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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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