Precision Vibrational Spectroscopy of Single Molecular Hydrogen Ions in a Penning trap

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This project addresses the topics ``metrology of fundamental constants" and the ``search for beyond-Standard-Model Physics". It proposes to develop high-precision spectroscopy of molecular hydrogen ions (MHI) as a probe for these topics. Our world is very successfully described at the microscopic level by the relativistic quantum field theories of the Standard Model. Charge-parity-time invariance (CPTI) is deeply implemented into the assumptions of such theories. CPTI has been the subject of experimental tests for many decades, and the precision of the tests has steadily improved. But it is imperative to continue improving the precision further. In fact, a violation of CPTI provides one possible path to explain the striking matter-antimatter imbalance that is observed on cosmological scales. Currently, advanced research programs on CPTI tests are being conducted at CERN’s antimatter factory. They address the mass and charge of electron and proton as well as and nuclear properties of the proton, and of their antiparticles. They are performed by Penning trap spectroscopy and by H-bar spectroscopy and will certainly improve over the years to come. Now, a completely new option is emerging: A CPTI test consisting in comparing the vibrational frequencies of the molecular hydrogen ions H_2^+ and anti-H_2^+. These frequencies are of interest because they have a first-order sensitivity to the masses of the proton/antiproton, electron/positron and a (small) sensitivity to the nuclear charge radius. The frequencies can be determined accurately by laser spectroscopy and optical frequency metrology. MHI can relatively easily be trapped and cooled in an ion trap, permitting high-resolution spectroscopy. Theoretical analyses indicate that fractional uncertainties in the 1E-17 range should be feasible, much lower than Penning trap mass spectroscopy will ever achieve. Moreover, vibrational frequencies also depend on the Coulomb interaction between the two nuclei, therefore a H_2^+ to anti-H_2^+ comparison would also implement a precision CPTI test of the p – p-bar interaction, which no current experiment can provide. The established trap type capable of storing charged anti-matter particles for months at a time is the Penning trap. Therefore, in this project we aim to demonstrate, for the first time, that vibrational spectroscopy of MHI in a cryogenic Penning trap is possible, and aim to reach a first milestone, 1E-12 fractional uncertainty, for both H_2^+ and HD^+. Knowledge of vibrational transition frequencies of the MHI can serve to determine the ratios of nuclear-to-electron mass, and to set upper bounds to a hypothetical additional force between the two nuclei, mediated by a dark-matter particle. To do so, the experimental frequencies must be confronted with ab initio predictions. In this project, we will for the first time obtain directly a spectroscopic value of m_e/m_p with an uncertainty competitive with the best direct mass measurements.