Entanglement in dipolar synthetic dimension platforms with ultracold Rydberg atoms or polar molecules

Synthetic dimension platforms offer pathways to study unique quantum matter. Recent studies (arXiv: 2307.16269) have revealed a rich phase diagram of a quantum many-body system of ultracold atoms (or polar molecules) with a set of Rydberg states (or rotational states) as synthetic dimension where the real particles are arranged in optical microtrap or optical tweezer arrays and interact via dipole-dipole exchange interaction. The Rydberg or the rotational states are coupled via microwaves which are easily tuned to the desired tunneling scheme. Three non-trivial symmetry-broken phases were characterized: two of which are string (1 synthetic dimension) or membrane (2 synthetic dimension) -like phase wherein the only a few synthetic states are populated, and one non-localized but ordered. In this talk, we discuss this system and their quantum phases. The string or membrane-like phase is highly entangled and for carefully chosen real-space geometries and number of synthetic sites, they seem to exhibit a large degeneracy, much like in a quantum liquid. The degeneracy is lifted in the presence of strong synthetic tunneling amplitudes. We will discuss the effects of real-space geometry, different synthetic tunneling schemes and the number of synthetic sites on the ground-state properties. Through this talk, we hope to elucidate that synthetic dimension platforms are very versatile and highly tunable which allows one to generate unique quantum matter by minimal tweaking of the system parameters.