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arXiv:1405.3975 · New Journal of Physics

Chiral topological orders in an optical Raman lattice

Xiong-Jun Liu, Zheng-Xin Liu, K. T. Law, W. Vincent Liu, Tai Kai Ng

Published Mar 1, 2016• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/18/3/035004

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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.
A Majorana zero bound mode exists in the vortex core of a chiral p+ipp+ipp+ip superconductor or superfluid, which can be driven from an sss-wave pairing state by two-dimensional spin-orbit coupling. We propose here a novel scheme based on realistic cold atom platforms to generate two-dimensional spin-orbit interactions in a blue-detuned square optical lattice, and predict both the quantum anomalous Hall effect and chiral topological superfluid phase in the experimentally accessible parameter regimes. This work may open a new direction with experimental feasibility to observe non-Abelian topological orders in cold atom systems.
We propose a simple experimental scheme to realize simultaneously the one-dimensional spin-orbit coupling and the staggered spin flip in ultracold pseudospin-1/21/21/2 atomic Fermi gases trapped in optical lattices. In the absence of interspecies interactions, the system supports type-I and II Weyl semimetals in three-dimensional and gapped Chern insulators and gapless topological semimetal states in two-dimensional lattices. By turning on the sss-wave interactions, a rich variety of gapped and gapless inhomogeneous topological superfluids can emerge. In particular, a gapped topological Fulde-Ferrell superfluid, which supports the chiral edge states at opposite boundaries with the same chirality, is predicted.
Spin-orbit coupling (SOC) in ultracold atoms is engineered by light-atom interaction, such as two-photon Raman transitions between two Zeeman spin states. In this paper, we propose and experimentally realize chiral Raman coupling to generate SOC in ultracold atomic gases, which exhibits high quantization axis direction dependence. Chiral Raman coupling for SOC is created by chiral light-atom interaction, in which a circularly polarized electromagnetic field generated by two Raman lasers interacts with two Zeeman spin states $\ensuremath{\delta}{m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ (chiral transition). We present a simple scheme of chiral one-dimensional (1D) Raman coupling by employing two Raman lasers at an intersecting angle ${90}^{\ensuremath{\circ}}$ with the proper polarization configuration. In this case, Raman coupling for SOC exists in one direction of the magnetic quantization axis and disappears in the opposite direction. Then we extend this scheme into a chiral two-dimensional (2D) optical square Raman lattice configuration to generate the 1D SOC. There are two orthogonal 1D SOCs, which exist in the positive and negative directions of the magnetic quantization axis respectively. This case is compared with 2D SOC based on the nonchiral 2D optical Raman lattice scheme for studying the topological energy band. This paper broadens the horizon for understanding chiral physics and simulating topological quantum systems.
Spin and orbital are two basic degrees of freedom that play significant roles in exploring exotic quantum phases in optical lattices with synthetic spin-orbit coupling (SOC) and high orbital bands, respectively. Here, we combine these two crucial ingredients for the first time by proposing a completely new orbital optical Raman lattice scheme to explore exotic high-orbital Bose condensates with Raman-induced SOC in a square lattice. We find that both the SOC and p-orbital interactions influence the condensed state of bosons. Their interplay results in two novel high-orbital many-body quantum phases: the uniform angular momentum superfluid phase, which exhibits a global topological chiral orbital current characterized by a uniform Chern number, and the two-dimensional topological spin-orbital supersolid phase, which is characterized by the spin and orbital angular momentum density wave patterns and topological excitations with opposite Chern numbers, respectively protecting the chiral and antichiral edge modes in the neighboring supersolid clusters. Our scheme may open a new avenue for exploring exotic SOC and high-orbital physics in optical lattices, and is expected to advance the experimental realization of novel supersolids in higher dimensions.
In static lattice systems, the Nielsen-Ninomiya theorem enforces the pairing of Weyl points with opposite chiralities, which precludes the chiral magnetic effect (CME) in equilibrium. Periodic driving provides a viable route to circumvent this no-go constraint. Here, we propose a scheme to realize and control unpaired Weyl points using ultracold atoms in a three-dimensional (3D) optical Raman lattice under continuous periodic driving. By engineering distinct relative symmetries between the lattice and multiple Raman potentials, the configuration generates an effective 3D spin-orbit coupling and yields a tunable topological-insulator phase. Through adiabatic periodic modulation of this system, we show that eight Weyl points emerge in the quasienergy spectrum of the low-energy sector, whose net chirality can be precisely tuned. A nonzero total chirality directly corresponds to the formation of unpaired Weyl points. Furthermore, by implementing a synthetic magnetic field via laser-assisted tunneling in this setup, we demonstrate that the chirality imbalance drives a quantized charge current in the weak-field regime, providing a direct signature of the CME. We verify that the adiabatic condition of the driving protocol, as well as the proposed experimental preparation and detection techniques, are within reach of current ultracold-atom experiments. This work establishes a realistic and controllable platform for exploring chiral-anomaly physics and nonequilibrium topological phenomena linked to Weyl fermions.