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

Journal Article · Sun May 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.053610· OSTI ID:21546823

Mateo, A Munoz; Delgado, V ^[1]; Malomed, Boris A ^[2]

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1. Departamento de Fisica Fundamental II, Facultad de Fisica, Universidad de La Laguna, E-38206 La Laguna, Tenerife (Spain)
2. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv IL-69978 (Israel)

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 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.

• OSTI ID: 21546823
• Journal Information: Physical Review. A, Vol. 83, Issue 5; Other Information: DOI: 10.1103/PhysRevA.83.053610; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
APPROXIMATIONS
BOSE-EINSTEIN CONDENSATION
CONFINEMENT
EQUATIONS
HARMONIC OSCILLATORS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
SIMULATION
SOLITONS
STABILITY
THREE-DIMENSIONAL CALCULATIONS
TRAPS
WAVE FUNCTIONS
CALCULATION METHODS
FUNCTIONS
QUASI PARTICLES