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arXiv:1701.05317 · Physical Review A

Artificial topological models based on a one-dimensional spin-dependent optical lattice

Zhen Zheng, Han Pu, Xu‐Bo Zou, Guang‐Can Guo

Published Jan 18, 2017• 5 citations
arXivHTMLPDF

Abstract

Topological matter is a popular topic in both condensed matter and cold-atom research. In the past decades, a variety of models have been identified with fascinating topological features. Some, but not all, of the models can be found in materials. As a fully controllable system, cold atoms trapped in optical lattices provide an ideal platform to simulate and realize these topological models. Here we present a proposal for synthesizing topological models in cold atoms based on a one-dimensional spin-dependent optical lattice potential. In our system, features such as staggered tunneling, staggered Zeeman field, nearest-neighbor interaction, beyond-near-neighbor tunneling, etc. can be readily realized. They underlie the emergence of various topological phases. Our proposal can be realized with current technology and hence has potential applications in quantum simulation of topological matter.

DOI
10.1103/physreva.95.013616

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Abstract. We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from non-interacting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize the majority of phases in the periodic table of topological insulators.
ppp-wave interaction in cold atoms may give rise to exotic topological superfluids. However, the realization of ppp-wave interaction in a cold atom system is experimentally challenging. Here we propose a simple scheme to synthesize effective ppp-wave interaction in conventional sss-wave interacting quantum gases. The key idea is to load atoms into a spin-dependent optical lattice potential. Using two concrete examples involving spin-1/2 fermions, we show how the original system can be mapped into a model describing spinless fermions with nearest-neighbor ppp-wave interaction, whose ground state can be a topological superfluid that supports Majorana fermions under proper conditions. Our proposal has the advantage that it does not require spin-orbit coupling or loading atoms onto higher orbitals, which is the key in earlier proposals to synthesize effective ppp-wave interaction in sss-wave quantum gases, and may provide a completely new route for realizing ppp-wave topological superfluids.
A quantum simulator is a well-controlled quantum system which can be used to simulate another quantum system. Quantum degenerate gases confined by optical standing waves(optical lattices) have been considered to simulate condensed matter systems. We focus on two issues in this problem. The first one is the realization of interesting quantum phases by engineering Hamiltonians with the cold atoms toolbox. Secondly, the systems we studied are often intractable to analytical methods, which makes it a crucial issue to solve them with numerical methods. For the first issue we find several interesting phases can be studied with cold atoms in optical lattices. We show that a ppp-wave superfluid is stablized through a dissipation blockade mechanism. This mechanism also induces a new insulator formed by ppp-wave Feshbach molecules. We find that the anisotropic nature of interaction between polar molecules or dipolar atoms can be used to realize two charge density waves with different patterns and a supersolid phase which has not been found conclusively in the condensed matter system. Finally, we propose to realize a long sought spin liquid phase with hard-core bosons subject to a spin-dependent lattice and Raman induced hoppings. For the second issue we choose to numerically study these systems with the so-called tensor network algorithm which is a variational method based on the matrix(tensor) product states product states which are designed to approximate generic wave functions from their entanglement properties. In general the tensor network algorithm has advantages that it is applicable beyond one dimension, and can be used to study physical properties in the thermodynamic limit directly. We apply this method to map out the phase diagrams of the above systems. Furthermore, we show that it is capable of capturing the phase diagram of a frustrated magnetism model, the Heisenberg model on a checkerboard lattice. The great controllability and isolation from the environment of a cold atom system offer a playground to study interesting physics in strongly correlated systems. Several proposed control schemes in this thesis have been demonstrated in experiments. By providing detailed evidence from numerical simulations, this work addresses practical routes to novel quantum phases.