  We have developed and demonstrated a scheme to achieve rotationally-closed
photon cycling in polyatomic molecules with complex hyperfine structure and
sensitivity to hadronic symmetry violation, specifically $^{171}$YbOH and
$^{173}$YbOH. We calculate rotational branching ratios for spontaneous decay
and identify repumping schemes which use electro-optical modulators (EOMs) to
address the hyperfine structure. We demonstrate our scheme by cycling photons
in a molecular beam and verify that we have achieved rotationally-closed
cycling by measuring optical pumping into unaddressed vibrational states. Our
work makes progress along the path toward utilizing photon cycling for state
preparation, readout, and laser cooling in precision measurements of polyatomic
molecules with complex hyperfine structure.
