# Topological polarons, quasiparticle invariants and their detection in 1D symmetry-protected phases

## TL;DR

This paper links the topological Zak phase of quasiparticles in 1D symmetry-protected phases to their potential for direct experimental detection using quantum impurities and interferometry, with applications in ultracold atoms.

## Contribution

It establishes a direct relation between many-body Zak phases and quasiparticle Zak phases, proposing a practical detection method in 1D topological systems.

## Key findings

- Quasiparticle Zak phases are related to many-body Zak phases in 1D topological systems.
- Quantum impurities can be used to measure quasiparticle topological invariants.
- Experimental protocols for ultracold atomic systems are proposed and analyzed.

## Abstract

In the presence of symmetries, one-dimensional quantum systems can exhibit topological order, which in many cases can be characterized by a quantized value of the many-body geometric Zak or Berry phase. We establish that this topological Zak phase is directly related to the Zak phase of an elementary quasiparticle excitation in the system. By considering various systems, we establish this connection for a number of different interacting phases including: the Su-Schrieffer-Heeger model, p-wave topological superconductors, and the Haldane chain. Crucially, in contrast to the bulk many-body Zak phase associated with the ground state of such systems, the topological invariant associated with quasiparticle excitations (above this ground-state) exhibit a more natural route for direct experimental detection. To this end, we build upon recent work [Nature Communications 7, 11994 (2016)] and demonstrate that mobile quantum impurities can be used, in combination with Ramsey interferometry and Bloch oscillations, to directly measure these quasiparticle topological invariants. Finally, a concrete experimental realization of our protocol for dimerized Mott insulators in ultracold atomic systems is discussed and analyzed.