Hydrogen molecular ions for improved determination of fundamental constants

Abstract

The possible use of high-resolution rovibrational spectroscopy of the hydrogen molecular ions H + 2 and HD+ for an independent determination of several fundamental constants is analyzed. While these molecules had been proposed for metrology of nuclear-to-electron mass ratios, we show that they are also sensitive to the radii of the proton and deuteron and to the Rydberg constant at the level of the current discrepancies colloquially known as the proton size puzzle. The required level of accuracy, in the 10 −12 range, can be reached both by experiments, using Doppler-free two-photon spectroscopy schemes, and by theoretical predictions. It is shown how the measurement of several well-chosen rovibrational transitions may shed new light on the proton-radius puzzle, provide an alternative accurate determination of the Rydberg constant, and yield new values of the proton-toelectron and deuteron-to-proton mass ratios with one order of magnitude higher precision. From Bohr's model of the atom to the advent of quantum electrodynamics (QED), precision spectroscopy of atomic hydrogen has played a key role in our understanding of matter and its interaction with light. Since the first measurement of the Lamb shift in 1947 [1, 2], the predictions of QED have been verified with an increasing level of accuracy which, together with stringent tests in other areas of physics, led to assume the validity of this theory and use it to extract the values of fundamental physical constants from experimental data [3]. Specifically, available data on the hydrogen (H) and deuterium (D) atoms are used to extract the Rydberg constant R ∞ and the charge radii of the proton (r p ) and deuteron (r d ). Data from electron-proton and electron-deuteron scattering experiments also contribute in this determination.Recently, the undisputed status of these results has been challenged by the measurement of the Lamb shift in muonic hydrogen [4,5]. The very precise value of r p deduced from this experiment is in strong disagreement with previous determinations. The discrepancy with the CODATA adjustment [6] amounts to 5.6σ, or to 4.5σ if only the H and D data are taken into account [3]. Similar discrepancies on the deuteron radius can be inferred through the very precise determination of r 2 d − r 2 p from the 1S-2S H/D isotopic shift [7]. Although many efforts have been undertaken in the last few years, no convincing solution of the "proton size puzzle" has been found so far (see [8] for a review). One of the possible explanations is that the error bars, both of hydrogen spectroscopy and scattering experiments [9] were underestimated. New scattering experiments are in preparation or underway, including electron-proton [10], electron-deuteron [11] and muon-proton scattering [12]. In atomic hydrogen, the 1S-3S(D) [13,14], 2S-2P [15], and 2S-4P [16] transitions are under study in order to cross-check and improve previous results. An independent determination of R ∞ , which is strongly correlated to r p and r d , is another way to shed new light on this prob...

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

“…Using counter-propagating laser beams with a narrow linewidth, the Lamb Dicke regime may be reached in the present apparatus, such that first-order Doppler broadening is entirely eliminated, while all other systematic effects could be controlled below the 1 × 10 −13 uncertainty level. Such spectroscopy would allow more stringent tests of molecular theory and QED, tighter bounds on new physics at the Ångström scale, a competitive determination of the proton-electron mass ratio and even contribute to the determination of several other fundamental constants including the Rydberg constant, the deuteron-electron mass ratio, and the proton and deuteron charge radii [41].…”

“…For example, in Refs. [22,41] an experiment was proposed in which the (v, L) = (0, 3) → (9, 3) line in HD + is addressed through a two-photon transition with nearly degenerate photons. Using counter-propagating laser beams with a narrow linewidth, the Lamb Dicke regime may be reached in the present apparatus, such that first-order Doppler broadening is entirely eliminated, while all other systematic effects could be controlled below the 1 × 10 −13 uncertainty level.…”

Fundamental Transitions and Ionization Energies of the Hydrogen Molecular Ions with Few ppt Uncertainty

“…As was pointed out already some time ago [3], and recently discussed more extensively [4], if the theory would be sufficiently precise, the spectroscopy of HMI may be used for determining of the fundamental physical constants such as the protonto-electron mass ratio. The ionization energy of HMI is also of high importance for the determination of ionization and dissociation energies of the hydrogen molecule from spectroscopic studies [5][6][7] as well as for the determination of atomic masses of light nuclei [8][9][10].On the experimental side there are many new projects started, which are now oriented towards Doppler-free spectroscopy with accuracy targeted to 1 ppt (one part per trillion) or better [4,[11][12][13]. These perspectives bring strong motivation for theory.…”

“…From the theoretical point of view the HMI is one of the simplest nonintegrable quantum system, which still allows very accurate numerical treatment. As was pointed out already some time ago [3], and recently discussed more extensively [4], if the theory would be sufficiently precise, the spectroscopy of HMI may be used for determining of the fundamental physical constants such as the protonto-electron mass ratio. The ionization energy of HMI is also of high importance for the determination of ionization and dissociation energies of the hydrogen molecule from spectroscopic studies [5][6][7] as well as for the determination of atomic masses of light nuclei [8][9][10].…”

Precision measurements and test of molecular theory in highly excited vibrational states of H2 (v = 11)

“…These are currently at lower precision than other methods but prospects exist that competitive values can be derived from molecular spectroscopy. Similarly Karr et al [14] recently discussed the possibility of determining R ∞ using H + 2 (or HD + ) transitions as an alternative to atomic hydrogen spectroscopy. Even for the neutral system of molecular hydrogen, the determination of r p from spectroscopy is projected to be achievable, from the ongoing efforts in both calculation [15] and experiments [16].…”