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New Journal of Physics

Fractionalized topological defects in optical lattices

Xing‐Hai Zhang, Wenjun Fan, Jinwei Shi, Su-Peng Kou

Published Oct 12, 2015• 3 citations
Publisher

Abstract

Topological objects are interesting topics in various fields of physics ranging from condensed matter physics to the grand unified and superstring theories.Among those, ultracold atoms provide a playground to study the complex topological objects.In this paper we present a proposal to realize an optical lattice with stable fractionalized topological objects.In particular, we generate the fractionalized topological fluxes and fractionalized skyrmions on two-dimensional optical lattices and fractionalized monopoles on three-dimensional optical lattices.These results offer a new approach to study the quantum many-body systems on optical lattices of ultracold quantum gases with controllable topological defects, including dislocations, topological fluxes and monopoles.

DOI
10.1088/1367-2630/17/10/103019

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Topological objects are interesting topics in various fields of physics ranging from condensed matter physics to the grand unified and superstring theories.Among those, ultracold atoms provide a playground to study the complex topological objects.In this paper we present a proposal to realize an optical lattice with stable fractionalized topological objects.In particular, we generate the fractionalized topological fluxes and fractionalized skyrmions on two-dimensional optical lattices and fractionalized monopoles on three-dimensional optical lattices.These results offer a new approach to study the quantum many-body systems on optical lattices of ultracold quantum gases with controllable topological defects, including dislocations, topological fluxes and monopoles.
Ultracold atoms in an optical lattice provide a unique approach to study quantum many-body systems, previously only possible by using condensed-matter experimental systems. This new approach, often called quantum simulation, becomes possible because of the high controllability of the system parameters and the inherent cleanness without lattice defects and impurities. In this article, we review recent developments in this rapidly growing field of ultracold atoms in an optical lattice, with special focus on quantum simulations using our newly created quantum many-body system of two-electron atoms of ytterbium. In addition, we also mention other interesting possibilities offered by this novel experimental platform, such as applications to precision measurements for studying fundamental physics and a Rydberg atom quantum computation.
Single topological defects and related structures have been experimentally created inside clouds of Bose-Einstein condensates. However, a practical protocol for creating multiple defects inside a single cloud—a prerequisite for studying defect interactions—has been lacking. Here we propose, and theoretically analyze, a practical protocol for the creation of configurations of topological monopoles, quantum knots, and skyrmions in Bose-Einstein condensates by employing fictitious magnetic fields induced by the interaction of the atomic cloud with coherent light fields. It is observed that a single coherent field is not enough for this purpose, but instead we find incoherent superpositions of several coherent fields that introduce topological point charges. We numerically estimate the experimentally achievable strengths and gradients of the induced fictitious magnetic fields and find them to be adjustable at will to several orders of magnitude greater than those of the physical magnetic fields employed in previous experimental studies. This property together with ultrafast control of the optical fields paves the way for advanced engineering of topological defects in quantum gases. Published by the American Physical Society 2024
This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have recently been explored in a range of different systems, which produced both fascinating physics findings and exciting opportunities for applications. Among the physical systems that have been considered to realize and probe these intriguing phases, ultracold atoms become promising platforms due to their high flexibility and controllability. Quantum simulation of topological phases with cold atomic gases is a rapidly evolving field, and recent theoretical and experimental developments reveal that some toy models originally proposed in condensed matter physics have been realized with this artificial quantum system. The purpose of this article is to introduce these developments. The article begins with a tutorial review of topological invariants and the methods to control parameters in the Hamiltonians of neutral atoms. Next, topological quantum phases in optical lattices are introduced in some detail, especially several celebrated models, such as the Su–Schrieffer–Heeger model, the Hofstadter–Harper model, the Haldane model and the Kane–Mele model. The theoretical proposals and experimental implementations of these models are discussed. Notably, many of these models cannot be directly realized in conventional solid-state experiments. The newly developed methods for probing the intrinsic properties of the topological phases in cold-atom systems are also reviewed. Finally, some topological phases with cold atoms in the continuum and in the presence of interactions are discussed, and an outlook on future work is given.
Topological matter is a popular topic in both condensed matter and cold-atom research. In the past decades, a variety of models have been identified with fascinating topological features. Some, but not all, of the models can be found in materials. As a fully controllable system, cold atoms trapped in optical lattices provide an ideal platform to simulate and realize these topological models. Here we present a proposal for synthesizing topological models in cold atoms based on a one-dimensional spin-dependent optical lattice potential. In our system, features such as staggered tunneling, staggered Zeeman field, nearest-neighbor interaction, beyond-near-neighbor tunneling, etc. can be readily realized. They underlie the emergence of various topological phases. Our proposal can be realized with current technology and hence has potential applications in quantum simulation of topological matter.
We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in “artificial” magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed. Motto: There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy Citation1