  We discuss how an $\eta$-condensate, corresponding to an exact excited
eigenstate of the Fermi-Hubbard model, can be produced with cold atoms in an
optical lattice. Using time-dependent density matrix renormalisation group
methods, we analyse a state preparation scheme beginning from a band insulator
state in an optical superlattice. This state can act as an important test case,
both for adiabatic preparation methods and the implementation of the many-body
Hamiltonian, and measurements on the final state can be used to help detect
associated errors.
