T1: Rotons and magnetism in dipolar condensates in optical lattices

In this project we will focus on qualitatively new phenomena occurring in dipolar Bose-Einstein condensates (BECs). This analysis is particularly relevant for on-going experiments on condensates of highly-magnetic atoms, as dysprosium (project E1) and erbium (project E2), but most of the conclusions may be extrapolated to polar molecules as well. We will be particularly concerned on roton-like excitations, a major novel feature in dipolar BECs when compared to non-dipolar ones. These excitations are expected in pancake-like traps with a large-enough aspect ratio, although no experimental detection has been reported. In our first subproject we will study roton-like excitations in dipolar BECs, and in particular the optimal conditions for the experimental observation of rotons in on-going experiments in projects E1 and E2, phonon-to-roton instability transition, roton confinement, inter-site roton hopping, and the spatial distribution of the condensate depletion. Our second subproject will analyse spinor BECs. We will be particularly interested on the idea of roton immiscibility, i.e. the instability against the formation of short-wavelength immiscible domains given by a roton-like feature in the spin-excitation spectrum. We will focus in particular on the spatial dependence of roton immiscibility in the presence of density inhomogeneity for a single pancake trap, on 3D domains in 1D lattices due to the hopping of spin-rotons, and on the modification of the miscibility properties when a 1D lattice is grown. In addition, we will study how binary dipolar BECs may be employed to simulate classical magnetism with inhomogeneous and possibly random spin couplings. We will investigate as well the simulation of quantum magnetism using Mott insulators of binary dipolar gases in deep optical lattices. Finally, in the last stage of this project we will extend our analysis to few-well systems of high-spin gases