Correlation and entanglement of two-component Bose-Einstein condensates in a double well

We consider a novel system of two-component atomic Bose-Einstein condensate in a double-well potential. Based on the well-known two-mode approximation, we demonstrate that there are obvious avoided level-crossings when both interspecies and intraspecies interactions of two species are increased. The quantum dynamics of the system exhibits revised oscillating behaviors compared with a single component condensate. We also examine the entanglement of two species. Our numerical calculations show the onset of entanglement can be signed as a violation of Cauchy-Schwarz inequality of second-order cross correlation function. Consequently, we use Von Neumann entropy to quantity the degree of entanglement.