Phase Transition, Entanglement and Squeezing in a Triple-Well Condensate

We provide an in-depth characterization of a three modes Bose-Einstein condensate trapped in a symmetric circular triple well potential. We analyze how a subsystem independent measure of entanglement, the purity related to the su(3) algebra, scales for increasing number of atoms and signals correctly the quantum phase transition between two dynamical regimes in a specific arrangement. Moreover, this measure, which is intrinsically related to particle entanglement, also depicts if some squeezing is occurring when we consider the system's ground state.