Multiparticle entanglement dynamics of quantum chaos in a Bose-Einstein condensate

We study the particle-entanglement dynamics witnessed by the quantum Fisher information (QFI) of a trapped Bose-Einstein condensate governed by the kicked rotor Hamiltonian. The dynamics is investigated with a beyond-mean-field approach. We link the time scales of the validity of this approximation in both classical regular and chaotic regions, with the maximum Lyapunov exponents of the classical system. This establishes an effective connection between the classical chaos and the QFI. We finally study the critical point of a quantum phase transition using the beyond-mean-field approximation by considering a two-mode bosonic Josephson junction with attractive interparticle interaction.