Multi-species systems in optical lattices From orbital physics in excited bands to effects of disorder

Abstract: In this thesis we explore different aspects of the physics of multi-species atomic systems in optical lattices. In the first part we will study cold gases in the first and second excited bands of optical lattices - the p and d bands. The multi-species character of the physics in excited bands lies in the existence of an additional orbital degree of freedom, which gives rise to qualitative properties that are different from what is known for the systems in the ground band. We will introduce the orbital degree of freedom in the context of optical lattices and we will study the many-body systems both in the weakly interacting and in the strongly correlated regimes.We start with the properties of single particles in excited bands, from where we investigate the weakly interacting regime of the many-body p- and d-orbital systems in Chapters 2 and 3. This presents part of the theoretical framework to be used throughout this thesis, and covers part of the content of Paper I and of Preprint II. In Chapter 4, we study Bose-Einstein condensates in the p band, confined by a harmonic trap. This includes the finite temperature study of the ideal gas and the characterization of the superfluid phase of the interacting system at zero temperature for both symmetric and asymmetric lattices. This material is the content of Paper I.We continue with the strongly correlated regime in Chapter 5, where we investigate the Mott insulator phase of various systems in the p and d bands in terms of effective spin models. This covers the results of Paper II, of Preprint I and parts of Preprint II. More specifically, we show that the Mott phase with a unit filling of bosons in the p and in the d bands can be mapped, in two dimensions, to different types of XYZ Heisenberg models. In addition, we show that the effective Hamiltonian of the Mott phase with a unit filling in the p band of three-dimensional lattices has degrees of freedom that are the generators of the SU(3) group. Here we discuss both the bosonic and fermionic cases.In the second part, consisting of Chapter 6, we will change gears and study effects of disorder in generic systems of two atomic species. This is the content of Preprint III, where we consider different systems of non-interacting but randomly coupled Bose-Einstein condensates in 2D, regardless of an orbital degree of freedom. We characterize spectral properties and discuss the occurrence of Anderson localization in different cases, belonging to the different chiral orthogonal, chiral unitary, Wigner-Dyson orthogonal and Wigner-Dyson unitary symmetry classes. We show that the different properties of localization in the low-lying excited states of the models in the chiral and the Wigner-Dyson classes can be understood in terms of an effective model, and we characterize the excitations in these systems. Furthermore, we discuss the experimental relevance of the Hamiltonians presented here in connection to the Anderson and the random-flux models.