Measurement of the electric quadrupole amplitude in atomic thallium $6P_{1/2}\rightarrow6P_{3/2}$ transition using electromagnetically induced transparency

We report a measurement of the transition amplitude ratio $\chi$ of an electric quadrupole ($E2$) to a magnetic dipole ($M1$) of the $6P_{1/2}\rightarrow6P_{3/2}$ transition in atomic thallium. We utilized the electromagnetically induced transparency (EIT) mechanism and the sideband-bridging technique to resolve the isotopic transitions and their hyperfine manifold. Our measurement gave $\chi_{205}~=~0.2550(20)(7)$ for $^{205}$Tl, and $\chi_{203}=0.2532(73)(7)$ for $^{203}$Tl, which was measured for the first time. Our result provides a reference point for the theoretical calculation of atomic structure and new input for the long dispute on the atomic thallium PNC measurements.