  In a Josephson junction (JJ), Cooper pairs are transported via Andreev bound
states (ABSs) between superconductors. The ABSs in the weak link of
multi-terminal (MT) JJs can coherently hybridize two Cooper pairs among
different superconducting electrodes, resulting in the Cooper quartet (CQ)
involving four fermions entanglement. The energy spectrum of these CQ-ABS can
be controlled by biasing MT-JJs due to the AC Josephson effect. Here, using
gate tunable four-terminal graphene JJs complemented with a flux loop, we
construct CQs with a tunable spectrum. The critical quartet supercurrent
exhibits magneto-oscillation associated with a charge of 4e; thereby presenting
the evidence for interference between entangled CQ-ABS. At a finite bias
voltage, we find the DC quartet supercurrent shows non-monotonic bias dependent
behavior, attributed to Landau-Zener transitions between different Floquet
bands. Our experimental demonstration of coherent non-equilibrium CQ-ABS sets a
path for design of artificial topological materials based on MT-JJs.
