  Coherent tunneling by adiabatic passage (CTAP) is a well-established
technique for robust spatial transport of quantum particles in linear chains.
Here we introduce two exactly-solvable models where the CTAP protocol can be
extended to two-dimensional lattice geometries. Such bi-dimensional lattice
models are synthesized from time-dependent second-quantization Hamiltonians, in
which the bosonic field operators evolve adiabatically like in an ordinary
three-level CTAP scheme thus ensuring adiabatic passage in Fock space.
