# Floquet-engineered vibrational dynamics in a two-dimensional array of trapped ions

## TL;DR

This paper demonstrates Floquet engineering in a scalable 2D trapped-ion system, enabling control over phonon flow and paving the way for simulating topological and gauge phenomena in quantum systems.

## Contribution

It introduces a method to control ion interactions and phonon dynamics via local parametric modulations in a 2D ion array, advancing quantum simulation capabilities.

## Key findings

- Controlled phonon trajectories and interferences achieved.
- Demonstrated tunable long-range ion couplings.
- Opened pathways for simulating topological phenomena.

## Abstract

We demonstrate Floquet engineering in a basic yet scalable 2D architecture of individually trapped and controlled ions. Local parametric modulations of detuned trapping potentials steer the strength of long-range inter-ion couplings and the related Peierls phase of the motional state. In our proof-of-principle, we initialize large coherent states and tune modulation parameters to control trajectories, directions and interferences of the phonon flow. Our findings open a new pathway for future Floquet-based trapped-ion quantum simulators targeting correlated topological phenomena and dynamical gauge fields.