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.
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All data generated used in this work are available at https://doi.org/10.5281/zenodo.6959554.
All code used in this work are available at https://doi.org/10.5281/zenodo.6959554.
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P.L.M. acknowledges financial support from a David and Lucile Packard Foundation Fellowship, and also membership of the CIFAR Quantum Information Science Program as an Azrieli Global Scholar. We thank NTT Research for their financial and technical support. Portions of this work were supported by the National Science Foundation (award CCF-1918549). We acknowledge helpful discussions with D. Hathcock, E. Mueller, S. Prabhu, E. Rosenberg and members of the NTT PHI Lab/NSF Expeditions research collaboration. We also thank A. Dutt for helpful discussions and for feedback on a draft of the manuscript. We thank M. Buttolph for assistance with fibre splicing and V. Tjong for contributing to the instrumentation-control code.
The authors declare no competing interests.
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Senanian, A., Wright, L.G., Wade, P.F. et al. Programmable large-scale simulation of bosonic transport in optical synthetic frequency lattices. Nat. Phys. 19, 1333–1339 (2023). https://doi.org/10.1038/s41567-023-02075-7
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