Abstract
We investigate the relation between quantum states and classical fixed-point bifurcations in a coupled two-component Bose-Einstein condensate (BEC). It is shown that the classical bifurcations are closely related to a topological change of the corresponding quantum levels, and such a structure change can be manifested in the entanglement properties of the corresponding quantum states. That is, the entanglement of the quantum states displays some peaks near the classical bifurcation points.
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