Generation of twin Fock states via transition from a two-component Mott insulator to a superfluid

We propose the dynamical creation of twin Fock states, which exhibit Heisenberg limited interferometric phase sensitivities, in an optical lattice. In our scheme a two-component Mott insulator with two bosonic atoms per lattice site is melted into a superfluid. This process transforms local correlations between hyperfine states of atom pairs into multi-particle correlations extending over the whole system. The melting time does not scale with the system size which makes our scheme experimentally feasible.