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We propose a new method to realize a two-dimensional magnetic lattice, having two different configurations of asymmetric magnetic lattice, which exhibits magnetic band gap structure, and a symmetric magnetic lattice. We also describe the tunneling mechanisms of magnetically trapped ultracold atoms, prepared in a degenerate quantum gas such as Bose-Einstein Condensate (BEC). A coherent quantum tunneling of ultracold atoms between the sites of the asymmetrical magnetic lattice can be realized which induces the adiabatically controlled dc Josephson current. At critical phase transitions, namely at certain values of site phase difference and population fraction, a plasma oscillation can be observed in which it forms a discharging Josephson state to be used as coherently coupled n quantum bits.