Shaffer, James PYang, Jin2019-08-222019-08-222019-08-22https://hdl.handle.net/11244/321267In this thesis, we investigate few-body physics and many-body physics of ultralong-range Rydberg molecules. Ultralong-range Rydberg molecules are formed through scattering processes between Rydberg electrons and ground state atoms. The huge size of the Rydberg electron's orbit makes the Rydberg electron able to interact with more than one ground state atom in cold atomic gases with atom number densities from 10$^{12}$ cm$^{-3}$ to 10$^{14}$ cm$^{-3}$. In cold atomic gases, the ground state atoms on average are far away from each other. They are weakly interacting. Depending on the angular momentum state of the Rydberg electron, two types of polyatomic Rydberg molecules have been studied. When the Rydberg electron is in an $ns$ state, the isotropic probability distribution of the Rydberg electron makes the Rydberg electron interact with different ground state atoms equally. The total binding energy is a summation of the binding energy from each scattering process. These additive interactions have been studied using Cs $6s+83s$ and $6s+90s$ polyatomic Rydberg molecules in this thesis. When the Rydberg electron is in an $l>0$ angular momentum state, spatial correlations between different ground state atoms are established through the anisotropic probability distribution of the Rydberg electron. The total binding energy depends on the relative positions of different ground state atoms. These nonadditive interactions are studied using Cs $6s+6s+34d$ and $6s+6s+36d$ triatomic Rydberg molecules in this thesis.Rydberg MoleculesMany-body PhysicsUltracold ScatteringRydberg Atoms