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We present a quantum logic scheme to detect atomic and molecular ions in different states of angular momentum based on their magnetic $g$-factors. The state-dependent magnetic $g$-factors mean that electronic, rotational or hyperfine states may be distinguished by their Zeeman splittings in a given magnetic field. Driving motional sidebands of a chosen Zeeman splitting enables reading out the corresponding state of angular momentum with an auxillary logic ion. As a proof-of-principle demonstration, we show that we can detect the ground electronic state of a ${^{174}}$Yb$^+$ ion using ${^{171}}$Yb$^+$ as the logic ion. Further, we can distinguish between the ${^{174}}$Yb$^+$ ion being in its ground electronic state versus the metastable ${^{2}}D_{3/2}$ state. We discuss the suitability of this scheme for the detection of rotational states in molecular ions.
The interaction between the electric dipole moment of a trapped molecular ion and the configuration of the confined Coulomb crystal couples the orientation of the molecule to its motion. We consider the practical feasibility of harnessing this intera
A mixed-species geometric phase gate has been proposed for implementing quantum logic spectroscopy on trapped ions that combines probe and information transfer from the spectroscopy to the logic ion in a single pulse. We experimentally realize this m
Precision spectroscopy of atomic systems is an invaluable tool for the advancement of our understanding of fundamental interactions and symmetries. Recently, highly charged ions (HCI) have been proposed for sensitive tests of physics beyond the Stand
Control over physical systems at the quantum level is a goal shared by scientists in fields as diverse as metrology, information processing, simulation and chemistry. For trapped atomic ions, the quantized motional and internal degrees of freedom can
Trapped atomic ions have proven to be one of the most promising candidates for the realization of quantum computation due to their long trapping times, excellent coherence properties, and exquisite control of the internal atomic states. Integrating i