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在强场激发的一般情况下，斯塔克效应对于瞬态双光子跃迁具有重要影响，且该过程的解析描述具有很大挑战。本文采用解析求解与数值模拟相结合的方法，系统地研究了弱场和强场啁啾脉冲激发的瞬态双光子跃迁过程，揭示了光场强度、啁啾因子、失谐量等参数对双光子跃迁几率时域演化的重要影响。首先，本文利用二阶微扰理论得到了双光子时域跃迁几率振幅的近似解析解表达式。该解析解表明，弱场激发的瞬态瞬态双光子跃迁过程类似于菲涅耳直边衍射效应。随着光场强度的增强，斯塔克效应对双光子跃迁的影响也随之增强。其次，本文通过一系列近似处理得到了强场作用下薛定谔方程的近似解析解。解析解表明，强场斯塔克效应引起能级分裂使得双光子跃迁几率时域的对称性遭到了破坏，其频域过程类似于“双缝干涉”效应。研究结果表明，强场激发时布居转移效率与光场强度具有重要关系，而啁啾因子不仅可以调节布居转移效率和时间位置，还可以改变布居几率在时域的振荡频率。这对于强场激发的布居几率时域演化描述提供了新思路，并对双光子显微成像研究提供了科学依据。In general cases of strong field excitation, the Stark effect has a significant impact on transient two-photon transitions, and the analytic description of this process is quite challenging. By combining analytical solutions and numerical simulations, we systematically study the transient two-photon transition processes excited by weak and strong chirped pulses, revealing the important influences of parameters such as light field intensity, chirp factor, and detuning on the time-domain evolution of two-photon transition probabilities. Firstly, we derive an approximate analytical expression for the amplitude of the time-domain two-photon transition probability using second-order perturbation theory. This analytical solution indicates that the transient two-photon transition process under weak field excitation is similar to the Fresnel rectangular edge diffraction effect. As the light field intensity increases, the influence of the Stark effect on two-photon transitions also intensifies. Secondly, through a series of approximations, we obtain the approximate analytical solutions of the Schrödinger equation under strong field interactions. The analytical solutions show that the strong field Stark effect induces energy level splitting, which disrupts the symmetry of the time-domain two-photon transition probabilities distribution, and its frequency domain process is similar to the'double-slit interference' effect. The research results indicate that the efficiency of population transfer during strong field excitation is significantly related to the light field intensity, while the chirp factor can not only regulate the efficiency and time position of population transfer but can also alter the oscillation frequency of the population probability in the time domain. This provides new insights for the description of the time-domain evolution of the population probability_under strong field excitation and offers a scientific basis for research in two-photon microscopy.
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Keywords:
- Two-photon transition /
- Femtosecond pulse /
- Perturbation theory /
- Chirp factor
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