In 2007-2013 he shared this position with a faculty appointment at Physics Department of the University of Massachusetts, Amherst (USA).
[11][12][13] Currently he is serving as the co-organiser and chair of the selection committee of the Lise Meitner Distinguished Lecture, the general audience lecture taking place at AlbaNova University Center in Stockholm on annual basis.
He coauthored the textbook on modern theory of superfluidity with Boris Svistunov and Nikolay Prokof'ev.
[14] In 2021, Babaev and collaborators published evidence of a "quartic metal", an exotic phase of low-temperature matter that exhibits the breaking of time-reversal symmetry.
[15] Göran Gustafsson Prize in Physics from the Royal Swedish Academy of Sciences "For original theoretical research which has already shown new ways to understand complex systems and processes in materials physics"[16][17] American Physical Society Fellow "For pioneering contributions to the theory of multicomponent superconductors and superfluids"[1] Tage Erlander prize in Physics of the Royal Swedish Academy of Sciences "For groundbreaking theoretical work that predicts new states of matter in the form of quantum fluids with novel properties"[18] Outstanding Young Researcher Award from Swedish Research Council US National Science Foundation CAREER Award