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Physical Review A

Simulation and measurement of topological phase transitions with alkaline-earth-metal atoms in optical lattices

Bin Wang, Yu‐Biao Wu, Zhen Zheng, Xu‐Bo Zou

Published Oct 11, 2019• 1 citation
Publisher

Abstract

We present a proposal to realize and detect topological phase transition in optical lattices with alkaline-earth-metal atoms. Using state-dependent lattices and laser-assisted tunneling, we realize a dimerized spin-$1/2$ antiferromagnetic chain with next-nearest-neighbor coupling. We show that the spin chain hosts two symmetric topological phases and undergoes the topological phase transition when we change the alternating strength of nearest-neighbor couplings. We propose to measure the topological phase transition by detecting the entanglement spectrum and nonlocal string order with a quantum gas microscope. Furthermore, from measurement results, we demonstrate the difference of statistical properties between two topological phases. Our proposal can be a promising platform for simulation of topological phase transition.

DOI
10.1103/physreva.100.043607

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We present a proposal to realize and detect topological phase transition in optical lattices with alkaline-earth-metal atoms. Using state-dependent lattices and laser-assisted tunneling, we realize a dimerized spin-1/21/21/2 antiferromagnetic chain with next-nearest-neighbor coupling. We show that the spin chain hosts two symmetric topological phases and undergoes the topological phase transition when we change the alternating strength of nearest-neighbor couplings. We propose to measure the topological phase transition by detecting the entanglement spectrum and nonlocal string order with a quantum gas microscope. Furthermore, from measurement results, we demonstrate the difference of statistical properties between two topological phases. Our proposal can be a promising platform for simulation of topological phase transition.
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.
Abstract We discuss a realization of topological superfluidity with fermionic atoms in an optical lattice. We consider a situation where atoms in two internal states experience different lattice potentials: one species is localized and the other itinerant, and show how quantum fluctuations of the localized fermions give rise to an attraction and spin–orbit coupling in the itinerant band. At low temperature, these effects stabilize a topological superfluid of mobile atoms even if their bare interactions are repulsive. This emergent state can be engineered with alkaline-earth atoms in a superlattice with a dimerized unit cell. To probe its unique properties we describe protocols that use high spectral resolution and controllability of a narrow clock transition, such as momentum-resolved spectroscopy and supercurrent response to a synthetic (laser-induced) magnetic field.
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.
We propose that ultracold alkaline-earth-like atoms confined in one-dimensional optical lattice can realize a Kondo lattice model which hosts a symmetry-protected topological (SPT) phase and an associated quantum phase transition in a controllable manner. The symmetry protection of the phase transition is discussed from two different viewpoints: topological properties related to spatial patterns of Kondo singlets and symmetry eigenvalues of the spin states. We uncover the role of various symmetries in the phase diagram of this system by combining a weak-coupling approach by Abelian bosonization and strong-coupling pictures of ground states. Furthermore, we show that the bosonization approach correctly describes a crossover from a fermionic SPT phase to a bosonic SPT phase and an associated change of protecting symmetries as the charge degrees of freedom are frozen by the Hubbard repulsion.
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 a majority of phases in the periodic table of topological insulators.
Recently, concepts of topological phases of matter are extended to nonequilibrium systems, especially periodically driven systems. In this paper, we construct an example which shows nonequilibrium topological phase transitions using ultracold fermions in optical lattices. We show that the Rabi oscillation has the possibility to induce nonequilibrium topological phases which are classified into time-reversal-invariant topological insulators for a two-orbital model of alkaline-earth-metal atoms. Furthermore, we study the nonequilibrium topological phases using time-dependent Schrieffer--Wolff-type perturbation theory, and we obtain an analytical expression to describe the topological phase transitions from a high-frequency limit of external driving fields.