  We report a detailed theoretical study of a coherent macroscopic
quantum-mechanical phenomenon - quantum beats of a single magnetic fluxon
trapped in a two-cell SQUID of high kinetic inductance. We calculate
numerically and analytically the low-lying energy levels of the fluxon, and
explore their dependence on externally applied magnetic fields. The quantum
dynamics of the fluxon shows quantum beats originating from its coherent
quantum tunneling between the SQUID cells. We analyze the experimental setup
based on a three-cell SQUID, allowing for time-resolved measurements of quantum
beats of the fluxon.
