  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.
