Creating locally interacting Hamiltonians in the synthetic frequency dimension for photons

TL;DR

This paper demonstrates how to realize locally interacting Hamiltonians in the synthetic frequency dimension of photonic systems using a specially designed nonlinear ring resonator, enabling new studies in many-body physics and quantum technologies.

Contribution

It introduces a method to achieve local interactions in the synthetic frequency dimension using dispersion-engineered nonlinear ring resonators, enabling simulation of Hamiltonians like the Bose-Hubbard model.

Findings

Successfully numerically implemented the Bose-Hubbard model in synthetic frequency space.

Observed photon blockade effect in the synthetic frequency dimension.

Showed potential for studying many-body physics and quantum information applications.

Abstract

The recent emerging field of synthetic dimension in photonics offers a variety of opportunities for manipulating different internal degrees of freedom of photons such as the spectrum of light. While nonlinear optical effects can be incorporated into these photonic systems with synthetic dimensions, these nonlinear effects typically result in long-range interactions along the frequency axis. Thus it has been difficult to use of the synthetic dimension concept to study a large class of Hamiltonians that involves local interactions. Here we show that a Hamiltonian that is locally interacting along the synthetic dimension can be achieved in a dynamically-modulated ring resonator incorporating $\chi^{(3)}$ nonlinearity, provided that the group velocity dispersion of the waveguide forming the ring is specifically designed. As a demonstration we numerically implement a Bose-Hubbard model, and explore photon blockade effect, in the synthetic frequency space. Our work opens new possiblities for studying fundamental many-body physics in the synthetic space in photonics, with potential applications in optical quantum communication and quantum computation.