Adiabatic Ground State Preparation for an Interacting Synthetic Dimension System

Synthetic dimensions provide a powerful framework for engineering and exploring quantum many-body physics through the reinterpretation of the internal states of atoms/molecules as extra spatial degrees of freedom. Here, we investigate adiabatic ground state preparation of synthetic dimension systems constructed from the internal states of ultracold molecules or Rydberg atoms. Specifically, we focus on realizing an interacting 2D synthetic dimension system with a 1D chain of ultracold molecules or Rydberg atoms, where effective tunneling between synthetic sites is controlled by highly tunable microwave fields and dipolar interactions connect neighboring lattice sites. By numerically simulating adiabatic state preparation, we explore optimal ramp protocols that maximize ground state fidelity and suppress diabatic excitations. Our results provide experimentally realistic protocols to prepare ground states with high fidelity in interacting synthetic dimensions, paving the way for the experimental investigation of ground state properties of synthetic dimension systems and novel quantum string phases.