Overlaying commensurate optical lattices with various configurations called superlattices can lead to exotic lattice topologies and, in turn, a discovery of novel physics. In this study, by overlapping the maxima of lattices, a new isolated structure is created, while the interference of minima can generate various sublattice patterns. Three different kinds of primitive lattices are used to demonstrate isolated square, triangular, and hexagonal sublattice structures in a two-dimensional optical superlattice, the patterns of which can be manipulated dynamically by tuning the polarization, frequency, and intensity of laser beams. In addition, we propose the method of altering the relative phase to adjust the tunneling amplitudes in sublattices. Our configurations provide unique opportunities to study particle entanglement in lattices formed by intersecting wells and to implement special quantum logic gates in exotic lattice geometries.
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