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A new search for the variation of fundamental constants using the rovibrational levels and isotope effects of the magnesium fluoride molecule
Di Wu(吴迪), Jin Wei(魏晋), Taojing Dong(董涛晶), Chenyu Zu(祖晨宇), Yong Xia(夏勇), and Jianping Yin(印建平)
Chin. Phys. B, 2025, 34 (2):
023101.
DOI: 10.1088/1674-1056/ad990e
The recently demonstrated methods for cooling and trapping diatomic molecules offer new possibilities for precision searches in fundamental physical theories. Here, we propose to study the variations of the fine-structure constant ($\alpha =e^{2}/(\hslash c)$) and the proton-to-electron mass ratio ($\mu = m_{\rm p}/m_{\rm e}$) with time by taking advantage of the nearly degenerate rovibrational levels in the electronic states of the magnesium fluoride (MgF) molecule. Specifically, due to the cancellation between the fine-structure splitting and the rovibrational intervals in the different MgF natural isotopes, a degeneracy occurs for A$^{2} \Pi_{3 / 2}$ $(v'=0,\, J'=18.5,\,-)$ and A$^{2}\Pi_{1 / 2}$ $(v''=0,\, J''=20.5,\, -)$. We find that using the nearly degenerate energy level of such states can be 10$^{4}$ times more sensitive than using a pure rotational transition to measure the variations of $\alpha $ and $\mu $. To quantify the small gap between A$^{2} \Pi_{3 / 2}$ $(v'=0,\, J'=18.5,\, -)$ and A$^{2} \Pi_{1 / 2}$ $(v''=0,\, J''=20.5,\, -)$, special transitions of choice are feasible: X$^{2} \Sigma_{1 /2}^{+}$ $(v=0,\, J=19.5,\, +)$ to A$^{2}{\Pi }_{3 / 2}$ $(v'=0,\, J'=18.5,\, -)$ and X$^{2} \Sigma_{1 / 2}^{+}$ $(v=0,\, J=19.5,\, +)$ to A$^{2}{\Pi }_{1 / 2}$ $(v''=0,\, J''=20.5,\, -)$. In addition, we estimate the frequency uncertainties caused by the narrow linewidth, Zeeman shift, Stark shift, Doppler broadening and blackbody radiation.
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