Coherent transfer by adiabatic passage in two-dimensional lattices

•New ways of coherent transport by adiabatic passage (CTAP) in 2D lattices.•Synthesis of exactly-solvable 2D lattices from a simple three-well model.•CTAP in 2D lattices can be exploited for quantum state transfer.

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.