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We discuss here ground-state and nonequilibrium poperties of ultracold atoms in optical lattices in the strongly correlated limit. Starting with the study of bosonic [1] and fermionic [2,3] Mott-insulators 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 [4], and their nonequilibrium dynamics, where a quasi-condensate emerges at finite momentum from a Fock state [5]. Moreover, it will be shown that 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 [6].
[1] G.G. Batrouni, V. Rousseau, R.T. Scalettar, M. Rigol, A. Muramatsu, P.J.H. Denteneer, and M. Troyer, Phys. Rev. Lett. 89, 117203 (2002). [2] M. Rigol, A. Muramatsu, G.G. Batrouni, and R.T. Scalettar, Phys. Rev. Lett. 91, 130403 (2003). [3] M. Rigol and A Muramatsu, Phys. Rev. A 69, 053612 (2004). [4] M. Rigol and A Muramatsu, Phys. Rev. A 70, 031603(R) (2004). [5] M. Rigol and A. Muramatsu, Phys. Rev. Lett. 93, 230404 (2004). [6] M. Rigol and A. Muramatsu, Phys. Rev. Lett. 94, 240403 (2005). |
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