QULEPSHYDRE

The molecular hydrogen ion H2+ has vibrational transitions of which the frequencies can be calculated with 12 digit precision, and measured with similar precision using current spectroscopy techniques. Quantum Logic Spectroscopy (QLS) would improve measurements by several orders of magnitude, which is extremely promising for the determination of fundamental constants, such as the proton-to-electron mass ratio (µ), the Rydberg constant and nuclear charge radii, and for searches for new physics such as variations of µ. The QULEPSHYDRE project aims to implement QLS of H2+ with 14 digit precision and to pave the way for future spectroscopy at the 17 digit level. QULEPSHYDRE involves two groups expert at precision spectroscopy of trapped ions. The Trapped Ion group at LKB (France) works with Be+ and H2+ ions, with a complementary expertise in the frequency control of mid-IR quantum cascade lasers (QCLs). The experimental quantum metrology group at PTB (Germany) is a world-leading group in QLS and works on MgH+ molecular ions. The synergies of the project stem from the complementarity of the two partner groups, and from the similarity between the H2+ and MgH+ (hyper)fine/ Zeeman structure. The QLS protocols developed at PTB on MgH+ will readily apply to H2+ at LKB, while the know-how of LKB in QCL frequency stabilization is essential to implement rotational laser cooling of MgH+ at PTB. The instruments developed during the QULEPSHYDRE project (QCL ion trap and mid-IR QCL) will enable rotational cooling of MgH+ at cryogenic temperatures and the development of quantum control methods in MgH+, which will then be used to performed precision spectroscopy of H2+ at LKB.