Quantum Control of Single Molecular Ions

Trapped atoms and ions are among the best-controlled quantum systems which find widespread applications in quantum sciences. For molecules, a similar degree of control is currently lacking owing to their complex energy-level structure. Quantum-logic protocols in which atomic ions serve as probes for molecular ions are a promising route for achieving this level of control, especially for homonuclear species that decouple from blackbody radiation.
In this thesis, we report experimental progress in the quantum state control of single trapped N2+ molecules. N2+ is a homonuclear diatomic molecule with no permanent dipole moment. Thus all rotational-vibrational (rovibrational) transitions are rendered dipole- forbidden in its electronic ground state. Therefore, N2+ is an ideal test bed for precision spectroscopic studies, for tests of fundamental physics, for the realization of mid-IR frequency standards and clocks, and for implementation of molecular qubits for quantum information and computation applications.
Here, a single N2+ ion is produced selectively in the ground rovibronic state and trapped in a radiofrequency ion trap together with one Ca+ ion. In a first step, the Ca+ ion is used to cool the N2+ to the ground state of the trapping potential. A quantum-nondemolition protocol is then implemented on the Ca+ – N2+ two-ion string in order to detect the rotational state of the N2+ ion. The protocol maps the internal state of the N2+ ion onto the external motion which is then detected by the Ca+ ion. The employed state-detection scheme is non-invasive and does not destroy the molecule or the molecular state. The spin-rovibronic state of the molecule is detected with fidelities exceeding 99%. Furthermore, as an application of the state-detection scheme, the transition frequency and the vibronic Einstein-A coefficient of an electric-dipole transition of the molecular ion is measured.
In an effort to develop a complete and conscientious understanding of the mechanism exploited in the rovibronic-state detection of the molecule, this thesis theoretically investigates electric-dipole transitions between molecular states best described by different Hund’s coupling cases. The Hamiltonians for specific states are presented and subtle effects due to the molecular-hyperfine structure and mixing of rotational states are discussed.
This thesis also discusses our setup of a system of narrow linewidth lasers for coherent manipulations of the atomic and the molecular ions. For the Ca+ ion, a cavity stabilized, 729 nm, ECDL is first stabilized to a high finesse cavity for linewidth narrowing and im- proved short term stability. In order to detect and compensate the long term drifts of the cavity, the 729 nm laser frequency is then compared to an UTC-referenced ultrastable laser at 1572 nm via an optical frequency comb. A stability of ~ 1×10−13 is demonstrated in 1 s. For experiments on the N2+ ion, a mid-IR quantum-cascade laser at 4574 nm is stabilized to the optical frequency comb. A sum-frequency generation process, with the cavity stabilized 729 nm laser, is employed in order to bridge the gap between the mid-IR laser and the near-IR comb. A tight lock with a signal-to-noise ratio of ~ 30 dB is demonstrated. The experimental and theoretical developments in this thesis lay the foundations for new approaches to precision spectroscopy and coherent control experiments on molecules.