Eigenstates and excitations of the simple atom-molecule Bose-Einstein condensate

Abstract

We analyze the mean-field eigenstates of the atom-molecule Bose-Einstein condensate (AMBEC) under the assumption that the background (elastic) scattering length of the atoms can be ignored. It is shown that the relevant eigenstates are localized in the space of the condensate parameters: The eigenstate has a different character in different regions of the parameter space, and at the interface of two local eigenstates the properties of the system may change nonanalytically. Using both analytical and numerical techniques, we find the approximate boundaries of the local eigenstates and identify the types of parametric excitations that occur when an eigenstate is forced outside of its region of validity by a parameter sweep. We contrast the properties of the mean-field parametric excitations found in AMBEC with the experimentally observed excitations of the BEC.