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Nonlinear Dynamics

Bifurcation response and Melnikov chaos in the dynamic of a Bose–Einstein condensate loaded into a moving optical lattice

Sylvin Tchatchueng, M. Siewe Siewe, F. M. Moukam Kakmeni, Clément Tchawoua

Published Oct 9, 2013• 4 citations
Publisher
DOI
10.1007/s11071-013-1078-2

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We have shown that the application of modulating the secondary lattice is an efficient route to suppressing the generation of chaotic traveling waves of a Bose–Einstein Condensate with attractive interatomic interaction loaded into a moving optical superlattice consisting of two lattices. With the Melnikov method, we obtain the optimal value of the relative phase between the two lattice harmonics for the control of chaos. We also find that the regularization route as the potential depth of the secondary lattice is varied and fairly rich, including the period-doubling bifurcations.
Chaotic space-time evolution is investigated for the particle number density of a Bose-Einstein condensate with attractive interatomic interaction loaded into a traveling optical lattice. Melnikov chaos is studied and the weakly chaotic regime is presented analytically. Transitions from transient to stationary chaos in the space-time evolution are illustrated numerically. The results show that, on increasing the strength of the optical potential, the transient chaos falls onto several different attractors. Meanwhile, these attractors undergo a series of period-doubling bifurcations when the optical potential intensity is increased continuously, and eventually stationary chaos arises for a critical depth of the optical lattice. The obstructions to chaos caused by the damping and the motion of lattice are also demonstrated.