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Regular and chaotic behaviors of collective atomic motion in two-component Bose-Einstein condensates | | Wei-Can Syu
; Da-Shin Lee
; Chi-Yong Lin
; | | Date: |
21 Jan 2020 | | Abstract: | We theoretically study binary Bose-Einstein condensates trapped in a
single-well harmonic potential to probe the dynamics of collective atomic
motion. The idea is to choose tunable scattering lengths through Feshbach
resonances such that the ground state wavefunction for two types of the
condensates are spatially immiscible where one of the condensates, located at
the center of the potential trap, can be effectively treated as a potential
barrier between bilateral condensates of the second type of atoms. In the case
of small wavefunction overlap between bilateral condensates, one can
parametrize their spatial part of the wavefunctions in the two-mode
approximation together with the time-dependent population imbalance $z$ and the
phase difference $phi$ between two wavefunctions. The condensate in the middle
can be approximated by a Gaussian wavefunction with the displacement of the
condensate center $xi$. As driven by the time-dependent displacement of the
central condensate, we find the Josephson oscillations of the collective atomic
motion between bilateral condensates as well as their anharmonic generalization
of macroscopic self-trapping effects. In addition, with the increase in the
wavefunction overlap of bilateral condensates by properly choosing tunable
atomic scattering lengths, the chaotic oscillations are found if the system
departs from the state of a fixed point. The Melnikov approach with a
homoclinic solution of the derived $z,phi$ and $xi$ equations can
successfully justify the existence of chaos. All results are consistent with
the numerical solutions of the full time-dependent Gross-Pitaevskii equations. | | Source: | arXiv, 2001.7379 | | Services: | Forum | Review | PDF | Favorites | |
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