  A resonantly driven bosonic Josephson junction supports stable collective
excitations, or quasiparticles, which constitute analogs of the Trojan wave
packets previously explored with Rydberg atoms in strong microwave fields. We
predict a quantum beating effect between such symmetryrelated many-body Trojan
states taking place on time scales which are long in comparison with the
driving period. Within a mean-field approximation, this quantum beating can be
regarded as a manifestation of dynamical tunneling. On the full N-particle
level, the beating phenomenon leads to an experimentally feasible, robust
strategy for probing highly entangled mesoscopic states.
