molecules*

I will present our latest results, implementing pure quantum state preparation, coherent manipulation, and non-destructive state readout of the hydrogen molecular ion H₂⁺. The hydrogen molecular ion is the simplest stable molecule, and its structure can be calculated ab-initio to high precision. However, challenging properties such as high reactivity, low mass, and the absence of rovibrational dipole transitions have thus far strongly limited spectroscopic studies of H₂⁺.

We trap a single H₂⁺ molecule together with a single beryllium ion using a cryogenic Paul trap apparatus, achieving trapping lifetimes of 11 h and ground-state cooling of the shared axial motion. With this platform we have recently implemented Quantum Logic Spectroscopy of H₂⁺. We utilize helium buffer-gas cooling to prepare the lowest rovibrational state of ortho-H₂⁺ (rotation L=1, vibration ν=0). We combine this with quantum-logic operations between the molecule and the beryllium ion for the preparation of single hyperfine states and non-destructive readout, achieving a combined state-preparation and readout fidelity of 66.5(8)%. We demonstrate Rabi flopping on several hyperfine transitions using stimulated Raman transitions and microwaves. Utilizing a magnetic field insensitive hyperfine transition driven with a microwave, we perform a proof-of-principle spectroscopy and achieve a statistical uncertainty of 2 Hz.

Our results pave the way for many high-precision spectroscopy studies of H₂⁺, which would enable tests of QED, metrology of fundamental constants, and the implementation of an optical molecular clock based on the simplest molecule in nature.