SL\((2,{\mathbb{C}})\) non-Abelian gauge fields in a photonic molecule array
摘要
Engineering the topological properties of the system has been a longstanding subject in physics. Here, we propose a scheme to simulate topological materials with a non-Abelian gauge field in synthetic space-frequency dimensions where the symmetry between spin-flipped hoppings can be levitated by using coupled photonic molecules under dynamic modulations. The frequency-split supermodes in these photonic molecules can serve the pseudospin degree of freedom, which can further be connected along the frequency axis in an independent way, offering the unique opportunity to explore topological physics with imbalanced spin-flipped hoppings leading to a complex generalization of the conventional SU(2) non-Abelian gauge field, i.e., an SL