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Register a new userPrecision spectroscopy of the hydrogen molecular ions HD$^+$
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Expectation values of the Breit operators and the $Q$ terms are calculated for HD$^+$ with the vibrational number $v=0-4$ and the total angular momentum $L=0-4$. Relativistic and radiative corrections to some ro-vibrational transition frequencies are determined. Numerical uncertainty in $R_{infty}alpha^2$ order correction is reduced to sub kHz or smaller. Our work provides an independent verification of Korobovs calculations [Phys. Rev. A {bf74}, 052506 (2006); {bf77}, 022509 (2008)].
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We describe the current status of high-precision ab initio calculations of the spectra of molecular hydrogen ions (H_2^+ and HD^+) and of two experiments for vibrational spectroscopy. The perspectives for a comparison between theory and experiment at a level of 1 ppb are considered.
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-to-electron and deuteron-to-proton mass ratios with one order of magnitude higher precision.
We study the feasibility of nearly-degenerate two-photon rovibrational spectroscopy in ensembles of trapped, sympathetically cooled hydrogen molecular ions using a resonance-enhanced multiphoton dissociation (REMPD) scheme. Taking advantage of quasi-coincidences in the rovibrational spectrum, the excitation lasers are tuned close to an intermediate level to resonantly enhance two-photon absorption. Realistic simulations of the REMPD signal are obtained using a four-level model that takes into account saturation effects, ion trajectories, laser frequency noise and redistribution of population by blackbody radiation. We show that the use of counterpropagating laser beams enables optical excitation in an effective Lamb-Dicke regime. Sub-Doppler lines having widths in the 100 Hz range can be observed with good signal-to-noise ratio for an optimal choice of laser detunings. Our results indicate the feasibility of molecular spectroscopy at the $10^{-14}$ accuracy level for improved tests of molecular QED, a new determination of the proton-to-electron mass ratio, and studies of the time (in)dependence of the latter.
Recently we reported a high precision optical frequency measurement of the (v,L):(0,2)->(8,3) vibrational overtone transition in trapped deuterated molecular hydrogen (HD+) ions at 10 mK temperature. Achieving a resolution of 0.85 parts-per-billion (p.p.b.) we found the experimental value ($ u_0= 383,407,177.38(41)$ MHz) to be in agreement with the value from molecular theory ($ u_text{th}=383,407,177.150(15)$ MHz) within 0.6(1.1) p.p.b. [Biesheuvel et al., Nat. Commun. 7, 10385 (2016)]. This enabled an improved test of molecular theory (including QED), new constraints on the size of possible effects due to new physics, and the first determination of the proton-electron mass ratio from a molecule. Here, we provide the details of the experimental procedure, spectral analysis, and the assessment of systematic frequency shifts. Our analysis focuses in particular on deviations of the HD+ velocity distribution from thermal (Gaussian) distributions under the influence of collisions with fast ions produced during (laser-induced) chemical reactions, as such deviations turn out to significantly shift the hyperfine-less vibrational frequency as inferred from the saturated and Doppler-broadened spectrum, which contains partly unresolved hyperfine structure.
We describe the first precision measurement of the electrons electric dipole moment (eEDM, $d_e$) using trapped molecular ions, demonstrating the application of spin interrogation times over 700 ms to achieve high sensitivity and stringent rejection of systematic errors. Through electron spin resonance spectroscopy on $^{180}{rm Hf}^{19}{rm F}^{+}$ in its metastable $^{3}Delta_{1}$ electronic state, we obtain $d_e = (0.9 pm 7.7_{rm stat} pm 1.7_{rm syst}) times 10^{-29},e,{rm cm}$, resulting in an upper bound of $|d_e| < 1.3 times 10^{-28},e,{rm cm}$ (90% confidence). Our result provides independent confirmation of the current upper bound of $|d_e| < 9.3 times 10^{-29},e,{rm cm}$ [J. Baron $textit{et al.}$, Science $textbf{343}$, 269 (2014)], and offers the potential to improve on this limit in the near future.
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