Quantum logic spectroscopy of the hydrogen molecular ion

The hydrogen molecular ion H₂⁺ is the simplest stable molecule, and its structure can be calculated ab initio with high precision using quantum electrodynamics. By comparing the calculations with experimental data, fundamental constants can be determined, and the validity of the theory itself can be tested. However, challenging properties such as high reactivity, low mass, and the absence of rovibrational dipole transitions have thus far limited spectroscopic studies of H₂⁺.

We trap a single H₂⁺ molecule together with a single beryllium ion using a cryogenic Paul trap, achieving trapping lifetimes of 11 h and ground-state cooling of the shared axial motion. With this platform, we have implemented quantum logic spectroscopy of H₂⁺. The H₂⁺ molecule is produced in a chosen rovibrational state using resonance-enhanced multiphoton ionization. We use quantum-logic operations between the molecule and the beryllium ion for the preparation of single hyperfine states and non-destructive state readout. In the lowest rovibrational state of ortho-H₂⁺ (rotation L = 1, vibration ν = 0), we achieve 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 observe sub-Hz linewidths and statistical uncertainties in the mHz range.

We are now performing a systematic measurement of the hyperfine structure, which will provide a stringent test of state-of-the-art molecular theory and enable us to place an improved bound on a possible tensor force between the two constituent protons of the H₂⁺ molecule.

Our results pave the way for high-precision rovibrational spectroscopy of single H₂⁺ molecules, which would enable tests of quantum electrodynamics, metrology of fundamental constants such as the proton-electron mass ratio, and the implementation of an optical molecular clock based on the simplest molecule in nature.