Synthetic space with arbitrary dimensions in a few rings undergoing dynamic modulation

TL;DR

This paper demonstrates that a single dynamically modulated ring resonator can generate a synthetic space of arbitrary dimensions, enabling exploration of high-dimensional topological physics and control of light spectra in low-dimensional structures.

Contribution

It introduces a method to create high-dimensional synthetic spaces using a single ring resonator with dynamic modulation, enabling simulation of complex topological models like the Haldane model.

Findings

Synthetic space of arbitrary dimensions can be realized with a single ring.

The Haldane model can be implemented in the synthetic space.

Photon dynamics in synthetic spaces allow spectrum control.

Abstract

We show that a single ring resonator undergoing dynamic modulation can be used to create a synthetic space with an arbitrary dimension. In such a system the phases of the modulation can be used to create a photonic gauge potential in high dimensions. As an illustration of the implication of this concept, we show that the Haldane model, which exhibits non-trivial topology in two dimensions, can be implemented in the synthetic space using three rings. Our results point to a route towards exploring higher-dimensional topological physics in low-dimensional physical structures. The dynamics of photons in such synthetic spaces also provides a mechanism to control the spectrum of light.