Enhanced Sensitivity to Variation of $m_e/m_p$ in Molecular Spectra

We propose new experiments with high sensitivity to a possible variation of the electron-to-proton mass ratio $\mu \equiv m_e/m_p$. We consider a nearly degenerate pair of molecular vibrational levels, each associated with a different electronic potential. With respect to a change in $\mu$, the change in the splitting between such levels can be large both on an absolute scale and relative to the splitting. We demonstrate the existence of such pairs of states in ${\mathrm{Cs}}_2$, where the narrow spectral lines achievable with ultracold molecules make the system promising for future searches for small variations in $\mu$.

Figure 1

Energy sensitivity vs binding energy, for the $X{}^1\Sigma _g^{+}$ and $a{}^3\Sigma _u^{+}$ states of ${\mathrm{Cs}}_2$. Inset: a zoom into the region discussed here. Colored circles are levels observed in this work; open diamonds are levels from previous data; small black dots are predictions from our fitted potentials. The arrow indicates the degeneracy described in the text.

Figure 2

Data indicating a degeneracy between the deeply bound $a{}^3\Sigma _u^{+}(v_a=37)$ and $X{}^1\Sigma _g^{+}(v_X=138)$ levels in ${\mathrm{Cs}}_2$s. Ion signals are plotted vs probe laser frequency (relative to the line from the $a|(1,7)8,0,8⟩$ state in the same vibrational level), for two adjacent vibrational levels tentatively assigned as $v_a=38$, 37 (upper and lower panels, respectively). The label ${\sigma }^{\pm }$ refers to the polarization of the probe laser. Frequency scales are slightly offset (by $\cong 20\mathrm{MHz}$) to align the $\mathcal{F}=8$, 9 spectral lines, and hence to emphasize the similarity between the two ${\sigma }^{+}$ spectra. The dashed vertical lines are meant to guide the eye in comparing the relative line positions.