Abstract:
Ultracold quantum gases have emerged in recent years as flexible platforms to experimentally access strongly correlated regimes. In the first part of this talk, I will discuss how novel techniques based on engineering long-range interactions using Rydberg gases pave the way for the investigation of frustrated magnetism in reduced dimensionality. In particular, using a combination of analytical and numerical methods, I will show how a certain class of soft-shoulder Hubbard models can support liquid states of matter which circumvent the restrictions imposed by Luttinger theorem, and that are separated from more conventional liquids by supersymmetric conformal critical points. In the second part of the talk, the focus will be on Majorana quasi-particles in fermionic quantum gases. These paradigmatic excitations have attracted a lot of interest recently due to their potential for quantum computing applications. However, their observation is challenging, as one has first to identify proper Hamiltonian setting supporting those, and then find a proper probing. After reviewing briefly which classes of cold atom Hamiltonians can support such states, I will present some recent results on how to employ a fractionalized Josephson effect to hallmark the presence of Majorana quasi-particles and distinguish them from more conventional excitations.