Frequency metrology of the HD+ molecular ion: THz and vibrational spectroscopy at the 10-10 accuracy level

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The HD+ molecule is of fundamental importance because it is one of the simplest molecules, containing just a single electron. Precise measurement of its vibrational transition frequencies will ultimately allow (i) to test theoretical methods of precision calculation of molecular levels; (ii) establish a new System allowing to measure QED effects / test QED theory in molecules; (iii) to determine the ratio of electron-to-proton mass in a novel way and with potentially higher precision than with alternative methods; (iv) to measure nuclear properties such as quadrupole moments, (v) to test the time-independence of nuclear mass ratios.We have recently performed ro-vibrational spectroscopy and measured the transition frequency with a relative accuracy of 2.3 parts per billion (ppb). Our experimental result is in agreement with theoretical predicitions that were obtained shortly before and allowed the determination of QED contributions of order α4 to about 10% accuracy.In this proposal, we intend to introduce several major experimental improvements in order to reach an accuracy close to the level of 2 parts in 1010 (0.2 ppb), a tenfold improvement. At this level of accuracy, the experimental results will challenge an improved theoretical formulation and calculation of the QED and hyperfine effects. Our measurements could lead to an alternative determination of the electron-to-proton mass ratio, with an accuracy similar to that of currently established approaches.Apart from this application in metrology, the new methods to be developed in the proposed project are of wide interest since they will be applicable to a large variety of other molecular ions.