Resonant energy transfer in electron - driven proton pumps

1 Frontier Research System, The Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama 351-0198, Japan 2 CREST, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan 3 Quantum Cat. Analytics, 1751 67 St. #E11, Brooklyn, New York 11204, USA 4 Department of Physics, Queens College, The City University of New York, Flushing, New York 11367, USA 5 Department of Engineering Science and Physics, College of Staten Island, The City University of New York, Staten Island, New York 10314, USA 6 Center for Theoretical Physics, Physics Department, University of Michigan, Ann Arbor, MI 48109, USA