Modulated continuous wave control for energy-efficient electron-nuclear spin coupling

We develop energy efficient, continuous microwave schemes to couple electron and nuclear spins, using phase or amplitude modulation to bridge their frequency difference. These controls have promising applications in biological systems, where microwave power should be limited, as well as in situations with high Larmor frequencies due to large magnetic fields and nuclear magnetic moments. These include nanoscale NMR where high magnetic fields achieves enhanced thermal nuclear polarization and larger chemical shifts. Our controls are also suitable for quantum information processors and nuclear polarization schemes.E. S. and J. C. acknowledge financial support from Spanish MINECO/FEDER FIS2015-69983-P, Basque Government IT986-16, as well as from QMiCS (820505) and OpenSuperQ (820363) of the EU Flagship on Quantum Technologies. J. C. acknowledges support by the Juan de la Cierva Grant No. IJCI-2016-29681. E. T. and J. J. G. R. acknowledge support from Spanish MINECO/FEDER Project No. FIS2015-70856-P, No. FIS2016-81891-REDT and CAMPRICYT ProjectQUITEMAD þ CMNo. S2013- ICE2801. M. B. P. acknowledges support by the ERC Synergy grant BioQ (Grant No. 319130), the EU project HYPERDIAMOND, the QuantERA project NanoSpin, the BMBF project DiaPol, the state of Baden-Württemberg through bwHPC, and the German Research Foundation (DFG) through Grant No. INST 40/467-1 FUGG. This material is also based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advance Scientific Computing Research (ASCR), Quantum Algorithms Teams project under field work proposal ERKJ335.Peer Reviewe