Nonlinear Phenomena in Complex Systems, 2007, Vol.10, No.2, pp.155-163

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2007, Vol.10, No.2, pp.155-163

Nonlinear Dynamics of Bose-Einstein Condensates: Wave Interference Versus Soliton Molecules.
Katsuhiro Nakamura

Role of nonlinearity in the dual (wave-and-particle) aspect of wavepacket dynamics in Bose-Einstein condensates (BECs) is considered. The analysis is based on the nonlinear Schrödinger equation (Gross-Pitaevskii equation). Firstly we investigate the wave aspect. Dynamics of a macroscopic wave packet for BECs falling through the double slits is analyzed. The subject is identified with a search for the fate of a soliton showing a head-on collision with a hard-walled obstacle of finite size. We explore the splitting of the wave packet and its reorganization to form an interference pattern. Particular attention is paid to the role of gravity and repulsive nonlinearity in the fringe pattern. Secondly we examine a particle picture for interacting wavepackets (WPs) and explore the emergence of chaos in soliton molecules. We choose multicomponent BECs with a harmonic trap in two dimensions, and develop the variational principle. The inclusion of intercomponent interaction (ICI) strongly mixes the motions between the separation of center-of-masses and WP width and results in a fat mode that breaks the particle picture, which, however, can be recovered by introducing a time-periodic ICI with zero average. In the case of a molecule of three wave packets for a three-component BEC, the increase of ICI amplitude yields a transition from regular to chaotic oscillations in the WP breathing.
Key words: wave packet dynamics, Bose-Einstein condensates, double slit, soliton molecule

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