Measurement of topological invariants from mean chiral displacements in dynamically-modulated photonic molecules

Photonic systems have been leveraged for demonstrating a plethora of topological phenomena, particularly utilizing the frequency degree of freedom in photonic resonators. Very recent theory work [1] suggests that one can measure the topological winding number of the SSH model in these synthetic lattices without well-defined boundaries by measuring the mean chiral displacement of the bulk bands. Here, we realize an SSH model in frequency synthetic dimensions using dynamically-modulated coupled ring resonators (also called a 'photonic molecule'), and measure the mean chiral displacement from time-resolved and phase-resolved band structure spectroscopy sampled on both rings. This directly gives us the topological winding number, allowing us to qualitatively and quantitatively distinguish the topological and trivial phases of the SSH model in the presence of loss and drive.

1. G. Villa et al, arXiv:2309.16101 (2023)