Modulated Amplitude Waves in Collisionally Inhomogeneous Bose-Einstein Condensates

Abstract

We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length $a$ subjected to a spatially periodic modulation, $a=a(x)=a(x+L)$. This "collisionally inhomogeneous" BEC is described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is a periodic function of $x$. We transform this equation into a GP equation with constant coefficient $a$ and an additional effective potential and study a class of extended wave solutions of the transformed equation. For weak underlying inhomogeneity, the effective potential takes a form resembling a superlattice, and the amplitude dynamics of the solutions of the constant-coefficient GP equation obey a nonlinear generalization of the Ince equation. In the small-amplitude limit, we use averaging to construct analytical solutions for modulated amplitude waves (MAWs), whose stability we subsequently examine using both numerical simulations of the original GP equation and fixed-point computations with the MAWs as numerically exact solutions. We show that "on-site" solutions, whose maxima correspond to maxima of $a(x)$, are significantly more stable than their "off-site" counterparts.

25 pages, 10 figures (many with several parts), to appear in Physica D; higher resolution versions of some figures are available at http://www.its.caltech.edu/~mason/papers

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Cited by in corpus (10)

• Localized nonlinear waves in systems with time- and space-modulated nonlinearities
• Spontaneous symmetry breaking in a nonlinear double-well structure
• Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity
• Matter-wave solitons with a periodic, piecewise-constant nonlinearity
• Solitary Waves Under the Competition of Linear and Nonlinear Periodic Potentials
• Solitary waves for linearly coupled nonlinear Schrodinger equations with inhomogeneous coefficients
• Dissipative Dynamics of Matter Wave Soliton in Nonlinear Optical Lattice
• Laser tweezers for atomic solitons
• Averaging of Nonlinearity Management with Dissipation
• Matter-Wave Solitons in the Presence of Collisional Inhomogeneities: Perturbation theory and the impact of derivative terms