  Nuclear coherent population transfer (NCPT) plays an important role in the
exploration and application of atomic nuclei. How to achieve high-fidelity NCPT
remains so far challenging. Here, we investigate the complete population
transfer of nuclear states. We first consider a cyclic three-level system,
based on the mixed-state inverse engineering scheme by adding additional laser
fields in an open three-level nuclear system with spontaneous emission. We find
the amplitude of the additional field is related to the ratio of the pump and
Stokes field amplitudes. As long as an appropriate additional field is
selected, complete transfer can be achieved even when the intensities of the
pump and Stokes fields are exceedingly low. The transfer efficiency exhibits
excellent robustness with respect to laser peak intensity and pulse delay. We
demonstrate the effectiveness through examples such as $^{229}$Th, $^{223}$Ra,
$^{113}$Cd, and $^{97}$Tc, which have a long lifetime excited state, as well as
$^{187}$Re, $^{172}$Yb, $^{168}$Er and $^{154}$Gd with a short lifetime excited
state. Focusing on the case without additional coupling, we further reduce the
three-level system to an effective two-level problem. We modify the pump and
Stokes pulses by using counterdiabatic driving to implement high-fidelity
population transfer. The schemes open up new possibilities for controlling
nuclear states.
