Stability of Counterflow Superfluidity*

We examine the stability of the counterflow superfluid state in two component mixtures of ultracold atoms in optical lattices. Using a Gutzwiller mean-field approach, we find a sharp boundary separating stable counterflow from a dynamically unstable regime. As the inter-component interaction strength increases, the critical counterflow rate drops, falling to zero when interactions are strong enough to induce phase separation of the two components. Going beyond mean-field theory, we compute the decay rate of counterflow within the stable regime due to phase slips. The results agree well with numerically exact simulations and are calculated in a regime of parameters relevant to current experiments on mixtures of ultracold alkali atoms.