Precision quantum logic spectroscopy and control of rotational and hyperfine states in a single trapped molecular CaOH⁺ ion

The technologies and methods developed for quantum computing with trapped atomic ions enable precision measurement of molecular transitions and control of their quantum state even in a noisy thermal environment. Quantum control of the rotational and hyperfine state of a molecule is a fundamental requirement for experiments which exploit its large Hilbert space, its symmetry properties, or its potentially large electric dipole moment. Examples of such experiments include encoding of a qudit or an error-corrected qubit and parity violation searches for an electron electric dipole moment. Quantum logic spectroscopy based on driving Raman transitions between hyperfine states in CaOH⁺ on a motional sideband is read out via a co-trapped Ca⁺ logic ion. We measure the signal arising from Raman transitions within the two hyperfine manifolds in each rotational level and their dependence on magnetic field. We also explore this measurement technique as a thermometry tool to assess the performance of rotational cooling via P-branch rovibrational optical pumping and the rotational signature of inter-manifold transitions coupling the two hyperfine manifolds. We discuss the challenges in resolving very small frequency Raman transitions and the strategies to overcome them which include false positive motional excitation from polarization impurity-driven optical dipole force, AC Stark coupling of Zeeman states, and thermal radiation. We will also present progress in state preparation, Bayesian state estimation, and quantum information processing preliminaries with trapped molecular ions.