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Sympathetic cooling of trapped ions has been established as a powerful technique for manipulation of non-laser-coolable ions [1][2][3][4]. For molecular ions, it promises vastly enhanced spectroscopic resolution and accuracy. However, this potential remains untapped so far, with the best resolution achieved being not better than 5 × 10 −8 fractionally, due to residual Doppler broadening being present in ion clusters even at the lowest achievable translational temperatures [5]. Here we introduce a general and accessible approach that enables Doppler-free rotational spectroscopy. It makes use of the strong radial spatial confinement of molecular ions when trapped and crystallized in a linear quadrupole trap, providing the Lamb-Dicke regime for rotational transitions. We achieve a line width of 1 × 10 −9 fractionally and 1.3 kHz absolute, an improvement by 50 and nearly 3 × 10 3 , respectively, over other methods. The systematic uncertainty is 2.5 × 10 −10 . As an application, we demonstrate the most precise test of ab initio molecular theory and the most precise (1.3 ppb) spectroscopic determination of the proton mass. The results represent the long overdue extension of Doppler-free microwave spectroscopy of laser-cooled atomic ion clusters [6] to higher spectroscopy frequencies and to molecules. This approach enables a vast range of high-precision measurements on molecules, both on rotational and, as we project, vibrational transitions. arXiv:1802.03208v1 [quant-ph] 9 Feb 2018 pair were split and resolved, the Zeeman shift uncertainty should be reduced at least 10-fold.This would then allow a total systematic uncertainty of < 3 × 10 −11 . ACKNOWLEDGMENTS This work has been partially funded by DFG project Schi 431/21-1. We thank U. Rosowski for important assistance with the frequency comb, A. Nevsky for assistance with a laser system, E. Wiens for characterizing H-maser instability, R. Gusek and P. Dutkiewicz for electronics development, J. Scheuer and M. Melzer for assistance, and S. Schlemmer (Universität zu Köln) for equipment loans. We thank K. Brown (Georgia Institute of Technology) for useful discussions and suggestions. Corresponding author, step.schiller@hhu.de Contributions S.A. and M.G.H. developed the apparatus and performed the experiments, S.A., M.G.H., and S.S. analyzed the data, S.A., S.S. and V.I.K. performed theoretical calculations, S.S.conceived the study, supervised the work and wrote the paper.

Ultra-precise optical clocks in space will allow new studies in fundamental physics and astronomy. Within an European Space Agency (ESA) program, the "Space Optical Clocks" (SOC) project aims to install and to operate an optical lattice clock on the International Space Station (ISS) towards the end of this decade. It would be a natural follow-on to the ACES mission, improving its performance by at least one order of magnitude. The payload is planned to include an optical lattice clock, as well as a fre-

Optical spectroscopy in the gas phase is one of the key tools for the elucidation of the structure of atoms and molecules and their interaction with external fields. The line resolution is usually limited by a combination of first-order Doppler broadening due to particle thermal motion and of a short transit time through the excitation beam. For trapped particles, suitable laser cooling techniques can lead to strong

Abstract-The use of ultra-precise optical clocks in space ("master clocks") will allow for a range of new applications in the fields of fundamental physics (tests of Einstein's theory of General Relativity, time and frequency metrology by means of the comparison of distant terrestrial clocks), geophysics (mapping of the gravitational potential of Earth), and astronomy (providing local oscillators for radio ranging and interferometry in space). Within the ELIPS-3 program of ESA, the "Space Optical Clocks" (SOC) project aims to install and to operate an optical lattice clock on the ISS towards the end of this decade, as a natural follow-on to the ACES mission, improving its performance by at least one order of magnitude. The payload is planned to include an optical lattice clock, as well as a frequency comb, a microwave link, and an optical link for comparisons of the ISS clock with ground clocks located in several countries and continents. Undertaking a necessary step towards optical clocks in space, the EU-FP7-SPACE-2010-1 project no. 263500 (SOC2) (2011-2015) aims at two "engineering confidence", accurate transportable lattice optical clock demonstrators having relative frequency instability below 1×10 -15 at 1 s integration time and relative inaccuracy below 5×10 -17 . This goal performance is about 2 and 1 orders better in instability and inaccuracy, respectively, than today's best transportable clocks. The devices will be based on trapped neutral ytterbium and strontium atoms. One device will be a breadboard. The two systems will be validated in laboratory environments and their performance will be established by comparison with laboratory optical clocks and primary frequency standards. In order to achieve the goals, SOC2 will develop the necessary laser systems -adapted in terms of power, linewidth, frequency stability, long-term reliability, and accuracy. Novel solutions with reduced space, power and mass requirements will be implemented. Some of the laser systems will be developed towards particularly high compactness and robustness levels. Also, the project will validate crucial laser components in relevant environments. In this paper we present the project and the results achieved during the first year.