  We consider a one-dimensional gas of cold atoms with strong contact
interactions and construct an effective spin-chain Hamiltonian for a
two-component system. The resulting Heisenberg spin model can be engineered by
manipulating the shape of the external confining potential of the atomic gas.
We find that bosonic atoms offer more flexibility for tuning independently the
parameters of the spin Hamiltonian through interatomic (intra-species)
interaction which is absent for fermions due to the Pauli exclusion principle.
Our formalism can have important implications for control and manipulation of
the dynamics of few- and many-body quantum systems; as an illustrative example
relevant to quantum computation and communication, we consider state transfer
in the simplest non-trivial system of four particles representing
exchange-coupled qubits.
