The dimensionality of a physical system strongly influences its classical and quantum behavior, be it for Ising phase transitions, or the recurrence properties of random walks, or for Anderson localization. Specifically for topological phenomena, richer topological and emergent phases can be expected in higher dimensions. However, experimentally realizing such high-dimensional systems is challenging in real space because it requires complicated spatial structures. I will describe our approach of using internal degrees of freedom of photons such as frequency, temporal modes or spin, to replace real-spatial dimensions. This approach, which is often termed synthetic dimensions (inspired by pioneering work in cold atoms), allows us to experimentally demonstrate analog simulation of many condensed matter phenomena (e.g. the quantum Hall effect, spin-momentum locking, spin-orbit coupling) in a single, periodically modulated resonator through time-resolved band-structure spectroscopy [1]. This elucidates how higher-dimensional physics can be implemented in simpler, experimentally feasible lower-dimensional structures by coupling these internal degrees of freedom. Examples of the flexible tunability of synthetic-space photonic circuits to realize reprogrammable unitary transformations for photons [2] that are useful for quantum computing and ML will also be provided. The talk will conclude with prospects for studying new phases of light and matter such as non-Hermitian topological phases [3], and provide an outlook for interfacing quantum optics with synthetic-space photonics for future quantum technologies.
[1] Dutt, Lin, Yuan, Minkov, Xiao, Fan, Science 367, 59 (2020).
[2] Buddhiraju, Dutt, Minkov, Williamson, Fan, Nature Comm. 12, 2401 (2021).
[3] Wang*, Dutt*, Yang, Wojcik, Vučković, Fan, Science 371, 1240 (2021); Wang, Dutt, Wojcik, Fan, Nature 598, 59 (2021).