Cold atoms and the 2D Bose-Hubbard model

Nikhil Monga, John B. Shumway, Kaden R. A. Hazzard +2 more

Anonymous

Wei Wang

In this dissertation, I present my work on ground state entanglement in Bose-Hubbard-type models. Bose-Hubbard-type models form a wide class of bosonic lattice models and describe systems that can be realized by cold atoms or molecules trapped in optical lattices. By studying ground state entanglement, one can understand quantum phases and phase transitions among them from a microscopic point of view. I will first introduce the two-component Bose-Hubbard model describing Bose-Bose mixtures, and discuss the role played by the interspecies entanglement in the Mott-insulator-to-superfluid phase transition of one component in the presence of a second component. I will show that interspecies entanglement provides a new perspective to understand quantum phases in mixtures. Then I will discuss long-range spatial entanglement in single-species Bose-Hubbard-type models. Specifically, I will build a generic framework for understanding under which conditions these models harbor certain types of topological order. My results provide guidance for future numerical studies which can pave the way for searching experimentally realizable bosonic lattice models harboring nontrivial topological order.

Jay D. Mancini, Vassilios Fessatidis, S.P. Bowen +2 more

Ian B. Spielman, William D. Phillips, J. V. Porto

Cold atoms in periodic potentials are versatile quantum systems for implementing simple models prevalent in condensed matter theory. Here we realize the 2D Bose-Hubbard model by loading a Bose-Einstein condensate into an optical lattice, and study the resulting Mott insulator. The measured momentum distributions agree quantitatively with theory (no adjustable parameters). In these systems, the Mott insulator forms in a spatially discrete shell structure which we probe by focusing on correlations in atom shot noise. These correlations show a marked dependence on the lattice depth, consistent with the changing size of the insulating shell expected from simple arguments.

Laura Rinaldi

The aim of this work is to study the dynamics of cold atoms trapped in a one-dimensional periodic lattice generated by an optical potential. Such a system is described by a standard model in condensed matter, namely the so-called Bose-Hubbard model. Arrays of cold neutral atoms or ions are the basic elements of some proposals of quantum computers, which motivates the interest of understanding their dynamics from a mathematical point of view. The main targets of this Master Thesis are the following. First, starting from a classical Hamiltonian of the Frenkel-Kontorova type and thanks to Perturbation Theory, to derive the discrete Bougolyubov-Gross-Pitaevskii (dBGP) equation. Second, starting from first principle formulation, to provide a systematic, quantum mechanical, perturbative derivation of the Bose-Hubbard (BH) model to orders higher than the first one in the small parameter.