Stability of Doublons

Abstract

In this thesis, I discuss my research of the behavior and stability of doublons. I describe the dynamics of a one-dimensional closed chain of spins ½. I show that by analyzing the eigenstates and eigenvalues of the Hamiltonian that describes the system, I can predict its dynamics. In the presence of strong interactions between the particles in the chain, particles can bind in pairs of excitations forming what is known as doublons. These doublons are very stable and they move together as a single particle, but contrary to it, doublons move slowly. Doublons were observed experimentally by many different physicists with cold atoms. In those experiments, because of strong on-site interactions between atoms, they would see sites that were doubly occupied, which is how the term “doublon” was coined. These doublons could move to other sites, but they always moved together as a bounded pair. They were never found to be split up with one in each site, they always moved together. In my thesis, the doublons are equivalent to bounded pairs of neighboring excitations in a chain instead of pairs of atoms.