  We investigate the existence of the $macroscopic$ $quantum$ $phase$ in
trapped ultracold quantum degenerate gases, such as Bose-Einstein condensate,
in an asymmetrical two-dimensional magnetic lattice. We show the key to
adiabatically control the tunneling in the new two-dimensional magnetic lattice
by means of external magnetic bias fields. The macroscopic quantum phase
signature is identified as a Rabi-like oscillation when solving the system of
coupled time-dependent differential equations, described here by the Boson
Josephson Junctions (BJJs). In solving the system of the BJJs we used an order
parameter that includes both time-dependent variational parameters which are
the fractional population at each lattice site and the phase difference. The
BJJs solution presents a clear evidence for the macroscopic quantum coherence.
