Theory and applications of ultracold atoms in optical superlattices - Vaucher, B; Vaucher, Benoit (2008)
﻿ Optical lattices make it possible to trap and coherently control large ensembles of ultracold atoms. They provide the possibility to create lattice potentials that mimic the structure of solid-state systems, and to control these potentials dynamically. In this thesis, we study how dynamical manipulations of the lattice geometry can be used to perform different tasks, ranging from quantum information processing to the creation of diatomic molecules. We first examine the dynamical properties of ultracold atoms trapped in a lattice whose periodicity is dynamically doubled. We derive a model describing the dynamics of the atoms during this process, and compute the different interaction parameters of this model. We investigate different ways of using this lattice manipulation to optimise the initialisation time of a Mott-insulating state with one atom per site, and provide a scaling law related to the interaction parameters of the system. We go on to show that entangling operations between the spin of adjacent atoms are realisable with optical lattices forming arrays of double-well potentials. We study the creation of a lattice containing a spin-encoded Bell-pair in each double-well, and show that resilient, highly-entangled many-body states are realisable using lattice manipulations. We show that the creation of cluster-like states encoded on Bell-pairs can be achieved using these systems, and we provide measurement networks that allow the execution of quantum algorithms while maintaining intact the resilience of the system. Finally, we investigate the possibility to create a diatomic molecular state and simulate Fermi systems via the excitation to Rydberg levels of ground-state atoms trapped in optical lattices. We develop a method based on symbolical manipulations to compute the interaction parameters between highly-excited electrons, and evaluate them for different electronic configurations. We use these parameters to investigate the existence of diatomic molecular states with equilibrium distances comparable to typical lattice spacings. Considering the possibility to excite atoms trapped in an optical lattice to Rydberg levels such that the electronic cloud of neighbouring atoms overlap, we propose a model describing their interactions and compute its parameters. If such systems were realised, they would allow the simulation of Fermi systems at a temperature much below the Fermi temperature, thus enabling the observation of quantum phenomena hitherto inaccessible with current technology.