Photonic simulators using synthetic frequency dimensions have enabled flexible experimental analogues of condensed-matter systems. However, so far, such photonic simulators have been limited in scale, yielding results that suffer from finite-size effects. Here we present an analogue simulator capable of simulating large two-dimensional (2D) and 3D lattices, as well as lattices with non-planar connectivity. Our simulator takes advantage of the broad bandwidth achievable in photonics, allowing our experiment to realize programmable lattices with over 100,000 lattice sites. We showcase the scale of our simulator by demonstrating the extension of bandstructure spectroscopy from 1D to 2D and 3D lattices. We then report the direct observation of time-reversal symmetry-breaking in a triangular lattice in both momentum and real space, as well as site-resolved occupation measurements in a tree-like geometry that serves as a toy model in quantum gravity. Moreover, we demonstrate a method to excite arbitrary multisite states, which we use to study the response of a 2D lattice to both conventional and exotic input states. Our work highlights the scalability and flexibility of optical synthetic frequency dimensions. Future experiments building on our approach will be able to explore non-equilibrium phenomena in high-dimensional lattices and to simulate models with nonlocal higher-order interactions.

使用合成频率维度的光子模拟器使凝聚态系统的灵活实验模拟成为可能。然而，到目前为止，此类光子模拟器的规模有限，产生的结果受到有限尺寸效应的影响。在这里，我们提出了一个模拟模拟器，能够模拟大型二维 (2D) 和 3D 晶格，以及具有非平面连接的晶格。我们的模拟器利用光子学可实现的宽带宽，使我们的实验能够实现具有超过 100,000 个晶格点的可编程晶格。我们通过演示能带结构光谱从 1D 到 2D 和 3D 晶格的扩展来展示我们模拟器的规模。然后，我们报告了在动量和真实空间中对三角晶格中时间反转对称性破缺的直接观察，以及作为量子引力玩具模型的树状几何体中的位置分辨占据测量。此外，我们展示了一种激发任意多点状态的方法，我们用它来研究二维晶格对传统和奇异输入状态的响应。我们的工作突出了光学合成频率维度的可扩展性和灵活性。以我们的方法为基础的未来实验将能够探索高维晶格中的非平衡现象，并模拟具有非局部高阶相互作用的模型。我们的工作突出了光学合成频率维度的可扩展性和灵活性。以我们的方法为基础的未来实验将能够探索高维晶格中的非平衡现象，并模拟具有非局部高阶相互作用的模型。我们的工作突出了光学合成频率维度的可扩展性和灵活性。以我们的方法为基础的未来实验将能够探索高维晶格中的非平衡现象，并模拟具有非局部高阶相互作用的模型。