Advanced techniques for manipulation of internal states, standard in atomic physics, are demonstrated for a charged molecular species for the first time. We address individual hyperfine states of ro-vibrational levels of a diatomic ion by optical excitation of individual hyperfine transitions, and achieve controlled transfer of population into a selected hyperfine state. We use molecular hydrogen ions (HD + ) as a model system and employ a novel frequency-comb-based, continuous-wave 5 µm laser spectrometer. The achieved spectral resolution is the highest obtained so far in the optical domain on a molecular ion species. As a consequence, we are also able to perform the most precise test yet of the ab-initio theory of a molecule.Cold trapped molecules [1, 2] currently represent an intense field of activity relying on sophisticated methods of molecule production, translational and internal cooling, spectroscopy and sensitive detection. Many applications, such as chemical reaction studies [3, 4], tests of molecular quantum theory [5], fundamental physics [6, 7] and quantum computing [8] would benefit strongly from the availability of advanced manipulation techniques, already standard in atomic physics. These are not straightforward for molecules, and for charged molecules have not been demonstrated yet. Production methods for molecular ions (usually by electron impact ionization) and, if heteronuclear, their interaction with the black-body radiation of the surrounding vacuum chamber, usually lead to significant population of a substantial number of internal states. A first, important step in the manipulation of internal states of molecular ions is population transfer between rotational states (heteronuclear molecules usually being cold vibrationally, i.e. are all in the v = 0 ground vibrational state). It has been demonstrated that a significant fraction (ca. 75%) of an ensemble of diatomic molecular ions can be pumped into the vibrational and rotational ground level (v = 0, N = 0) [9, 10], see Fig. 1.For a general diatomic molecule, however, this pumping is usually not capable of preparing molecules in a single quantum state, because spin interactions generate a hyperfine structure with several states in each ro-vibrational level. For example, a diatomic molecule with one unpaired electron (s e = 1/2), and nuclei with nuclear spins I 1 = 1/2, I 2 = 1 (such as HD + ) has 4 hyperfine states in zero magnetic field if the rotational angular momentum N = 0, but 10 if N = 1, and 12 if N ≥ 2, see Fig. 2 a. The ability to address selectively molecules in one particular hyperfine state (or even in a single quantum state with a particular magnetic quantum number J z ) and to transfer molecules from one hyperfine state to another are clearly important tools of a molecular quantum toolbox that can be part of a full quantum state preparation procedure.Complicating the addressing, the number of strong transitions between two given ro-vibrational levels (v, N ), (v , N ) is equal to the larger of the two numbers of hyperfine s...
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.
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
We demonstrate rotational excitation of molecular ions that are sympathetically cooled by lasercooled atomic ions to a temperature as low as ca. 10 mK. The molecular hydrogen ions HD + and the fundamental rotational transition (v = 0, N = 0) → (v = 0, N = 1) at 1.3 THz, the most fundamental dipole-allowed rotational transition of any molecule, are used as a test case. This transition is here observed for the first time directly. Rotational laser cooling was employed in order to increase the signal, and resonance-enhanced multiphoton dissociation was used as detection method. The black-body-radiation-induced rotational excitation is also observed. The extension of the method to other molecular species is briefly discussed.
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