Evaluation of variation in $$\left( m_\mathrm{p}/m_\mathrm{e}\right)$$ m p / m e from the frequency difference between the $${{}^{15}\hbox {N}_{2}}^{+}$$ 15 N 2 + and $${}^{87}\hbox {Sr}$$ 87 Sr transitions

Abstract

The uncertainty of the $${}^{87}\hbox {Sr}\, {}^{1}\hbox {S}_{0}-{}^{3}\hbox {P}_{0}$$ transition frequency (429 THz) has been reduced to the level of $$10^{-18}$$ . Also, the $${{}^{15}\hbox {N}_{2}}^{+}\, \hbox {Q}(0)$$ vibrational transition frequency is expected to be measured with an uncertainty of $$10^{-17}$$ , and the v = 0–7 transition frequency (422 THz) is close to the $${}^{87}\hbox {Sr}$$ transition frequency. In this paper, we propose a test for the variation in the proton-to-electron mass ratio $$\mu$$ via precise measurement of the difference $$(f_\mathrm{d}=7 \hbox { THz})$$ between these transition frequencies. By measuring $$f_\mathrm{d}$$ within the uncertainty of $$10^{-16}$$ , a variation in $$\mu$$ of $$4 \times 10^{-18}$$ can be detected. The $${{}^{15}\hbox {N}_{2}}^{+}\, v =0 -7\, \hbox {Q}(0)$$ transition frequency is free from Zeeman and electric quadrupole shifts. The dc Stark coefficient is about $$0.2 \hbox { mHz}/(\hbox {V}/\hbox {cm})^{2}$$ , and the measurement of $$f_\mathrm{d}$$ with an uncertainty lower than $$10^{-16}$$ appears to be attainable using molecular ions in a string crystal. The $${{}^{15}\hbox {N}_{2}}^{+}$$ transition frequency is observed via the two-photon excitation of a laser with a wavelength of 1422 nm (laser A). Another laser with a wavelength of 1396 nm (laser B) is used as a $${}^{87}\hbox {Sr}$$ clock laser after frequency doubling. The frequency difference between lasers A and B (3.5 THz) should be measured using a frequency comb. Lasers A and B can be transferred to another laboratory via an optical fiber. Therefore, a sensitive test of the variation in $$\mu$$ can be performed in cooperation between two distant laboratories.