Toward an Ab-initio Understanding of Ultracold Boson Experiments in One Dimension

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The quantum world is a source of uncommon phenomena, such as lasing and superconductivity, that have had tremendous impacts on society. Intrinsically fragile, quantum phenomena are difficult to observe and study, let alone explain. Since the observation of Bose-Einstein condensation in the mid-1990s, ultracold gases (gases at nearly zero absolute temperature) that are trapped and manipulated with electromagnetic fields in vacuum chambers have provided a unique window for the exploration of the quantum world. Experiments with ultracold gases are examining quantum effects when atoms are allowed to move only in one spatial direction. This reduced dimensionality can exaggerate "quantum-ness" and produce novel states of matter. This project will develop theoretical models to describe such states and study their observable properties. The models to be developed are expected to aid in the understanding of materials in which electrons interact strongly and in which their motion along some spacial direction is constrained; for example, in nano-scale wires. The properties of these systems, at odds with those of traditionally studied unconstrained (three-dimensional) quantum systems, might be essential to the understanding of a wide range of nano-devices. This theoretical research will explore phenomena in quantum gases in equilibrium and far from equilibrium. In equilibrium, one of the questions to be answered is whether the adiabatic loading of three-dimensional Bose-Einstein condensates in two-dimensional optical lattices results in one-dimensional gases that are in thermal equilibrium, or whether generalized Gibbs ensembles are needed to describe them. The researchers will also study phenomena which result when an additional weaker lattice is added along the one-dimensional gas, and the associated quantum phases that are realized experimentally. Far from equilibrium, this project will explore the expansion dynamics of one-dimensional gases in the presence of interactions, with or without an optical lattice along the expansion direction, as well as experiments in which parameters such as the strength of the confining potential or the lattice depth are periodically modulated in time. Another problem to be explored is the result of band-mapping procedures in experiments in which the atoms are far-from-equilibrium and interact strongly. The research proposed will be mostly carried out by two graduate students who will be trained in computational and many-body quantum physics. The PI will design an advanced graduate course on quantum statistical mechanics, and will contribute to the Hazleton Integration Project (http://www.hazletonintegrationproject.com) by giving talks at the Hazleton One Community Center about science in general and physics in particular.