In the first part of the talk, I will give an overview of some problems that we have studied, in which cold atoms in optical lattices can be used as a quantum simulator to help us understand the phenomenon of high-Tc superconductivity. These include the generation of a pi-flux phase [1,2], p-wave superfluidity in higher bands [3], the realization of eta pairing [4], and the loss of phase coherence in the presence of lattice distortions [5]. Then, I will concentrate on topological states of matter, which
are peculiar quantum phases showing different edge and bulk transport properties connected by the bulk-boundary correspondence. While non-interacting fermionic topological insulators are well established by now and have been classified according to a ten-fold scheme, the possible realisation of topological states for bosons has not been much explored yet. Furthermore, the role of interactions is far from being understood. We show that a topological state of matter exclusively driven by interactions may occur in the p-band of a Lieb optical lattice filled with ultracold bosons. The single-particle spectrum of the system displays a remarkable parabolic band-touching point, with both bands exhibiting non-negative curvature. Although the system is neither topological at the single-particle level, nor for the interacting ground state, on-site interactions induce an anomalous Hall effect for the excitations, carrying a non-zero Chern number. Our work introduces an experimentally realistic strategy for the formation of interaction-driven topological states of bosons [6].
[1] A. Hemmerich and C. Morais Smith, Phys. Rev. Lett. 99, 113002 (2007)
[2] Lih-King Lim, C. Morais Smith, Andreas Hemmerich, Phys. Rev. Lett. 100, 130402 (2008)
[3] M. Ölschläger, T. Kock, G. Wirth, A. Ewerbeck, C. Morais Smith, A. Hemmerich, New Journal of Physics 15, 083041 (2013)
[4] M. Di Liberto, C. E. Creffield, G. I. Japaridze, C. Morais Smith Phys. Rev. A 89, 013624 (2014)
[5] M. Di Liberto, T. Comparin, T. Kock, M. Ölschläger, A. Hemmerich, C. Morais Smith, Nature Communications 5, 5735 (2014)
[6] M. Di Liberto, A. Hemmerich, C. Morais Smith, Phys. Rev. Lett. 117, 163001 (2016)
