Macroscopic quantum self-trapping in bosonic Josephson junctions: An exact quantum treatment

We investigate the fully quantum evolution of the population imbalance in a perfectly symmetric Bose-Josephson junction modeled by a two-mode Bose-Hubbard Hamiltonian, focusing on the validity of macroscopic quantum self-trapping beyond the mean-field theory. We show that for any finite number of particles, the exact quantum dynamics leads to the breakdown of macroscopic quantum self-trapping after a finite time, regardless of the initial state. Using the symmetries of the Bose-Hubbard Hamiltonian, we provide a mathematical demonstration of this result and analyze the spectral properties governing the dynamics. We identify a branching behavior in the eigenvalue differences and a nontrivial structure of the population-imbalance amplitudes. These features allow us to distinguish two clearly different dynamical regimes and to elucidate the mechanism leading to the emergence of a quasi–macroscopic quantum self-trapping regime for large particle numbers. These findings bridge the gap between mean-field predictions and exact quantum dynamics and provide insight into the emergence of classical nonlinear behavior from finite quantum many-body systems.