Quantum logic for molecular quantum information processing

Very recently, molecular ions have been trapped and cooled to the mK regime in well defined internal states [1] opening a new window for precision spectroscopy of molecular species and quantum information with cold molecular ions. A first requirement for both applications is the ability to control and measure the state of molecular ions. I will present our proposal [2] of a fast, non-destructive and temperature independent spectroscopy method suitable to study electronic, vibrational, rotational and Zeeman transitions in complex ions that implements quantum logic schemes~[3] between an atomic ion and the molecular ion of interest, using optical forces on the atom, and optical forces or magnetic field gradients on the molecule. This method sets a starting point for a hybrid quantum computation scheme with molecular and atomic ions, covering the measurement and entangling steps. Finally I will discuss the remarkable decoherence properties of two Zeeman states of the $^{16}$O$_2^+$ molecular ion that make it a promising system for QIPC purposes~[4].\\[4pt] [1] X. Tong {\em et al.}, Phys. Rev. Lett. {\bf 105}, 143001 (2010).\\[0pt] [2] J. Mur-Petit {\em et al.}, arXiv:1106.3320\\[0pt] [3] P. O. Schmidt {\em et al.}, Science {\bf 309}, 749 (2005).\\[0pt] [4] J. Mur-Petit {\em et al.}, in preparation.