Formation and propagation of stable high-dimensional soliton molecules and breather molecules in a cold Rydberg atomic gas

We investigate the mechanisms of formation of stable (2+1)-dimensional optical soliton molecules (SMs) and breather molecules (BMs) in a Rydberg atomic gas, highlighting the distinct roles of nonlocality. The underlying giant, nonlocal nonlinearity induced via Rydberg electromagnetically induced transparency (EIT), supports diverse, large-size lattice SMs (rhombic, square, checkerboard, hexagonal lattice SMs). Crucially, we identify two distinct formation regimes: In the nonlocal regime, long-range interactions alone stabilize the SMs without requiring initial motion. In contrast, within the strongly nonlocal regime, an initial velocity is essential to generate a centrifugal force that counteracts the strong attraction, resulting in rotating SMs. Furthermore, specific initial velocities can induce a periodic breathing instability, leading to the formation of BMs. Our study offers a new scheme for engineering SMs with diverse configurations and opens new avenues for data processing and transmission in optical systems.