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 multiparticle correlations extending over the whole system. The melting time does not scale with the system size which makes our scheme experimentally feasible.