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Description
The molecular hydrogen ion $\mathrm{H}_{2}^{+}$ is the simplest molecule. This iconic system has been the subject of innumerous theoretical studies, from the earliest days of quantum mechanics [1] until today, culminating in highly precise predictions of its level energies [2]. Comparisons of these predictions and measured vibrational transition frequencies would offer excellent opportunities in fundamental physics that go beyond the results achieved with the related molecule [3, 4]: a direct determination of the proton-electron mass ratio and the proton's charge radius. Furthermore, achieving precision spectroscopy of $\mathrm{H}_{2}^{+}$ is an essential prerequisite for a future CPT test that compares $\mathrm{H}_{2}^{+}$ with its antimatter counterpart [5, 6].
In this work we report the first vibrational laser spectroscopy of $\mathrm{H}_{2}^{+}$, between low-lying rovibrational levels of para-$\mathrm{H}_{2}^{+}$ [7]. We employed sympathetically laser-cooled and trapped $\mathrm{H}_{2}^{+}$ ensembles. A first-overtone electric-quadrupole (E2) transition [8, 9] was driven by a unique $10^{-13}$-level optical frequency metrology system reliably delivering Watt-level laser power at 2.4$\mu$m. Both hyperfine components were measured. We determined the spin-averaged rovibrational transition frequency with $3\times10^{-8}$ fractional uncertainty, finding agreement with the predicted value. By using $\text{HD}^{+}$ as a test molecule, we also show that E2 spectroscopy is possible with $1\times10^{-12}$ uncertainty. This demonstrates that E2 transitions are suitable for precision spectroscopy of molecular ions and that determining $m_{p}/m_{e}$ spectroscopically with accuracy competitive with mass spectroscopy is a realistic prospect.
This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 786306, “PREMOL”).
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[2] V. I. Korobov and J.-P. Karr, Phys. Rev. A 104, 032806 (2021).
[3] M. Germann et al., Phys. Rev. Research 3, L022028 (2021).
[4] S. Alighanbari et al., Nat. Phys. 10.1038/s41567-023-02088-2 (2023).
[5] H. Dehmelt, Physica Scripta T59, 423 (1995).
[6] E. G. Myers, Phys. Rev. A 98, 010101 (2018).
[7] M. R. Schenkel et al., subm. (2023).
[8] M. Germann et al., Nat. Phys. 10, 820 (2014).
[9] V. I. Korobov et al., Phys. Rev. A 97, 032505 (2018).
