Towards quantum simulation using Rydberg-excited atoms in optical tweezer arrays

Trapped neutral atoms in optical tweezers present a versatile platform for quantum simulation, metrology and quantum information processing. We present a scheme where a synthetic dimension can be added to a one-dimensional array of individually trapped $^{39}K$ atoms by exciting them to Rydberg states. A synthetic lattice of coupled internal states is created by coupling multiple Rydberg levels using microwave fields. Enhanced dipole moments associated with atoms in Rydberg states lead to strong dipole-dipole interactions. These interactions and control of synthetic lattice parameters open up avenues for studying a wide range of quantum many-body phenomena. The near arbitrary ability to engineer a generic tight-binding Hamiltonian in the synthetic dimension allows new capabilities for the exploration of interaction effects in topological and disordered systems. Specifically, we will investigate formation of stable quantum strings which has been predicted to occur in such synthetic systems.