Simplest Molecules as Candidates for Precise Optical Clocks

Abstract

The precise measurement of transition frequencies in cold, trapped molecules has applications in fundamental physics, and extremely high accuracies are desirable. We determine suitable candidates by considering the simplest molecules with a single electron, for which the external-field shift corrections can be calculated theoretically with high precision. Our calculations show that H(2)(+) exhibits particular transitions whose fractional systematic uncertainties may be reduced to 5×10(-17) at room temperature. We also generalize the method of composite frequencies, introducing tailored linear combinations of individual transition frequencies that are free of the major systematic shifts, independent of the strength of the external perturbing fields. By applying this technique, the uncertainty of the composite frequency is reduced compared to what is achievable with a single transition, e.g., to the 10(-18) range for HD(+). Thus, these molecules are of metrological relevance for future studies.

High-precision spectroscopy of the HD+ molecule at the 1-p.p.b. level

“…Recently, the precision of relativistic and radiative energy corrections to the nonrelativistic energies was strongly improved. With the inclusion of the full set of contributions of order mα 7 and leading-order terms of order mα 8 , the relative uncertainty is now below 4 × 10 −11 .…”

“…Optical clocks based on trapped atomic ions have shown that laser spectroscopy at very high accuracy (below one part in 10 17 ) is possible [6]. Recent theoretical studies point out that also for molecular hydrogen ions experimental uncertainties in the 10 −16 range should be possible [7,8].…”

Observation of electric-dipole-forbidden infrared transitions in cold molecular ions

“…By contrast, to the best of our knowledge no dipole-forbidden vibrational-that is, IR-spectra of molecular ions have been reported so far. Studies of vibrational transitions in molecules, however, are attractive as they probe different spectral domains and dynamic regimes from those in studies of atomic systems 5,8,12 .Dipole-forbidden vibrational transitions in molecules 13 are several orders of magnitude weaker than dipole-forbidden optical transitions typically used in atoms 2,3 , rendering their observation challenging. Thus far, they were observed only in a handful of neutral diatomics, such as H 2 , N 2 and O 2 , using high-pressure samples and/or very long absorption path lengths [14][15][16] .…”

“…By contrast, to the best of our knowledge no dipole-forbidden vibrational-that is, IR-spectra of molecular ions have been reported so far. Studies of vibrational transitions in molecules, however, are attractive as they probe different spectral domains and dynamic regimes from those in studies of atomic systems 5,8,12 .…”

“…In these systems, direct vibrational transitions are allowed within the electrical quadrupole approximation. The advantages offered by vibrational quadrupole transitions for precision measurements have recently been highlighted 5,17 and, in particular, vibrational transitions in N 2 + have been suggested as attractive candidates for precision spectroscopic experiments 18 . Our approach capitalizes on the very long interrogation times (up to several minutes) enabled by the sympathetic cooling and subsequent spatial localization of individual N 2 + ions in a Coulomb crystal 10 .…”