Due to their rich level structure, molecules are well-suited for probing time variation of fundamental constants, precisely measuring parity violation and time-reversal non-invariance effects, studying quantum mechanical aspects of chemical reactions, and implementing scalable quantum information processing architectures. Molecular ions are particularly attractive for these applications due to their long storage times and the near-perfect isolation from environment that result in long coherence times required to achieve high measurement precision and reduce systematic errors. However, the control of molecular quantum states remains a challenge. Based on quantum logic techniques, we propose a scheme for preparation, manipulation, and detection of quantum states of single molecular ions. The scheme relies on coherent coupling between internal and motional degrees of freedom of the molecular ion via a frequency comb laser field, while detection and cooling of the motion of ions is done via a co-trapped atomic ion.
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