High-fidelity nuclear coherent population transfer via mixed-state inverse engineering

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 $^{229}\mathrm{Th}, ^{223}\mathrm{Ra}, ^{113}\mathrm{Cd}$, and $^{97}\mathrm{Tc}$, which have a long lifetime excited state, as well as $^{187}\mathrm{Re}, ^{172}\mathrm{Yb}, ^{168}\mathrm{Er}$, and $^{154}\mathrm{Gd}$ 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.