Beyond Vector Potentials: Synthetic Tensor Gauge Fields

The study of synthetic gauge fields has led to a wealth of exciting developments across multiple areas of physics over the past two decades. Until recently, these efforts have focused almost exclusively on vector gauge fields. In this talk, I will show how this paradigm can be extended to a new and largely unexplored regime of synthetic tensor gauge fields. I will discuss experimentally realistic routes for realizing such fields and highlight the qualitatively new phenomena that emerge from their coupling to exotic quantum phases. I will also demonstrate that these tensor gauge fields can be made complex, enabling access to an entirely new class of non-Hermitian phenomena.