Out-of-equilibrium dynamics in the two-component Bose-Hubbard model

We study the out-of-equilibrium dynamics of the Bose-Hubbard model for two-component bosons using a strong-coupling approach within the closed-time-path formalism and develop an effective theory for the action of this problem. We obtain equations of motion for the superfluid order parameters of both boson species for both the superfluid and Mott-insulating phases and study these in the low-frequency, long-wavelength limit during a quantum quench for various initial conditions. We find that an additional degree of freedom for bosons leads to a richer phase diagram and out-of-equilibrium dynamics than the single-component situation.