Interactions in novel low-dimensional quantum systems: arrays of cold atoms and graphene monolayers

Abstract

El objetivo de esta tesis es avanzar en el conocimiento de los efectos que dichas interacciones pueden tener en ambos sistemas, grafeno y redes de átomos fríos. Las interacciones pueden ser entre partículas de dicho sistema, pero estas a su vez también pueden verse influenciadas por la presencia de agentes externos en el entorno en el que el sistema vive.De cara a estudiar la fenomenología experimental de estos sistemas, ambos tipos de interacciones son muy importantes, por lo que han sido abordadas en distintos capítulos de la tesis. La tesis incluye tres capítulos introductorios, con los que se trata de dar una resentación autocontenida de los resultados. Uno general, en el que se pasa revista al campo de sistemas cuánticos de dimensionalidad reducida, incluyendo las nuevas realizaciones de las que trata esta tesis. Y otros dos, uno al principio de cada parte de la tesis, que incluyen resultados y técnicas relevantes para el estudio de las interacciones en los siguientes capítulos.

This thesis is devoted to the study of interactions in novel low-dimensional quantum systems from a theoretical point of view. Quantum Physics in the verge of dimensionality is not a recent subject. One might say that it already started when the Hydrogen atom was studied from a quantum mechanical point of view, though its golden age belongs to the seventies and the eighties, when a great improvement of experimental techniques for the synthesis and characterization of artificial nanostructures was achieved. However, in the recent years we have witnessed a real revolution in the field due to the experimental realization of genuinely low-dimensional systems like graphene, a carbon based two-dimensional crystal, or the possibility of engineering highly isolated and tunable lattices where cold atoms become trapped. The particles that propagate along these systems are not independent, but they interact with each other, something that might lead to collective phenomena never observed before in nature. The unraveling of some of the effects that interactions could have in these systems is the leitmotiv of this thesis. Interactions can be present within the system, but also the existence of an environment may produce important perturbations that drive it far from its isolated expected behavior. Therefore, both kinds of interactions will be studied here.