Synthetic dimensions in ultracold molecules: quantum strings, membranes, and dissipation-induced topology

Ultracold molecules give rise to new types of correlated matter driven by their strong dipolar interactions and numerous rotational states. I will describe how one can exploit these rotational states as a "synthetic dimension", an extra effective spatial dimension in addition to the real physical ones. Hundreds of fully tunable synthetic lattice sites are feasible, in contrast to atoms, where synthetic dimensions are typically restricted to three sites. Molecules with synthetic dimensions show intriguing novel phenomena when frozen in place in a deep optical lattice and with microwaves applied to couple the rotational states. One possibility is a type of dissipation-driven topology. Another phase of matter spontaneously reduces its dimension, forming a fluctuating quantum string or membrane on which a strongly interacting condensate lives. I will describe this mechanism and our progress understanding the properties of this quantum membrane.