Speaker
Description
H$_2^+$ is the simplest molecular system, and its energy-level structure can now be calculated at the parts-per-trillion level[1]. Comparing experimental and theoretical transition frequencies enables the improvement of the value of fundamental constants, such as the proton-to-electron mass ratio $\frac{m_p}{m_e}$[2].
An increased sensitivity to $\frac{m_p}{m_e}$ can be obtained when measuring microwave transitions between weakly-bound levels located just below the H(1s) + H$^+$ dissociation threshold. These levels are comprised of spin-rotational states from the highest vibrational level of the electronic ground state $X^{+~^2}\Sigma_g^+$ and the lowest vibrational level of the first excited electronic state $A^+~^2\Sigma_u^+$[3]. Using fast ion beams, microwave transitions between these levels have been observed[4].
In an ongoing experiment, H$_2^+$ ions are selectively prepared in weakly-bound levels using a resonant multi-photon excitation of H$_2$ Rydberg states, followed by field ionization. The resulting ions will then be injected into an RF ion trap for precision measurements[5].
To avoid destructive detection and ion loss, Quantum-Logic Spectroscopy can be employed[6], as already demonstrated in the determination of the hyperfine structure interval of the H$_2^+$ $X^+$ vibrational ground state[7]. In such measurements, a stimulated Raman transition in the infrared is used, which overcomes the small Lamb-Dicke parameter, typical of long-wavelength microwave transitions.
We discuss whether stimulated Raman transitions remain feasible for the weakly-bound states, where the lasers can access the vibrational continuum, potentially resulting in loss of the molecules because of photodissociation.
AC polarizabilities of the molecular levels and Rabi frequencies for the stimulated Raman transitions are calculated using a Green’s function technique. This eliminates the necessity for an explicit sum-over-states approach and naturally includes the effect of the continuum. Implemented using both the Numerov method and Discrete Variable Representation, the effects of all other rotational, vibrational (bound & continuum), and electronic levels are taken into account systematically.
In addition to a specific calculation for H$_2^+$, we also provide a widely applicable model involving Morse potentials, which can be easily adapted to other molecules.
References:
[1] V. I. Korobov et al., Phys. Rev. Lett. 118, 233001 (2017).
[2] S. Alighanbari et al., Nature 644, 69–75 (2025).
[3] R. Moss, Molecular Physics 80, 1541–1554 (1993).
[4] A. Carrington et al., Faraday Trans. 89, 603 (1993).
[5] D. Y. Knapp et al., 10.48550/arXiv.2602.15668 (2026).
[6] P. O. Schmidt, edited by D. Bruß et al., 799–826 (2016).
[7] D. Holzapfel et al., Phys. Rev. X 15, 031009 (2025).
| Academic level | PhD student |
|---|