Topological phases of ultracold molecules in an optical tweezer ladder

The recent experimental realization of optical tweezer arrays of ultracold molecules provides a versatile platform for exploring molecular phases of matter. Here we show that by programming tweezers, the dipolar interactions in an optical tweezer ladder could be tailored to implement a generalized Su-Schrieffer-Heeger model. Through calculating topological invariants, nonlocal string-order parameters, many-particle ground-state degeneracy, and entanglement spectrum, we demonstrate that this ladder at the single-particle level supports two different chiral topological phases and at the many-particle level features two different interacting topological phases and, respectively, possesses much richer topological edge states. We also discuss the detection of these topological phases and their robustness to systematic imperfections. Further generalization to a high dimension could offer opportunities for preparing diverse ultracold molecular topological phases.