  Due to the low sensitivity of the thulium optical clock to black-body
radiation and good accuracy and stability estimations, it appears to be one of
the most promising transportable optical clocks. One of the leading systematic
effects for Tm clock transition, namely the second-order Zeeman effect, can be
canceled by probing two clock transitions between different hyperfine levels of
ground and metastable states during the clock operation. We prepare the atoms
in $m_F=0$ state of both ground hyperfine levels simultaneously and excite
alternately two clock transitions. Here we demonstrate efficient optical
pumping into both target states via single-frequency radiation at 418.8 nm. The
resulting population of $m_F=0$ states of ground hyperfine levels is 36% and
3.8% of the initial number of atoms with less than 4% and 0.4% on non-zero
magnetic sublevels, correspondingly. We performed numerical simulations of the
optical pumping process which is able to explain experimental results
reasonably well.
