Programmable large-scale simulation of bosonic transport in optical synthetic frequency lattices

Photonic simulators using synthetic frequency dimensions have enabled flexible experimental analogues of condensed-matter systems, realizing phenomena that are impractical to observe in real-space systems. However, to date such photonic simulators have been limited to small systems suffering from finite-size effects. Here, we present an analog simulator capable of simulating large 2D and 3D lattices, as well as lattices with non-planar connectivity, including a tree lattice that serves as a toy model in quantum gravity. Our demonstration is enabled by the broad bandwidth achievable in photonics, allowing our simulator to realize lattices with over 100,000 lattice sites. We explore these large lattices in a wide range of previously inaccessible regimes by using a novel method to excite arbitrary states. Our work establishes the scalability and flexibility of programmable simulators based on synthetic frequency dimensions in the optical domain. We anticipate that future extensions of this platform will leverage advances in high-bandwidth optoelectronics to support simulations of dynamic, non-equilibrium phases at the scale of millions of lattice sites, and Kerr-frequency-comb technology to simulate models with higher-order interactions, ultimately in regimes and at scales inaccessible to both digital computers and realizable materials.