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.
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