Investigating the $4D_{3/2}|3,\pm2\rangle$--$4D_{5/2}|3,\pm2\rangle$ transition in Nb$^{4+}$ for a THz atomic clock

In this work, the $4D_{3/2}|3,\pm2\rangle \rightarrow 4D_{5/2}|3,\pm2\rangle$ transition in the Nb$^{4+}$ ion is identified as a promising candidate for a terahertz (THz) atomic clock, with the transition frequency occurring at 56.0224 THz. This transition is primarily driven by the magnetic dipole decay channel, which can easily be accessed by a laser. We focus on the stable $^{93}$Nb isotope, which has 100\% natural abundance and a nuclear spin of $I=9/2$ for experimental advantage. Our data analysis allows us to estimate potential systematic shifts in the proposed clock system, including those due to blackbody radiation, electric quadrupole, second-order Zeeman, and second-order Doppler {shifts}. {The scheme presented in this study can help suppress the AC Stark and electric quadrupole shifts in the clock frequency measurement.} {All these analyses} suggest that the proposed THz atomic clock using Nb$^{4+}$ could be valuable in both quantum thermometry and frequency metrology.