Many-body interactions play important roles in a variety of systems ranging from simple atoms to complex biological molecules. Dipole-dipole interactions are essential in protein formation and folding. The interactions can lead to collective and emergent phenomena that cannot be understood by a simple extrapolation of the microscopic laws of a few particles. The research supported by this NSF award aims to gain an experimentally confirmed understanding of many-body dipole-dipole interactions in atomic ensembles. This will be accomplished by using an advanced laser spectroscopic technique that is uniquely sensitive to many-body interactions in complex systems. The experimental results will be compared to simulated results to help develop a theoretical model. This research will contribute to the general understanding of many-body physics in an ensemble of interacting particles, which has profound implications in fields ranging from optical atomic clocks to photosynthesis. The experimental and theoretical approaches developed in the project can be used to study other many-body systems as well. This project also includes efforts to enhance the capacity to train students at Florida International University, a minority serving institution, in science and technology, to strengthen the education of underrepresented groups in the STEM fields. The goal of this project is to quantitatively understand many-body dipole-dipole interactions in atomic ensembles, at densities varying across nine orders of magnitude, and both with or without the presence of thermal motion. The effects of dipole-dipole interactions will be probed by double-quantum two-dimensional coherent spectroscopy, which provides a sensitive and background-free detection of many-body dipole-dipole interactions. The temporal resolution of femtosecond laser pulses allows one to probe the dynamics during the transient processes of interactions. The experiments will be performed on a hot atomic rubidium vapor and also with cold rubidium atoms. The hot atomic vapor provides a broad range of mean interatomic separations and many-body dynamics associated with thermal motion. In comparison, the cold atoms provide an environment in the virtual absence of thermal motion. Comparing the results from cold and hot atoms enables this group to study the effects of thermal motion on the dipole-dipole interactions. The resulting structural and dynamic information will contribute to the development of a theoretical model based on the exciton formalism that accounts for the dipole-dipole interactions in an atomic ensemble. The study will determine fundamental parameters such as dipole-dipole interaction strength, effective interaction range, the number of interacting atoms, excitation-induced many-body states, effects of a buffer gas, and effects of thermal motion of the dipole-dipole interaction in atomic ensembles.