Optimal control of population transfer in multi-level systems by dynamical quantum geometric tensor

The optimal control of population transfer for multi-level systems is investigated from the perspective of quantum geometry. Firstly, the general theoretical framework of optimizing the STIRAP scheme based on the dynamical quantum geometric tensor is given, and then the dynamical quantum geometric tensor and the nonadiabatic transition rate are calculated by taking the detuned <inline-formula><tex-math id="M2">\begin{document}$ {{\Lambda }} $\end{document}</tex-math></inline-formula>-type three-level system and tripod-type four-level system for example. Secondly, the transfer dynamics of the particle population of the system are investigated in detail. For a three-level system, the optimal STIRAP scheme has an efficiency of over 98% in transferring the population to the state <inline-formula><tex-math id="M3">\begin{document}$ \left|3\right.\rangle $\end{document}</tex-math></inline-formula>, while the transfer efficiency of traditional STIRAP is about 72%. The superposition states with arbitrary proportions can be efficiently prepared for a four-level system due to the decoupling of the degenerate dark states. Finally, the influences of system parameters, such as the operating time of the Rabi pulses, the amplitude fluctuation and the single-photon detuning, on the transfer process are discussed. Especially, the phenomena of the adiabatic resonance transfer are revealed. Choosing the pulse parameters in the resonance window can reduce the infidelity of the population transfer to below 10<sup>–3</sup>. It is found that the optimal STIRAP scheme by the dynamical quantum geometric tensor provides faster and more efficient transfer than the traditional STIRAP scheme.