one-dimensional dynamics of elongated Bose-Einstein condensates
• Three-dimensional gap solitons in Bose-Einstein condensates supported by one-dimensional optical lattices
• Collisional-inhomogeneity-induced generation of matter-wave dark solitons

Cited by in corpus (11)

• Nonlinear waves of Bose-Einstein condensates in rotating ring lattice potentials
• Quasi-one-dimensional Bose-Einstein condensates in nonlinear lattices
• Effective equations for matter-wave gap solitons in higher-order transversal states
• Self-trapping of Fermi and Bose gases under spatially modulated repulsive nonlinearity and transverse confinement
• Effective equations for repulsive quasi-1D BECs trapped with anharmonic transverse potentials
• Exactly solvable Gross-Pitaevskii type equations
• Quasi-one-dimensional approximation for Bose-Einstein condensates transversely trapped by a funnel potential
• Soliton appearing in boson-fermion mixture at the third order of the interaction radius
• Accurate one-dimensional effective description of realistic matter-wave gap solitons
• Stable symmetry-protected 3D embedded solitons in Bose-Einstein condensates
• Tilt-Induced Localization in Interacting Bose-Einstein Condensates for Quantum Sensing