Topological order in 1D super-lattice Bose-Hubbard models

Xiao Zhang

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.

Fuyuki Matsuda, Masaki Tezuka, Norio Kawakami

Recently, the relation between one-dimensional (1D) quasicrystals and 2D topological insulators has been demonstrated theoretically and also experimentally by using optical waveguides.It has been shown that 1D quasicrystals can be classified in terms of topology for 2D integer quantum Hall systems.Such quasicrystals can be also realized in ultracold atoms loaded in optical superlattices.In this study, we consider a 1D Bose-Hubbard model in a quasiperiodic superlattice.It is known that a gap in the excitation spectrum is induced by the interaction, and the resulting Mott insulating phase is characterized by a nonzero Chern number.The system is called a topological Mott insulator.In the non-interacting case, topological equivalence between the Fibonacci quasicrystal and the Harper model is already known.However, it has not been clarified whether such topological equivalence exists in topological Mott insulators.We show numerically that the topological equivalence exists in a wide range of quasiperiodic Bose-Hubbard model.

Fabian Grusdt, Michael H oning, Michael Fleischhauer

V. W. Scarola, S. Das Sarma

Certain proposed extended Bose-Hubbard models may exhibit topologically ordered ground states with excitations obeying non-Abelian braid statistics. A sufficient tuning of Hubbard parameters could yield excitation braiding rules allowing implementation of a universal set of topologically protected quantum gates. We discuss potential difficulties in realizing a model with a proposed non-Abelian topologically ordered ground state using optical lattices containing bosonic dipoles. Our direct implementation scheme does not realize the necessary anisotropic hopping, anisotropic interactions, and low temperatures.

Stefanos Kourtis, Titus Neupert, Claudio Chamon +1 more