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arXiv:1403.0210 · Physical Review A

Shaping topological properties of the band structures in a shaken optical lattice

Shaoliang Zhang, Qi Zhou

Published Nov 6, 2014• 48 citations
arXivHTMLPDF

Abstract

The realization of band structures with nontrivial topological properties in an optical lattice is an exciting topic in current studies of ultracold atoms. Here we point out that this lofty goal can be achieved by using a simple scheme of shaking an optical lattice, which is directly applicable in current experiments. The photon-assisted band hybridization leads to the production of an effective spin-orbit coupling, in which the band index represents the pseudospin. When this spin-orbit coupling has finite strengths in multiple directions, nontrivial topological structures emerge in the Brillouin zone, such as topological defects with a winding number of 1 or 2 in a shaken square lattice. The shaken lattice also allows one to study the transition between two band structures with distinct topological properties.

DOI
10.1103/physreva.90.051601

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The realization of band structures with nontrivial topological properties in an optical lattice is an exciting topic in current studies of ultracold atoms. Here we point out that this lofty goal can be achieved by using a simple scheme of shaking an optical lattice, which is directly applicable in current experiments. The photon-assisted band hybridization leads to the production of an effective spin-orbit coupling, in which the band index represents the pseudospin. When this spin-orbit coupling has finite strengths in multiple directions, nontrivial topological structures emerge in the Brillouin zone, such as topological defects with a winding number of 1 or 2 in a shaken square lattice. The shaken lattice also allows one to study the transition between two band structures with distinct topological properties.
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In the present paper, we consider the steady state of Fermi atoms coupled to a shaken cavity field at half filling. This shaking generates a time-dependent dynamical optical lattice with backaction on the atomic degrees of freedom. In the high-frequency limit, the shaken dynamical optical lattice produces interesting cavity-field-dependent long-range hoppings, including the nearest-, next-nearest-, and next-next-nearest-neighbor hoppings. They can change the band structures of the system and thus induce nontrivial topological superradiant phases, especially with a large winding number and four degenerate edge states. We also briefly address possible experimental observations of the predicted topological superradiant phases. Our results provide an alternative way to explore novel many-body physics in cavity quantum electrodynamics systems.
The recent experimental realization of spin-orbit (SO) coupling for ultracold bosons and fermions opens an exciting avenue for engineering quantum matter that may be challenging to realize in solid-state materials such as SO-coupled pseudospin-1 fermions. While one-dimensional SO coupling for spin-1 bosons has been experimentally realized, the generation of two-dimensional (2D) SO coupling and its topological properties are largely unexplored. Here we propose an experimental scheme for realizing a 2D Rashba-type SO coupling in a square lattice for pseudospin-1 Fermi gases. Because of the extended spin degree of freedom, many interesting topological phases could exist without relying on lattice point group symmetries that are crucial in solid-state materials. These exotic phases include triply degenerate points, quadratic band touching, a large Chern number (C=5C=5C=5) superfluid with five Majorana modes, triple-Weyl fermions, and so on. Our scheme can be generalized to larger spins and provides a distinctive route for engineering topological quantum matter by utilizing large spin degrees of freedom, instead of specific lattice symmetries.
The geometry of Bloch bands affects many physical properties of crystalline solids and other spatially periodic systems. Direct experimental determination of such geometry is an active area of research. In this work, we focus on the fundamental connection between optical excitations and the relative geometry of pairs of Bloch bands, as characterized by the interband Berry connection. We simulate the response of electrons in solids to optical excitation by the response of ultracold fermionic atoms in optical lattices to periodic modulation of the lattice position. The strength of resonant excitation between bands, measured at each quasimomentum and for various lattice-shaking polarizations, directly maps out the interband Berry connection. We apply this method to the optical honeycomb lattice, driving excitations between the ground n=1n=1n=1 band and the excited n′={2,3,4}n'=\{2,3,4\}n′={2,3,4} bands. We observe transparency lines of quasimomenta at which the response to excitation of specific polarization is zero. Further, the interband Berry connection between bands 1 and 3 shows irreducible Dirac strings connecting the KKK and K′K'K′ points in the Brillouin zone, lines along which the interband Berry connection abruptly changes orientation. Our work establishes optical response as a powerful tool for characterizing geometrical and topological properties of band structure.
Abstract We report the experimental realization of a Creutz ladder for ultracold fermionic atoms in a resonantly driven 1D optical lattice. The two-leg ladder consists of the two lowest orbital states of the optical lattice and the cross inter-leg links are generated via two-photon resonant coupling between the orbitals by periodic lattice shaking. The characteristic pseudo-spin winding structure in the energy bands of the ladder system is demonstrated using momentum-resolved Ramsey-type interferometric measurements. We discuss a two-tone driving method to extend the inter-leg link control and propose a topological charge pumping scheme for the Creutz ladder system.
Spin-orbit coupling (SOC) is at the heart of many exotic band structures and can give rise to many-body states with topological order. Here we present a general scheme based on a combination of microwave driving and lattice shaking for the realization of two-dimensional SOC with ultracold atoms in systems with inversion symmetry. We show that the strengths of Rashba and Dresselhaus SOC can be independently tuned in a spin-dependent square lattice. More generally, our method can be used to open gaps between different spin states without breaking time-reversal symmetry. We demonstrate that this allows for the realization of topological insulators with nontrivial spin textures closely related to the Kane-Mele model.