Adiabatic evolution of on-site superposition states in a completely-connected optical lattice

We analyze the dynamical melting of two-component atomic Mott-Insulator states in a completely-connected optical lattice within the adiabatic approximation. We examine in detail the effect of the dynamical phase acquired by the state during the adiabatic melting of the lattice potential. We show how for certain limits an on-site superposition state with two particles per site melts into a macroscopic superposition state, while an on-site superposition state with only one particle per site melts into a coherent state.