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arXiv:0804.1850 · Physical Review Letters

Realizing and Detecting the Quantum Hall Effect without Landau Levels by Using Ultracold Atoms

L. B. Shao, Shi-Liang Zhu, Li Sheng, D. Y. Xing, Z. D. Wang

Published Dec 12, 2008• 140 citations
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Abstract

We design an ingenious scheme to realize Haldane's quantum Hall model without Landau levels by using ultracold atoms trapped in an optical lattice. Three standing-wave laser beams are used to construct a wanted honeycomb lattice, where different on site energies in two sublattices required in the model can be implemented through tuning the phase of one laser beam. The staggered magnetic field is generated from the light-induced Berry phase. Moreover, we establish a relation between the Hall conductivity and the atomic density, enabling us to detect the Chern number with the typical density-profile-measurement technique.

DOI
10.1103/physrevlett.101.246810

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We design an ingenious scheme to realize Haldane's quantum Hall model without Landau levels by using ultracold atoms trapped in an optical lattice. Three standing-wave laser beams are used to construct a wanted honeycomb lattice, where different on site energies in two sublattices required in the model can be implemented through tuning the phase of one laser beam. The staggered magnetic field is generated from the light-induced Berry phase. Moreover, we establish a relation between the Hall conductivity and the atomic density, enabling us to detect the Chern number with the typical density-profile-measurement technique.
With ultracold atoms in an optical lattice, we propose an experimental scheme to simulate and detect the integer quantum Hall effect and a peculiar phase transition in a uniform magnetic field and an additional staggered magnetic field. The phase transition is characterized by the direct change from Hall plateau state $N\ensuremath{-}1$ to $\ensuremath{-}1$ due to Chern number redistribution when the staggered magnetic field is varied. We propose the possibility to observe the Hall conductivity and the phase transition by varying experimental parameters and measuring the number density of the ultracold atoms.
We propose a model which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian in the kagome lattice and promises to host the transition from the quantum spin Hall insulator to the normal insulator. In addition, we design an experimental scheme to simulate and detect this transition in the ultracold atom system. The lattice intrinsic spin-orbit coupling is generated via the laser-induced-gauge-field method. Furthermore, we establish the connection between the spin Chern number and the spin-atomic density which enables us to detect the quantum spin Hall insulator directly by the standard density-profile technique used in atomic systems.
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 setups 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.
Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field. We present the realization of artificial gauge fields for the observation of anomalous Hall effect. Two species of attractively interacting ultracold fermions are considered to be trapped in a shaken two dimensional triangular lattice. A combination of interaction induced tunneling and shaking can result in an emergent Dice lattice. In such a lattice the staggered synthetic magnetic flux appears and it can be controlled with external parameters. The obtained synthetic fields are non-Abelian. Depending on the tuning of the staggered flux we can obtain either anomalous Hall effect or its quantized version. Our results are reminiscent of Anomalous Hall conductivity in spin-orbit coupled ferromagnets.
Ultracold fermions trapped in a honeycomb optical lattice constitute a versatile setup to experimentally realize the Haldane model (1988 Phys. Rev. Lett. 61 2015). In this system, a non-uniform synthetic magnetic flux can be engineered through laser-induced methods, explicitly breaking time-reversal symmetry. This potentially opens a bulk gap in the energy spectrum, which is associated with a non-trivial topological order, i.e. a non-zero Chern number. In this paper, we consider the possibility of producing and identifying such a robust Chern insulator in the laser-coupled honeycomb lattice. We explore a large parameter space spanned by experimentally controllable parameters and obtain a variety of phase diagrams, clearly identifying the accessible topologically non-trivial regimes. We discuss the signatures of Chern insulators in cold-atom systems, considering available detection methods. We also highlight the existence of topological semi-metals in this system, which are gapless phases characterized by non-zero winding numbers, not present in Haldane's original model.