Topology with Synthetic dimensions in Rydberg Atoms

The recent realization of a 6-site synthetic dimension with Rydberg states of ultracold ⁸⁴Sr atoms, using microwaves as synthetic tunnelings between synthetic lattice sites demonstrates a new platform to study topological quantum matter. The ability to adjust each tunneling rate and on-site potential offers capabilities to create not only conventional topological band structures, but also Floquet bands, disorder, and interacting topological systems. To harness this potential, we must understand to what extent the experimental platform matches its idealized model of a synthetic dimension. We do this by calculating the effects of going beyond the rotating-wave-approximation, unwanted nearby magnetic levels, and possible decoherence mechanisms, and we compare with experimental measurements. We conclude that these pose no significant obstacles to scaling to more levels and atoms, making the platform promising to study synthetic quantum matter. Looking forward, we describe how interacting topological matter can be studied by loading these atoms in microtraps and exploiting the strong dipole-dipole interaction of Rydberg atoms.