Abstract
Crystals are ubiquitous in nature and are at the heart of material research, solid-state science, and quantum physics. Unfortunately, the controllability of solid-state crystals is limited by the complexity of many-body dynamics and the presence of defects. In contrast, synthetic crystal structures, realized by, e.g., optical lattices, have recently enabled the investigation of various physical processes in a controllable manner, and even the study of new phenomena. Past realizations of synthetic optical crystals were, however, limited in size and dimensionality. Here we theoretically propose and experimentally demonstrate optical frequency crystal of arbitrary dimensions, formed by hundreds of coupled spectral modes within an on-chip electro-optic frequency comb. We show a direct link between the measured optical transmission spectrum and the density of states of frequency crystals in one, two, three, and four dimensions, with no restrictions to further expanding the dimensionality. We demonstrate that the generation of classical electro-optic frequency comb can be modeled as a process described by random walks in a tight-binding model, and we have verified this by measuring the coherent distribution of optical steady states. We believe that our platform is a promising candidate for exploration of topological and quantum photonics in the frequency domain.
Highlights
While most solid-state crystal structures occurring in nature are three-dimensional, recent research efforts have resulted in the discoveries of lower-dimensional structures such as graphene or carbon nanotubes
High-dimensional synthetic crystal structures are of significant interest: they can be used to investigate complex dynamics of solid-state materials, where e.g. the impact of forces, gauge fields, defects or multi-particle interactions could be mapped to higher dimensions[14,15,16]
Discrete lattice points are formed by spectral modes of an optical microring resonator realized in thin-film lithium niobite (LN) integrated photonic platform[18], while the coupling between lattice points is controlled by electro-optic phase modulation[11], enabled by the second-order nonlinearity of LN
Summary
While most solid-state crystal structures occurring in nature are three-dimensional, recent research efforts have resulted in the discoveries of lower-dimensional structures such as graphene or carbon nanotubes. In agreement with the theoretical predictions, we measure the generation of synthetic optical frequency crystals in high-dimensional space.
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