Greiner is the George Vasmer Leverett Professor of Physics at Harvard University, where he is also a co-director of both the Harvard-MIT Center for Ultracold Atoms and the Max Planck-Harvard Research Center for Quantum Optics.
He is a pioneer in quantum science and uses ultracold atoms in optical lattices to create highly controlled artificial many-body quantum systems. In 2003, while earning his Ph.D. in experimental physics from the Ludwig-Maximilians-Universität in Munich, Germany, he carried out the first quantum simulation. From 2003 to 2005, he completed postdoctoral research with Deborah Jin at JILA (the joint institute of the University of Colorado Boulder and the National Institute of Standards and Technology), where he realized a cold atom fermionic superfluid. In his research group at Harvard, he has developed quantum gas microscopy, enabling single atom control for quantum simulations. He is currently working on Fermi-Hubbard, Bose-Hubbard, dipolar and Rydberg array systems.