Abstract
We discuss in this paper ground‐state and nonequilibrium properties of ultracold atoms in optical lattices in the strongly correlated limit. We review fermionic Mott‐insulators studied on the basis of quantum Monte Carlo simulations, where local quantum criticality is displayed in one dimension. We continue with exact results for hard‐core bosons in one dimension, showing their universal properties in equilibrium, and their nonequilibrium dynamics. Here we show that starting from a Fock state, a quasi‐condensate emerges at finite momentum during free expansion. On the other hand, the free evolution of an initially confined quasi‐condensate of hard‐core bosons leads to a bosonic gas with a Fermi edge, and hence a fermionization that can only be obtained out of equilibrium.
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