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本文从量子几何的角度研究多能级系统布居转移的优化控制。首先，我们建立基于动力学量子几何张量对受激拉曼绝热跟随（STIRAP）方案进行优化设计的一般理论框架。然后，以具有单光子失谐的$\Lambda$型三能级系统和三脚架型四能级系统为例，分别计算了体系的动力学量子几何张量和非绝热跃迁率，研究了系统的布居转移动力学。此外，文中还讨论了拉比脉冲工作时间、幅度涨落以及单光子失谐等参数对转移过程的影响，揭示了系统的绝热共振转移现象。研究发现，利用动力学量子几何张量优化的STIRAP方案比传统的STIRAP方案具有更快更高效的布居转移。The optimal control of population transfer for multi-level systems is investigated from the standpoint 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 $\Lambda$-type three-level system and tripod-type four-level system as examples. Secondly, the transfer dynamics of the system's particle population is investigated in detail. The optimal STIRAP scheme transfers the population to the state |3> for the three-level system with an efficiency of more than 98%, while the transfer efficiency of the conventional STIRAP is about 72%. The superposition states with arbitrary proportions can be efficiently prepared for the four-level system due to the decoupling of the degenerate dark states. Finally, the effects of system’s parameters such as the operating time of the Rabi pulses, the amplitude’s 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 at the resonance window allows the infidelity of the population transfer to be reduced to less than 10-3. It is found that the optimal STIRAP scheme based on the dynamical quantum geometric tensor provides faster and more efficient transfer than the conventional STIRAP scheme.
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Keywords:
- Stimulated Raman adiabatic passage /
- Dynamical quantum geometric tensor /
- Adiabatic population transfer /
- $\Lambda$-type three-level system /
- Tripod-type four-level system /
- Dark states
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