Resumen de Àtoms ultrafreds amb càrrega de moment angular orbital
Due to their high degree of tunability and controllability, ultracold atom systems constitute an ideal playground for simulating a wide variety of condensed matter models and are one of the most promising platforms for the implementation of novel quantum technologies. In this context, the emerging field of atomtronics aims at realizing matter-wave circuits with ultracold atoms in versatile optical micro-traps. These efforts have a two-fold purpose: exploring new fundamental physics and constructing quantum devices such as sensors or computers. The simplest atomtronic circuits are formed by ring-shaped potentials, which provide closed loops for the atoms that naturally support Orbital Angular Momentum (OAM) states. Motivated by these advances, in this thesis we investigate different systems that have the common characteristic of being formed by ultracold atoms carrying OAM in cylindrically symmetric potentials. Our interest is focused on three aspects of OAM states: their potential use for sensing purposes, their applications as quantum simulators of models of quantum magnetism, and the possibilities that they offer for realizing topological phases of matter. We start by considering a Bose Einstein Condensate (BEC) trapped in a single ring potential and prepared in a superposition of counter-rotating OAM states. The density profile of this state has a minimal line that rotates due to the non-linear interaction between the atoms. After deriving an expression that relates the frequency of this rotation with the strength of the interactions, we propose protocols to use the system as a device for sensing two-body interactions, magnetic fields and rotations. Next, we explore several configurations of side-coupled potentials where ultracold atoms in OAM states experience tunnelling dynamics that are governed by complex amplitudes with phases that can be tuned by modifying the geometry of the system. First, we study a lattice with a diamond chain shape filled with non-interacting ultracold atoms carrying OAM. In this system, the phases in the tunnelling rates give rise to a topological band structure with its corresponding protected edge states. Furthermore, a proper tuning of the tunneling parameters may lead to an energy spectrum composed entirely of flat bands. In this scenario, the system exhibits Aharonov-Bohm caging. We then analyse a family of systems consisting of arrays of ring potentials with a flexible geometry filled with strongly correlated bosons in OAM states. We focus on the Mott insulator regime at unit filling, for which one can establish a correspondence between OAM and spin−1/2 states. We demonstrate that by properly arranging the traps, these systems can realize different spin models of interest related to a general Heisenberg model. Then, we turn our attention back to the diamond chain to examine the physics of two attractively interacting bosons in the limit when all bands are flat. In this situation, the kinetic energy is frozen and the properties of the system are solely determined by the interactions. We show that the low-energy sector of the two-boson spectrum can be described in terms of effective single-particle models that are topologically non-trivial. Finally, we investigate a two-dimensional square lattice with different intra- and inter-cell spacings in the non-interacting limit. We show that this system constitutes an example of a second-order topological insulator, displaying a finite quadrupole moment and protected corner states.
