The two-level system is the simplest system in the quantum system, and it is also the basic unit of other multi-level systems. Therefore, it is of great significance to investigate the quantum properties of two-level system acting by light field for understanding the internal mechanism and physical essence of quantum effects. With the continuous development of laser technology, the interaction of ultra intense and ultra short laser pulses with atoms, molecules and other quantum systems has produced many new physical phenomena. In recent years, pulse shaping technology has been widely used to precisely control the coherent quantum effect by customizing and optimizing the characteristics of the light field. In this study, the optical field with a chirped frequency parameter is used to drive the excitation-ionization quantum system. The spectrum property of the ionization photoelectron of the quantum system can be effectively controlled by the chirp factor. The population probability of transition particles in the dressed state of the excited energy state, and the characteristics of ionized photoelectrons in the quantum system can be controlled by adjusting the chirp factor of the pump light, so as to achieve accurate and efficient quantum manipulation.

Under the rotating wave approximation and rotating coordinate transformation, the Hamiltonian operator of the interaction between the two-level system and the light field is obtained. Considering that the light field is a strongly chirped Gaussian field with the initial phase is zero, the particle population probability amplitudes of the two dressed states and excited states in the dressed state representation are obtained by solving the interaction Hamiltonian. Using perturbation theory, the probability amplitude of two-photon ionization photoelectron is calculated under the condition of weak field limit approximation, and the characteristics of ionization photoelectron spectrum of quantum system are obtained. Based on the dressed state theory and adiabatic following technique, the population probability of particles in dressed states modulated by different chirp factors is given.

The quantum properties of ionized photoelectrons in the excitation-ionization model under the influence of a strong chirped pulse light field are investigated by solving the Schr?dinger equation and using perturbation theory. The results reveal that the ionization photoelectron spectrum of the quantum system splits into two symmetrical spectral lines when the chirp factor of the light field is zero (Fig. 2). The reason is that the particles are equally likely to reside in the two dressed states when there is no chirp factor modulation, so the probability of ionization from the two dressed states is equal. However, an asymmetric distribution of spectral line splitting emerges when the chirp factor is non-zero. In the case of positive chirp, when the chirp factor is increased, the intensity of slow electron lines in the ionization spectrum gradually decreases, while the intensity of fast electron lines increases. In the case of negative chirp, the intensity of fast electron spectral lines gradually decreases with the increase of chirp factor, while the intensity of slow electron spectral lines gradually increases. When the positive and negative chirp factors reach a certain value respectively, only fast electron spectral lines or slow electron spectral lines can be detected in the ionization photoelectron spectrum (Fig. 3). In addition, the population probability of excited state particles is related to the absolute value of chirp factor. The positive and negative chirp factors with equal absolute values have the same effect on the population probability of excited state particles and on the population transfer efficiency. The selective population and evolution of particles in the dressed state are analyzed by the dressed state theory (Fig. 4). Positive chirp can conducive to the distribution of excited state particles in the upper dressed state, while negative chirp can conducive to the distribution of excited state particles in the lower dressed state. In the process of two-photon ionization, the electrons of ionization transition come from two different transition channels of dressed states. The interfere of two channels in the process of ionization transition results interference fringes on the envelope of ionization photoelectron spectrum. Through the adiabatic following technique, the selective population of particles in the dressed state in the quantum system modulated by the chirp factor of the light field is analyzed, so as to realize the coherent regulation of the ionization photoelectron spectrum.

The coherent modulation of the driving light field chirp factor on the two-photon ionization photoelectron spectrum in the excitation-ionization model is studied. The results show that the chirp factor of the pump light field has a very obvious modulation effect on the ionization photoelectron spectrum. The characteristics and laws of the chirp factor regulating the ionization photoelectron spectrum are analyzed through the theoretical calculation and dressing theory. The selective population of particles in the dressed state is realized by modulating the chirp factor of the light field, so as to realize the coherent regulation of the ionization photoelectron spectrum. The internal mechanism and physical essence of the interaction between the chirped light field and the quantum system are clearly presented. The results have certain theoretical guiding significance for the realization of precise quantum coherent control, and have potential application value in the fields of quantum communication, bond selection quantum chemistry and precision measurement.