# Protocols for dynamically probing topological edge states and dimerization with fermionic atoms in optical potentials

## TL;DR

This paper proposes feasible experimental protocols to detect topological edge states and dimerization in ultracold fermionic atoms confined in optical ring lattices, overcoming background trap challenges.

## Contribution

It introduces methods to generate and detect topological edge states and dimerization in cold-atom systems by manipulating boundary conditions and observing system dynamics.

## Key findings

- Edge states can be generated by opening boundary conditions in a ring lattice.
- Occupation and correlation measurements reveal signatures of dimerization.
- Memory effects distinguish different topological phases.

## Abstract

Topological behavior has been observed in quantum systems including ultracold atoms. However, background harmonic traps for cold-atoms hinder direct detection of topological edge states arising at the boundary because the distortion fuses the edge states into the bulk. We propose experimentally feasible protocols to probe localized edge states and dimerization of ultracold fermions. By confining cold-atoms in a ring lattice and changing the boundary condition from periodic to open using an off-resonant laser sheet to cut open the ring, topological edge states can be generated. A lattice in a topological configuration can trap a single particle released at the edge as the system evolves in time. Alternatively, depleting an initially filled lattice away from the boundary reveals the occupied edge states. Signatures of dimerization in the presence of contact interactions can be found in selected correlations as the system boundary suddenly changes from periodic to open and exhibit memory effects of the initial state distinguishing different configurations or phases.