HD⁺ ions cooled to 18 mK yield most precise vibrational-rotational spectra to date

A research team from the Innovation Academy for Precision Measurement Science and Technology (APM) of the Chinese Academy of Sciences has made significant progress in precisely measuring the vibrational-rotational spectra of hydrogen molecular ions (HD⁺).

The researchers prepared a Be⁺-HD⁺ two-component ion Coulomb crystal at millikelvin temperatures in a linear ion trap. They developed an innovative quantum state preparation and spatially resolved fluorescence detection techniques and used these to measure the high-resolution vibrational-rotational transition spectra of HD⁺ molecular ions. Their findings were published in Physical Review A.

HD⁺ is the simplest heteronuclear molecular ion, composed of one proton, one deuteron, and one electron. Its vibrational-rotational transition energies can be precisely calculated, making it an ideal system for testing quantum electrodynamics (QED) theory and determining fundamental physical constants, such as the proton-electron mass ratio.

To minimize the effects of Doppler broadening on their measurements, the researchers employed laser-cooled beryllium ions to cool the HD⁺ ions, reducing their temperature to 18 millikelvins (mK). To address the low population of HD⁺ molecules in the vibrational-rotational ground state (v = 0, N = 0), they employed the resonance-enhanced threshold photoionization (RETPI) technique to prepare HD⁺ ions precisely in the vibrational-rotational ground state. This technique achieved an initial quantum state population degree of 93%.

Compared with traditional cryogenic cooling or optical pumping methods, this technique significantly increases the ground-state population rate, laying a solid foundation for subsequent high-resolution transition detection.

Additionally, in the two-component ion crystal, HD⁺ ions appear as non-fluorescent “dark ions,” and the change in the number of HD⁺ ions during resonant dissociation is the key to spectral measurement. To address this issue, the researchers developed a spatially resolved fluorescence collection technique using a high-sensitivity, electron-multiplying intensified CCD (EMICCD) camera. This setup enabled the real-time acquisition of ion crystal images and the real-time, non-destructive measurement of HD⁺ ion numbers.

Using these innovative methods, the researchers measured, for the first time, the vibrational-rotational transition spectrum of HD⁺ ions (v,N):(0,0)→(6,1). The transition frequency value is 303,396,506.7(20) MHz, with a relative accuracy reaching parts per billion (ppb), which is consistent with the current most precise QED theoretical prediction.

Combining theoretical calculations, they further deduced that the value of the proton-electron mass ratio (μ_pe) is 1836.152648(45). This value aligns with the 2022 recommended value from the International Council for Science: Committee on Data for Science and Technology.