Quantum simulation of exotic PT-invariant topological nodal loop bands with ultracold atoms in an optical lattice

TL;DR

This paper classifies PT-invariant topological metals using KO-theory, constructs a realistic cold atom model for topological nodal loops, and proposes experimental methods to detect and study these exotic states.

Contribution

It provides the first rigorous classification of PT-invariant topological metals and proposes a feasible cold atom setup to realize and detect topological nodal loop states.

Findings

Topological NL states characterized by a Z2 invariant in cold atom systems.

Detection of nodal loops via Bloch-Zener oscillations and time-of-flight imaging.

Surface states can be probed through Bragg spectroscopy.

Abstract

Since the well-known PT symmetry has its fundamental significance and implication in physics, where PT denotes the combined operation of space-inversion P and time-reversal T, it is extremely important and intriguing to completely classify exotic PT-invariant topological metals and to physically realize them. Here we, for the first time, establish a rigorous classification of topological metals that are protected by the PT symmetry using KO-theory. As a physically realistic example, a PT-invariant nodal loop (NL) model in a 3D Brillouin zone is constructed, whose topological stability is revealed through its PT-symmetry-protected nontrivial Z2 topological charge. Based on these exact results, we propose an experimental scheme to realize and to detect tunable PT-invariant topological NL states with ultracold atoms in an optical lattice, in which atoms with two hyperfine spin states are loaded in a spin-dependent 3D OL and two pairs of Raman lasers are used to create out-of-plane spin-flip hopping with site-dependent phase. Such a realistic cold-atom setup can yield topological NL states, having a tunable ring-shaped band-touching line with the two-fold degeneracy in the bulk spectrum and non-trivial surface states. The states are actually protected by the combined PT symmetry even in the absence of both P and T symmetries, and are characterized by a Z2-type invariant (a quantized Berry phase). Remarkably, we demonstrate with numerical simulations that (i) the characteristic NL can be detected by measuring the atomic transfer fractions in a Bloch-Zener oscillation; (ii) the topological invariant may be measured based on the time-of-flight imaging; and (iii) the surface states may be probed through Bragg spectroscopy. The present proposal for realizing topological NL states in cold atom systems may provide a unique experimental platform for exploring exotic PT-invariant topological physics.