Interferometric Measurements of Many-body Topological Invariants using Mobile Impurities

TL;DR

This paper introduces a novel interferometric method using mobile impurities to measure topological invariants and fractional charges in many-body quantum systems, enabling direct detection of topological order.

Contribution

It proposes a general scheme employing mobile impurities and interferometry to detect topological invariants in strongly correlated many-body states.

Findings

Demonstrates how to measure Chern numbers of quasiparticles.

Shows fractional charge detection in fractional quantum Hall systems.

Suggests extensions to other topological phases like spin liquids.

Abstract

Topological quantum phases cannot be characterized by Ginzburg-Landau type order parameters, and are instead described by non-local topological invariants. Experimental platforms capable of realizing such exotic states now include "synthetic" many-body systems such as ultracold atoms or photons. Unique tools available in these systems enable a new characterization of strongly correlated many-body states. Here we propose a general scheme for detecting topological order using interferometric measurements of elementary excitations. The key ingredient is the use of mobile impurities which bind to quasiparticles of a host many-body system. Specifically we show how fractional charges can be probed in the bulk of fractional quantum Hall systems. We demonstrate that combining Ramsey interference with Bloch oscillations can be used to measure Chern numbers of individual quasiparticles, which gives a direct probe of their fractional charges. We discuss possible extensions of our method to other topological many-body systems, such as spin liquids.