Energy spectrum and entanglement of two tunnel- coupled Bose--Einstein condensates

This paper obtains the energy-spectrum and eigenstate corrections of two-mode Bose--Einstein condensates (BECs) coupled by quantum tunnelling by perturbation method in both strong and weak tunnelling regions. The population imbalance between two BECs are then studied in terms of the low-lying eigenstates which also characterize the intrinsic entanglement between the two-mode BECs. The strong parity effect in the weak tunnelling region is also investigated.