The building principle of triatomic trilobite Rydberg molecules

We investigate triatomic molecules that consist of two ground state atoms and a highly excited Rydberg atom, bound at large internuclear distances of thousands of \AA ngstroms. In the molecular state the Rydberg electron is in a superposition of high angular momentum states whose probability densities resemble the form of trilobite fossils. The associated potential energy landscape has an oscillatory shape and supports a rich variety of stable geometries with different bond angles and bond lengths. Based on an electronic structure investigation we analyze the molecular geometry systematically and develop a simple building principle that predicts the triatomic equilibrium configurations. %based on the properties of diatomic trilobite molecules. As a representative example we focus on $^{87}$Rb trimers correlated to the $n=30$ Rydberg state. Using an exact diagonalization scheme we determine and characterize localized vibrational states in these potential minima with energy spacings on the order of 100 MHz$\times h$.