# Experimental band structure spectroscopy along a synthetic dimension

## TL;DR

This paper demonstrates the first direct experimental measurement of band structure along a synthetic frequency dimension in a dynamically modulated ring resonator, enabling flexible engineering of photonic band structures.

## Contribution

It provides the first experimental measurement of synthetic dimension band structure and shows how to reconfigure couplings and engineer complex band features.

## Key findings

- Successful direct measurement of synthetic band structure
- Reconfigurable coupling strengths and ranges
- Implementation of long-range coupling and gauge potentials

## Abstract

In recent years there has been significant interest in the concepts of synthetic dimensions, where one couples the internal degrees of freedom of a particle to form higher-dimensional lattices in lower-dimensional physical structures. For these systems the concept of band structure along the synthetic dimension plays a central role in their theoretical description. Here we provide the first direct experimental measurement of the band structure along the synthetic dimension. By dynamically modulating a ring resonator at frequencies commensurate with its mode spacing, we realize a periodically driven system with a synthetic frequency dimension lattice. The strength and range of the couplings along the lattice can be dynamically reconfigured by changing the amplitude and frequency of modulation. We show theoretically and demonstrate experimentally that time-resolved transmission measurements of this system result in a direct "read out" of its band structure. We also show how long-range coupling, photonic gauge potentials and nonreciprocal bands can be realized in the system by simply incorporating additional frequency drives, enabling great flexibility in engineering the band structure.