Stationary states of a nonlinear Schrödinger lattice with a harmonic trap
arXiv:1110.3172 · doi:10.1063/1.3625953
Abstract
We study a discrete nonlinear Schrödinger lattice with a parabolic trapping potential. The model, describing, e.g., an array of repulsive Bose-Einstein condensate droplets confined in the wells of an optical lattice, is analytically and numerically investigated. Starting from the linear limit of the problem, we use global bifurcation theory to rigorously prove that - in the discrete regime - all linear states lead to nonlinear generalizations thereof, which assume the form of a chain of discrete dark solitons (as the density increases). The stability of the ensuing nonlinear states is studied and it is found that the ground state is stable, while the excited states feature a chain of stability/instability bands. We illustrate the mechanisms under which discreteness destabilizes the dark-soliton configurations, which become stable only inside the continuum regime. Continuation from the anti-continuum limit is also considered, and a rich bifurcation structure is revealed.
17 pages, 9 figures
References in corpus (7)
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons
- Nonlinear modes for the Gross-Pitaevskii equation -- demonstrative computation approach
- Stability of excited states of a Bose-Einstein condensate in an anharmonic trap
- High-Order-Mode Soliton Structures in Two-Dimensional Lattices with Defocusing Nonlinearity
- Surface modes and breathers in finite arrays of nonlinear waveguides