  Hexagonal optical lattices offer a tunable platform to study exotic orbital
physics in solid state materials. Here, we present a versatile high-precision
scheme to implement a hexagonal optical lattice potential, which is engineered
by overlapping two independent triangular optical sublattices generated by
laser beams with slightly different wavelengths around 1064 nm. This enables us
to precisely control the detailed structure of the hexagonal lattice by
adjusting the relative position and the relative lattice depth of the two
triangular optical sublattices. Taking advantage of the sensitive dependence of
the second Bloch band on small lattice deformations, we propose a strategy to
optimize the optical lattice geometry with an extremely high precision. This
method can also be extended to other lattice configurations involving more than
two sublattices. Our work provides the experimental requirements in the search
for novel orbital physics of ultracold atoms, for example, in the flat $p$-band
of the hexagonal optical lattice.

Quantum Gases