Rotational spectroscopy of cold and trapped molecular ions in the Lamb–Dicke regime

Abstract

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.

High-precision mass spectrometer for light ions

“…Therefore, no correlation of the uncertainties for the two measurements is assumed. This result is in good agreement with recent results determined by other experiments using different approaches [67,68]. The result for m p changes also the mass of the neutron, since it is determined via the mass of the deuteron subtracted by the deuteron binding energy and the mass of the proton [8].…”

Frequency-comb spectroscopy on pure quantum states of a single molecular ion

“…Direct laser cooling of molecules shows promise for species with advantageous level structures that only require a few laser wavelengths [6-8], but is infeasible for the vast majority of molecules.Furthermore, even with trapped and cooled molecules [9], commonly used detection methods, such as state-dependent photo-dissociation or ionization [10,11], destroy the molecules under study, making them unavailable for further manipulation.In this work, we perform high resolution spectroscopy on rotational states of a molecular ion using methods that are generally applicable to a broad range of molecular ions, which are readily trapped in electromagnetic potentials [12] and cooled by coupling to co-trapped atomic ions amenable to laser cooling [13,14]. The long interrogation times and low translational temperature enabled by trapping and sympathetic cooling lead to high resolution [15], which has, among other advances, enabled the most stringent test of fundamental theory carried out by molecular ions [16]. We prepare a trapped 40 CaH + molecular ion at rest in a single, known quantum state and coherently drive stimulated Raman transitions between levels of different rotational quantum numbers J, ranging from J = 1 to J = 6 in the electronic and vibrational ground state manifold.…”

“…In this work, we perform high resolution spectroscopy on rotational states of a molecular ion using methods that are generally applicable to a broad range of molecular ions, which are readily trapped in electromagnetic potentials [12] and cooled by coupling to co-trapped atomic ions amenable to laser cooling [13,14]. The long interrogation times and low translational temperature enabled by trapping and sympathetic cooling lead to high resolution [15], which has, among other advances, enabled the most stringent test of fundamental theory carried out by molecular ions [16]. We prepare a trapped 40 CaH + molecular ion at rest in a single, known quantum state and coherently drive stimulated Raman transitions between levels of different rotational quantum numbers J, ranging from J = 1 to J = 6 in the electronic and vibrational ground state manifold.…”

Leading-order relativistic corrections to the rovibrational spectrum of H2+ and HD+ molecular ions

“…Recently a very promising pure rotational transition experiment has been carried out [5], which realized conditions of the Lamb-Dicke regime and got for the first time experimental value of the transition frequency with relative precision of 3 · 10 −10 . It is realistic that this precision may be improved in a recent future by about two orders of magnitude.…”