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arXiv:1003.2736 · Physical Review A

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

Xiong-Jun Liu, Xin Liu, Congjun Wu, Jairo Sinova

Published Mar 24, 2010• 119 citations
arXivHTMLPDF

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 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.

DOI
10.1103/physreva.81.033622

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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.
We study the quantum anomalous Hall states in the ppp-orbital bands of the honeycomb optical lattices loaded with single-component fermions. Such an effect has not yet been realized in both condensed-matter and cold-atom systems. By applying the available experimental techniques to rotate each lattice site around its own center, the band structures become topologically nontrivial. At a certain rotation angular velocity $\ensuremath{\Omega}$, a flat band structure appears with localized eigenstates carrying chiral current moments. By imposing the soft confining potential, the density profile exhibits a wedding-cake-shaped distribution with insulating plateaus at commensurate fillings. Moreover, the inhomogeneous confining potential induces dissipationless circulation currents, the magnitudes and chiralities of which vary with the distance from the trap center. In the insulating regions, the Hall conductances are quantized, and in the metallic regions, the directions and magnitudes of chiral currents can not be described by the usual local-density approximation. The quantum anomalous Hall effects are robust at temperature scales that are small compared to band gaps, which increase the feasibility of experimental realizations.
We find an optical Raman lattice without spin-orbit coupling showing chiral topological orders for cold atoms. Two incident plane-wave lasers are applied to simultaneously generate a double-well square lattice and periodic Raman couplings, the latter of which drive the nearest-neighbor hopping and create a staggered flux pattern across the lattice. Such a minimal setup can yield the quantum anomalous Hall effect with a large gap-bandwidth ratio in the single particle regime, while in the interacting regime it achieves the J 1 - J 2 - K spin model, with the nearest-neighboring ( J 1 ) and next-nearest-neightboring ( J 2 ) exchange coupling coefficients, and the three three-spin interacting parameter ( K ) is controllable. We show that the J 1 - J 2 - K spin model may support a chiral spin liquid phase. It is interesting that the quantum anomalous Hall state can be detected by only measuring the Bloch states in the two symmetric momentum points of the first Brillouin zone. Further, we also show that heating in the present optical Raman lattice can be essentially reduced compared with the conventional laser-assisted tunneling schemes. This suggests that the predicted topological states be reachable with the current experimental capability.
We describe a scheme to engineer non-Abelian gauge potentials on a square optical lattice using laser-induced transitions. We emphasize the case of two-electron atoms, where the electronic ground state g is laser-coupled to a metastable state e within a state-dependent optical lattice. In this scheme, the alternating pattern of lattice sites hosting g and e states depicts a chequerboard structure, allowing for laser-assisted tunnelling along both spatial directions. In this configuration, the nuclear spin of the atoms can be viewed as a ‘flavour’ quantum number undergoing non-Abelian tunnelling along nearest-neighbour links. We show that this technique can be useful to simulate the equivalent of the Haldane quantum Hall model using cold atoms trapped in square optical lattices, offering an interesting route to realize Chern insulators. The emblematic Haldane model is particularly suited to investigate the physics of topological insulators, but requires, in its original form, complex hopping terms beyond nearest-neighbouring sites. In general, this drawback inhibits a direct realization with cold atoms, using standard laser-induced tunnelling techniques. We demonstrate that a simple mapping allows us to express this model in terms of matrix hopping operators that are defined on a standard square lattice. This mapping is investigated for two models that lead to anomalous quantum Hall phases. We discuss the practical implementation of such models, exploiting laser-induced tunnelling methods applied to the chequerboard optical lattice.
We propose to realize and observe Chern Kondo insulators in an optical superlattice with laser-assisted s and p orbital hybridization and a synthetic gauge field, which can be engineered based on the recent cold atom experiments. Considering a double-well square optical lattice, the localized s orbitals are decoupled from itinerant p bands and are driven into a Mott insulator due to the strong Hubbard interaction. Raman laser beams are then applied to induce tunnelings between s and p orbitals, and generate a staggered flux simultaneously. Because of the strong Hubbard interaction of s orbital states, we predict the existence of a critical Raman laser-assisted coupling, beyond which the Kondo screening is achieved, and then a fully gapped Chern Kondo phase emerges, with the topology characterized by integer Chern numbers. Being a strongly correlated topological state, the Chern Kondo phase is different from the single-particle quantum anomalous Hall state, and can be identified by measuring the band topology and double occupancy of s orbitals. The experimental realization and detection of the predicted Chern Kondo insulator are also proposed.
In this work we consider a system of spinless fermions with nearest and next-to-nearest neighbor repulsive Hubbard interactions on a honeycomb lattice, and propose and analyze a realistic scheme for analog quantum simulation of this model with cold atoms in a two-dimensional hexagonal optical lattice. To this end, we first derive the zero-temperature phase diagram of the interacting model within a mean-field theory treatment. We show that besides a semimetallic and a charge-density-wave ordered phase, the system exhibits a quantum anomalous Hall phase, which is generated dynamically, i.e., purely as a result of the repulsive fermionic interactions and in the absence of any external gauge fields. We establish the topological nature of this dynamically created Mott-insulating phase by the numerical calculation of a Chern number, and we study the possibility of coexistence of this phase with any of the other phases characterized by local order parameters. Based on the knowledge of the mean-field phase diagram, we then discuss in detail how the interacting Hamiltonian can be engineered effectively by state-of-the-art experimental techniques for laser dressing of cold fermionic ground-state atoms with electronically excited Rydberg states that exhibit strong dipolar interactions.
We study the transport of cold fermionic atoms trapped in optical lattices in the presence of artificial Abelian or non-Abelian gauge potentials. Such external potentials can be created in optical lattices in which atom tunneling is laser assisted and described by commutative or non-commutative tunneling operators. We show that the Hall-like transverse conductivity of such systems is quantized by relating the transverse conductivity to topological invariants known as Chern numbers. We show that this quantization is robust in non-Abelian potentials. The different integer values of this conductivity are explicitly computed for a specific non-Abelian system which leads to a fractal phase diagram.