Non-Abelian gauge fields and topological insulators in shaken optical lattices (1205.1398v3)

Abstract: Time-periodic driving like lattice shaking offers a low-demanding method to generate artificial gauge fields in optical lattices. We identify the relevant symmetries that have to be broken by the driving function for that purpose and demonstrate the power of this method by making concrete proposals for its application to two-dimensional lattice systems: We show how to tune frustration and how to create and control band touching points like Dirac cones in the shaken kagom\'e lattice. We propose the realization of a topological and a quantum spin Hall insulator in a shaken spin-dependent hexagonal lattice. We describe how strong artificial magnetic fields can be achieved for example in a square lattice by employing superlattice modulation. Finally, exemplified on a shaken spin-dependent square lattice, we develop a method to create strong non-Abelian gauge fields.

• The paper demonstrates a novel lattice shaking method that generates both Abelian and non-Abelian gauge fields by breaking critical lattice symmetries.
• It employs various lattice geometries, such as kagome and hexagonal, to tune magnetic fluxes and induce topological features like robust edge states.
• The study utilizes spin-dependent modulations and microwave couplings, offering a scalable platform to explore strongly correlated quantum phases and non-Abelian excitations.

Non-Abelian Gauge Fields and Topological Insulators in Shaken Optical Lattices

The paper "Non-Abelian gauge fields and topological insulators in shaken optical lattices" explores the innovative technique of utilizing time-periodic driving through lattice shaking to generate artificial gauge fields within optical lattices. These artificial fields have promising implications for the potential creation and paper of topological insulators and strongly correlated quantum phases.

Key Contributions and Methodology

The authors address the challenging task of generating both Abelian and non-Abelian gauge fields in two-dimensional lattice systems. The method leverages the simplicity of periodic lattice shaking, which circumvents the complexities associated with alternative generation methods such as trap rotation or laser-induced tunneling. The paper identifies critical symmetries that must be broken by the driving function to achieve the desired gauge fields and provides explicit scenarios in various lattice geometries, including kagome and hexagonal lattices.

1. Abelian Gauge Fields: Through lattice shaking, the authors demonstrate how frustration can be tuned in optical lattices, mimicking magnetic flux in traditional solid-state systems. The adjustable staggered flux through triangular plaquettes allows for control over frustration levels, leading to the potential realization of exotic quantum phases, such as the spin-liquid states in optical analogs of materials like kagome lattices.
2. Topological Insulators: The research delineates a pathway to realize topological insulators within a spin-dependent hexagonal lattice. By engineering artificial fluxes and utilizing a homogeneous driving force, they are able to simulate systems where spin-orbit interactions yield nontrivial Chern numbers, thus inducing topological characteristics such as robust edge states.
3. Non-Abelian Gauge Fields: The paper extends to non-Abelian SU(2) gauge fields achieved through lattice shaking and spin-dependent modulations. By incorporating spinful particles in bipartite square lattices and using magnetic and microwave fields for tunable atomic couplings, the authors provide a framework for realizing complex gauge fields that cannot be described by a simple scalar potential.

Implications and Future Prospects

The implications of this research are significant for advancing the understanding and development of quantum simulators. By providing a more accessible experimental setup for generating gauge fields without compromising on flexibility or scalability, this approach presents an advantageous alternative to existing methods. It notably enables studies of strongly-interacting fermions and the exploration of non-Abelian anyonic excitations, which are fundamental in the pursuit of effective quantum computing paradigms.

Furthermore, the generation of controlled topological states through optical lattices provides a promising platform for investigating novel quantum phenomena and quasiparticles in a highly adjustable environment. The ability to manipulate and explore the coupling constants and gauge fields in these artificial quantum systems could lead to new insights into quantum coherence and entanglement.

The research paves the way for future studies into other non-trivial geometric configurations and the potential scaling of these systems in three dimensions. As quantum technologies advance, the methodologies and insights provided in this paper could significantly contribute to the development of robust and versatile quantum devices. Through continued exploration and refinement, the techniques discussed hold the promise of shedding light on the underpinnings of quantum matter and facilitating breakthroughs in quantum information science.