Jean-Philippe Karr

We calculate the bound-electron $g$ factor for a wide range of rovibrational states of the molecular hydrogen ions H$_2^+$ and HD$^+$. Relativistic and QED corrections of orders up to $α^5$ are taken into account. All contributions are calculated in a nonrelativistic QED framework, except for relativistic corrections of order $(Zα)^4$ and above, which are obtained by calculating the relativistic $g$ factor using a precise minmax finite element solution of the two-center Dirac equation. A relative accuracy of $4-5 \times 10^{-11}$ is achieved for the scalar $g$ factor component, which represents an improvement by more than three orders of magnitude over previous calculations. These results are useful for internal state identification and rovibraional spectroscopy of single molecular hydrogen ions in Penning traps, and open a new avenue towards precision tests of QED.

We report on the production of cold, state-selected H$_2^+$ molecular ions in a linear RF trap. The ions are produced by (3+1) resonance-enhanced multi-photon ionisation (REMPI) of H$_2$, and sympathetically cooled by laser-cooled Be$^+$ ions. After demonstrating and characterizing the REMPI process, we use photodissociation by a deep UV laser at 213~nm to verify the high vibrational purity of the produced H$_2^+$ ion samples. Moreover, the large difference between the photodissociation efficiencies of ions created in the $v=0$ and $v=1$ levels provides a way to detect a $v=0 \to 1$ transition. These results pave the way towards high-resolution vibrational spectroscopy of H$_2^+$ for fundamental metrology applications.

The motional electric field experienced by an H2+ ion moving in a magnetic field induces an electric dipole, so that one-photon dipole transitions between rovibrational states become allowed. Field induced spontaneous decay rates are calculated for a wide range of states. For an ion stored in a high-field (B ~ 10 T) Penning trap, it is shown that the lifetimes of excited rovibrational states can be shortened by typically 1-3 orders of magnitude by placing the ion in a large cyclotron orbit. This can greatly facilitate recently proposed [E. G. Myers, Phys. Rev. A 98, 010101 (2018)] high-precision spectroscopic measurements on H2+ and its antimatter counterpart for tests of CPT symmetry.

We discuss an experimental approach allowing to prepare antihydrogen atoms for the GBAR experiment. We study the feasibility of all necessary experimental steps: The capture of incoming $\bar{\rm H}^+$ ions at keV energies in a deep linear RF trap, sympathetic cooling by laser cooled Be$^+$ ions, transfer to a miniaturized trap and Raman sideband cooling of an ion pair to the motional ground state, and further reducing the momentum of the wavepacket by adiabatic opening of the trap. For each step, we point out the experimental challenges and discuss the efficiency and characteristic times, showing that capture and cooling are possible within a few seconds.

We study the feasibility of nearly-degenerate two-photon rovibrational spectroscopy in ensembles of trapped, sympathetically cooled hydrogen molecular ions using a resonance-enhanced multiphoton dissociation (REMPD) scheme. Taking advantage of quasi-coincidences in the rovibrational spectrum, the excitation lasers are tuned close to an intermediate level to resonantly enhance two-photon absorption. Realistic simulations of the REMPD signal are obtained using a four-level model that takes into account saturation effects, ion trajectories, laser frequency noise and redistribution of population by blackbody radiation. We show that the use of counterpropagating laser beams enables optical excitation in an effective Lamb-Dicke regime. Sub-Doppler lines having widths in the 100 Hz range can be observed with good signal-to-noise ratio for an optimal choice of laser detunings. Our results indicate the feasibility of molecular spectroscopy at the $10^{-14}$ accuracy level for improved tests of molecular QED, a new determination of the proton-to-electron mass ratio, and studies of the time (in)dependence of the latter.