In this paper we propose to utilize the $X{}^2{\Sigma }_g(\nu ,N,F,M)=(0,0,1/2,\pm 1/2)\to (1,0,1/2,\pm 1/2)$ or $(2,0,1/2,\pm 1/2)$ transition of N${}_2{}^{+}$ $(I=0)$ to test variations of the proton-to-electron mass ratio. The $X{}^2{\Sigma }_g$ ground state exhibits no quadrupole shift and the Zeeman shift of the $N=0\to N=0$ transition is exactly zero. Because N${}_2{}^{+}$ is nonpolar, systematic level shifts such as Stark shifts induced by trap electric field or blackbody radiation are very small and the thermalization of the rotational states is inhibited. This eases the requirements on the experimental setup significantly. Employing Raman transitions at the “magic” wavelength the $(0,0,1/2,\pm 1/2)\to (1,0,1/2,\pm 1/2)$ or $(2,0,1/2,\pm 1/2)$ transition frequency can be measured very precisely.

• Received 12 February 2014

DOI:https://doi.org/10.1103/PhysRevA.89.032509