An experimental test of the ab initio theory of the hyperfine structure of the molecular hydrogen ion at the 10^-7 fractional level

• Applicants: Dr. Soroosh Alighanbari; Professor Stephan Schiller, Ph.D.
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas ; Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 524038941

This proposal focuses on a precision measurement of the hyperfine structure (HFS) of molecular hydrogen ions (MHI) and confrontation with its theoretical prediction. The HFS structure of MHIs offers much more opportunity for a high-precision comparison of theory and experiment than the HFS of hydrogen (H) and deuterium (D). In these atoms, the nuclear contributions (3x10^-5), that cannot be determined ab initio, limit the precision. In contrast, the HFS of MHI can be predicted to the level of 1x10^-6 by making use of already obtained theoretical and experimental results on H/D combined with a sophisticated quantum electrodynamics treatment of the MHI (Korobov et al. 2020, Karr et al. 2020, Haidar et al 2022). This fractional uncertainty is approximately 40 times smaller than for the atomic systems. These newest theoretical results have considerably improved the uncertainties of the largest HFS hamiltonian coefficients, the nuclear-spin- electron-spin interaction coefficient (Karr et al. 2020) and the electron-spin-rotation interaction coefficient (Korobov et al. 2020, Haidar et al 2022). Now, the predicted differences between HFS components of the rotational transition of the HD+ show deviations as large as 10 sigma from the experimental results (Alighanbari et al, 2020). Therefore, new high-precision experimental measurements, complementary to previous measurements, are required to resolve or confirm the discrepancy. We propose to measure a particular set of so far unexplored hyperfine components of the rotational transition that will allow us to directly determine the nuclear-spin-electron-spin interaction coefficients in the ground state and in the first rotationally excited state. We will also determine the electron-spin-rotation interaction coefficient for the excited state. We aim to measure these hyperfine structure hamiltonian coefficients with uncertainties smaller or comparable to the theory predictions, therefore achieving the stringent test of the HFS theory prediction. To achieve this, we will carefully determine the systematic shifts of the transition frequencies and correct for them. The proposed work can also contribute to the search for new physics beyond the standard model by searching for exotic interactions between electrons, protons, and deuterons. Previous spectroscopic results on HD+ were interpreted as providing upper limits to spin-independent exotic interactions. In the proposed work, we will be able to test for the existence of spin-dependent new forces with ranges on the order of 1 Ångstrom by analyzing the deviations between experimental and theoretical values, if found.

• DFG Programme: Research Grants