Synthetic dimensions have attracted recent attention in the photonics society. It has been difficult to use the synthetic dimension concept to study a large class of Hamiltonians that involves local interactions. How to achieve a Hamiltonian with local interactions in the synthetic space for photons, thus represents an important open theoretical question.

(a) A ring resonator composed by two types of single-mode waveguides A and B. (b) A ring under the dynamic modulation supports a synthetic lattice along the frequency dimension. (c) Normalized distribution of the two-photon correlation probability P_(m,n) for demonstration of the Bose–Hubbard model.

We consider a synthetic frequency dimension of light, formed in a dynamically modulated ring resonator consisting of two sections of waveguides. The two sections have the same χ(3) nonlinear susceptibility but opposite group velocity dispersion (GVD). This design supports an effective Hamiltonian with local photon-photon interactions along the synthetic frequency dimension. As a demonstration we numerically implement a Bose–Hubbard model and explore photon blockade effect in the synthetic frequency space. This work makes an essential step towards achieving locally interacting Hamiltonians in the synthetic frequency dimension for photons, which significantly broadens the range of physics phenomena that can be studied in photonic synthetic space, with potential applications in optical quantum communication and quantum computation.

The paper has been published in Photonics Research with the title “Creating locally interacting Hamiltonians in the synthetic frequency dimension for photons”.

Link: https://doi.org/10.1364/PRJ.396731