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

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 kagome 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.

Floquet topological insulators

“…When the static (non-irradiated) system is already topological, photons are also useful to probe the properties and the robustness of the chiral/helical edge modes. Finally, cold atomic vapors trapped in optical lattices provide very interesting routes to design synthetic gauge fields and induce topological phases [51], either by using Raman resonances or by using periodic driving (shaking) of the lattice [52].…”

Artificial honeycomb lattices for electrons, atoms and photons

“…Cold atoms in optical lattices, moreover, can be forced into regimes of parameters or subject to external fields, which are difficult to achieve in or unaccessible to natural graphene. Examples include the regime of ultrastrong spin-orbit coupling [62] and nonAbelian gauge fields [63,64] akin to those that appear in the Langrangian of quantum chromodynamics. Note that with the advent of molecular graphene and Abelian gauge fields [19], proposals now also exist for realizing non-Abelian gauge fields in solid-state incarnations [65].…”

Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

“…Theoretical models based on Floquet's theorem are being developed to simulate systems in regimes otherwise inaccessible in conventional condensed matter materials [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] . Experimentally, cold atoms' unique controllability was employed to observe dynamical localisation and phase-coherence in strongly shaken bosonic systems [19][20][21][22][23][24] .…”