  There has been much recent progress in controlling $p$-orbital degrees of
freedom in optical lattices, for example with lattice shaking, sublattice
swapping, and lattice potential programming. Here, we present a protocol of
preparing lowest Landau level (LLL) states of cold atoms by adiabatically
compressing $p$-orbital Bose-Einstein condensates confined in two-dimensional
optical lattices. The system starts from a chiral $p+ip$ Bose-Einstein
condensate (BEC) state, which acquires finite angular momentum by spontaneous
symmetry breaking. Such chiral BEC states have been achieved in recent optical
lattice experiments for cold atoms loaded in the $p$-bands. Through an
adiabatic adjustment of the lattice potential, we compress the
three-dimensional BEC into a two-dimensional system, in which the orbital
degrees of freedom continuously morph into LLL states. This process is enforced
by the discrete rotation symmetry of the lattice potential. The final quantum
state inherits large angular momentum from the original chiral $p+ip$ state,
with one quantized unit per particle. We investigate the quantum many-body
ground state of interacting bosons in the LLL considering contact repulsion.
This leads to an exotic gapped BEC state. Our theory can be readily tested in
experiments for the required techniques are all accessible to the current
optical lattice experiments.
