Quantum anomalous Hall effect with cold atoms trapped in a square lattice

Abstract

We propose an experimental scheme to realize the quantum anomalous Hall effect in an anisotropic square optical lattice which can be generated from available experimental set-ups of double-well lattices with minor modifications. A periodic gauge potential induced by atom-light interaction is introduced to give a Peierls phase for the nearest-neighbor site hopping. The quantized anomalous Hall conductivity is investigated by calculating the Chern number as well as the chiral gapless edge states of our system. Furthermore, we show in detail the feasability for its experimental detection through light Bragg scattering of the edge and bulk states with which one can determine the topological phase transition from usual insulating phase to quantum anomalous Hall phase.

Optical-lattice Hamiltonians for relativistic quantum electrodynamics

“…They also appear in a square lattice with appropriate complex hopping matrix elements [21]. This has led to a number of proposals to emulate relativistic physics with cold atoms [21][22][23][24][25][26]. Here we extend these previous proposals by showing how to emulate QED3 with cold atoms.…”

“…We require that the system exhibits "Dirac points" instead of a Fermi surface; all zero-or low-energy fermionic excitations must occur near some finite set of points K in momentum space, and have the dispersion relation ǫ p = ± v 2 F p 2 + m 2 for small p measured with respect to K. The most well-known system of this type is the hexagonal lattice [15][16][17][18][19], realized in condensed matter in graphene [20] and carbon nanotubes. In cold atoms, the ability to directly manipulate the phases of lattice hopping amplitudes enables the creation of Dirac points in a square lattice [21,26], something that hasn't been realized in materials. We describe both approaches.…”

“…Conceptually, the best way to implement these phases is to work in a larger space, allowing the fermions to hop onto the y sites, with a total energy cost of U relative to the x sites. Using the techniques from [21,23,33,35], one can engineer a spatially dependent phase on the hopping matrix elements, and produce a Hamiltonian,…”

“…Our square lattice approach is based on the geometry proposed by Liu et al [21] to study the anomalous quantum Hall effect. Consider noninteracting fermions in an square optical lattice with nearest neighbor hopping t and lattice spacing l. We add to the hopping amplitude a set of phases such that…”

“…Dirac fermions appear at half filling in a hexagonal optical lattice [15][16][17][18][19], mimicking the relativistic band structure of graphene [20]. They also appear in a square lattice with appropriate complex hopping matrix elements [21]. This has led to a number of proposals to emulate relativistic physics with cold atoms [21][22][23][24][25][26].…”