Tailoring synthetic curved spacetimes

Recent experimental progress has allowed physicists to explore quantum matter in curved spacetimes. I will discuss some new approaches to engineer synthetic curved spacetimes [1-3]. One is to exploit a duality between non-Hermiticity and curved spaces, which equates two distinct languages to unfold deep connections between two active research areas. While providing solutions to long-lasting questions in non-Hermitian quantum mechanics, this duality also enables an unprecedented recipe to design synthetic curved spaces. The other approach is mapping quantum dynamics to certain geometries that are governed by the same symmetries. This geometrization not only delivers new protocols to control quantum dynamics but also leads to a unique perspective of studying spacetimes emergent from quantum dynamics.