Spectroscopy using dipole-phonon quantum logic

Dipole-phonon quantum logic (DPQL) offers novel approaches for state preparation, measurement, and control of quantum information in molecular ion qubits. Here we report the first experimental demonstration of DPQL as a spectroscopic tool using the shared motional mode of a CaO${}^{+}$-Ca${}^{+}$ ion chain to measure the frequency splitting of the ground $\mathrm{\Omega }$-doublet of CaO${}^{+}$. By comparing the dipole-phonon signal across three trap-frequency ramp ranges, we determine the splitting to be ${\omega }_{mol}=2\pi \times 454\pm 1$ kHz and place a lower bound on the effective dipole-phonon coupling. The rate of observation is limited by the low thermal population in the molecular ground rotational state.