Interacting Quantum Matter in Synthetic Dimensions

Synthetic dimension platforms offer unique ways of exploring quantum matter. These highly tunable platforms can be used to mimic solid-state phenomena, as well as to realize novel Hamiltonians beyond the realms of usual solid-state materials or even optical lattices.

In this talk, I will present the many-body physics of atoms and molecules combining internal synthetic lattices with real-space microtrap arrays. In this setup, the atoms/molecules interact via dipole-dipole angular-momentum-exchange interactions, and I focus on the case of uniform synthetic tunneling rates. Through a combination of mean-field theory and quantum Monte Carlo results, I will show that the interplay between the interaction and synthetic tunneling gives rise to several different phases, symmetry-breaking and otherwise.

One particularly interesting phase is one where the system is localized along the synthetic dimension, forming a quantum string or membrane that fluctuates in a higher dimensional space. We find tri-critical points on the phase boundaries between this string phase and a disordered gas when the finite size of the synthetic dimension is six sites or larger.

I will conclude with some open questions and motivate other systems that can be engineered with synthetic dimension platforms in general that are hard to build elsewhere.