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International Journal of Modern Physics B

Regular and chaotic solutions in BEC for tilted bichromatical optical lattice

Eren Tosyalı, F. Aydogmus Sen, Ayberk Yılmaz

Published Aug 14, 2018• 5 citations
Publisher

Abstract

We investigate a Bose–Einstein condensate held in a 1D tilted bichromatical optical lattice potential by constructing its Poincaré sections in phase space. We explore dynamic of the system based on the relations between the system parameters and the solution behaviors. It is demonstrated that the system exhibits shock-wave like dynamic. The power spectrum graphs, bifurcation and Lyapunov exponents of BEC system are also presented.

DOI
10.1142/s0217979218502545

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We investigate a Bose–Einstein condensate held in a 1D tilted bichromatical optical lattice potential by constructing its Poincaré sections in phase space. We explore dynamic of the system based on the relations between the system parameters and the solution behaviors. It is demonstrated that the system exhibits shock-wave like dynamic. The power spectrum graphs, bifurcation and Lyapunov exponents of BEC system are also presented.
Using the direct perturbation technique,a general unstable chaotic solution was obtained of the Bose-Einstein condensates trapped in one-dimensional tilted optical lattice potential.The dynamical phase dia-gram of this system was studied.Theoretical analysis results and the corresponding numerical results showed the chaotic behavior of the system.It was found that Bose-Einstein condensate chaos could be controlled by chang-ing the wave length of the incident laser light or adjusting the system parameters.
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The chaotic dynamic characteristic in Bose-Einstein Condensate (BEC) system of a 1D tilted optical superlattice potential with attractive interaction is investigated in this paper. The spatial evolution of chaos was shown numerically by resolving Gross-Pitaevskii (G-P) equation for the system with the fourth Runge-Kutta(RK) algorithm. Numerical analysis reveals that as the tilt or the amplitude of the optical superlattice potential is increased the chaos in the BEC system increases. These elements make the chaotic system more unstable and the phase-space orbit becomes more chaotic. The chaotic system can be effectively controlled to a stable periodic orbit through adjusting the amplitude of the optical superlattice potential and initial condition. Controlling chaos can also be realized by spatial constant bias in the BEC system of a 1D tilted optical superlattice potential with attractive interaction. Phase orbits are suppressed gradually then the chaotic states of the BEC system are converted into period one through quais-period.
We study the dynamics of Bose-Einstein condensates in tilted and driven optical superlattices. For a bichromatic lattice, each Bloch band splits up into two minibands such that the dynamics is governed by the interplay of Bloch oscillations and transitions between the bands. Thus, bichromatic potentials provide an excellent model system for the study of nonlinear Landau-Zener tunneling, and they allow for a variety of applications in matter-wave interferometry and quantum metrology. In the present paper, we investigate the coherent dynamics of an interacting Bose-Einstein condensate as well as its stability. Different mechanisms of instability are discussed, which lead to a rapid depletion of the condensate.