H2+ and HD+

Abstract

We investigate the leading systematic effects in ro-vibrational spectroscopy of the molecular hydrogen ions H + 2 and HD + , in order to assess their potential for the realization of optical clocks that would be sensitive to possible variations of the proton-to-electron mass ratio. Both two-photon (2E1) and quadrupole (E2) transitions are considered. In view of the weakness of these transitions, most attention is devoted to the light shift induced by the probe laser, which we express as a function of the transition amplitude, differential dynamic polarizability and clock interrogation times. Transition amplitudes and dynamic polarizabilites including the effect of hyperfine structure are then calculated in a full three-body approach to get a precise evaluation of the light shift. Together with the quadrupole and Zeeman shifts that are obtained from previous works, these results provide a realistic estimate of the achievable accuracy. We show that the lightshift is the main limiting factor in the case of two-photon transitions, both in H + 2 and HD + , leading to expected accuracy levels close to 5 × 10 −16 in the best cases. Quadrupole transitions have even more promising properties and may allow reaching or going beyond 1 × 10 −16 .

Constraints on extra dimensions from precision molecular spectroscopy

“…After having performed a 15-digit accuracy calculation on Born-Oppenheimer energies [16], calculations of strongly improved accuracy have just been published [62], while improved calculations of non adiabatic corrections are underway [63]. Immediate improvements, based on existing technologies, the experimental accuracies of the dissociation limits in the neutral hydrogen and its isotopomers [64], and the spectroscopy of HD + [12,65,66] were discussed recently.…”

“…However, the recently improved determination of m m p e [11] demonstrates active progress on the experimental side. While experiments on the ro-vibrational spectrum of the H 2 + isotopomer are still under way [12], the small dipole moment of the HD + isotopomer has enabled the accurate study of electric-dipole-allowed transitions in various bands [13][14][15].…”

Quantum state preparation of homonuclear molecular ions enabled via a cold buffer gas: An ab initio study for the H2+ and the D2Schiller1, Kortunov2, Vera3 et al. 2017Phys. Rev. A293290View full textAdd to dashboardCite

“…One of the outstanding challenges in the fields of fewbody quantum physics and metrology is the achievement of ultrahigh-precision laser vibrational spectroscopy of the molecular hydrogen ion (MHI) H 2 + , a member of the family of one-electron molecules. These ab initio calculable systems at the intersection of atomic and molecular physics have enormous potential for ultraprecise spectroscopy at the 10 −17 fractional inaccuracy level [1,2]. So far, experiments have reached the 10 −9 level [3][4][5].…”

Simplest Molecules as Candidates for Precise Optical Clocks

“…are the vibrational quantum numbers) they can be reduced to a negligible level [31]. This can also be achieved for light shifts for E1 transitions in HD þ .…”