Frequency-encoded synthetic dimensions for Hamiltonian simulation and topological photonics

The frequency modes of photonic resonators offer tantalizing possibilities for analog simulators of Hamiltonians both in the quantum and classical realm. We show how synthetic frequency dimensions can be formed by coupling such modes through external drives, enabling experimental demonstrations of a wide variety of topologically nontrivial effects that are challenging in other platforms. Harnessing the long-range coupling, coherent phase control and unprecedented reconfigurability afforded by synthetic dimensions, we observe phenomena such as the 2D quantum Hall effect and topological phase transitions in 0D structures consisting of one or two resonators. Our work elucidates how higher-dimensional physics can be implemented in simpler, experimentally feasible lower-dimensional structures. We also highlight the potential of scalably constructing new phenomena such as topological energy pumps showing quantized transport that is robust to dissipation by introducing an additional Floquet dimension in coupled resonators.