An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators

TL;DR

This paper proposes a cold-atom quantum simulator using optical lattices to emulate relativistic fermionic theories and topological insulators across various dimensions, enabling exploration of complex quantum phases.

Contribution

It introduces a versatile setup combining bi-chromatic lattices and Raman transitions to engineer spin-dependent tunneling for simulating diverse relativistic and topological models.

Findings

Design of a spin-independent optical lattice trapping hyperfine states

Implementation of assisted-hopping processes for model simulation

Capability to realize multiple topological insulator phases

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.