Solitons in nonlinear media can bind to each other. Two solitons at the right separation, with the right relative phase, form a bound state — a soliton molecule. The binding force is mediated by the overlap of their tails: attractive at some separations, repulsive at others, with equilibrium points where the two forces balance. In local media, soliton molecules are fragile. Small perturbations break the balance and the molecule dissociates.
Cold Rydberg atoms provide a nonlocal nonlinearity that stabilizes soliton molecules in (2+1) dimensions (arXiv:2603.21955). Rydberg electromagnetically induced transparency creates a medium where the nonlinear response at one point depends on the light intensity over a range set by the Rydberg blockade radius. This nonlocal coupling generates long-range interactions between solitons that are much stronger than the tail overlap in local media.
The nonlocality enables diverse molecular configurations: rhombic, square, checkerboard, hexagonal lattices — patterns impossible in local media because the tail-mediated binding is too weak to support multi-soliton structures. Two formation mechanisms emerge depending on the nonlocality strength. In the moderately nonlocal regime, long-range interactions alone stabilize the structure. In the strongly nonlocal regime, the solitons must orbit each other — centrifugal force balances the attractive interaction, producing rotating molecular configurations.
At specific orbital velocities, the balance becomes periodic — the bound state breathes, expanding and contracting in a stable cycle. These breather molecules are dynamically stable oscillating bound states of light.
The structural insight: the transition from individual solitons to soliton molecules parallels the transition from atoms to chemical molecules. Both require a binding mechanism that balances attraction and repulsion at a characteristic distance. In local media, the binding is too weak for stable molecules — the optical analog of noble gases that resist bonding. Nonlocality provides the analog of covalent bonding: a long-range interaction that stabilizes multi-particle configurations. The medium's nonlocality plays the role that electron sharing plays in chemistry. The physics of molecular bonding is not chemistry-specific; it's a general consequence of balanced nonlocal interactions.