Two-photon Transition Of Control And Quantum Focus

Quantum control is booming as a brand new discipline, it is one of the most active element in the modern scientific front edge discipline, which involved in quantum mechanics, optics, chemical, cybernetics, information science, etc. With the rapid development of laser, observation and nanometer technology, quantum control methods carried out experimental research are also improving and increasing constantly, which will promote the development of quantum cybernetics, promote the development of chemical reaction, biological cells, quantum information, nano-materials and other fields'quantum control research associated with quantum mechanics system.With the rapid development of the ultrafast pulse, laser pulse shaping technology have made breakthrough progress.people can get any complex optical pulse waveform to realize more elaborate quantum control. The research of interaction between laser and material attracts a lot of scientific researchers. Different stimulated mechanisms produce different phenomena or effects.The chirped pulse light field who's instantaneous frequency vary linearly with time produce some peculiar quantum effects when interact with atom,which have more prodigious advantages in some coherent quantum control physical process researches,thus the chirped pulse light field was often used in theory and experiment.The chirp sweep frequency effect can implement multiple resonance stimulate processes,thus causing the multi-channel quantum interference effect or quantum diffraction effect. At the same time, the interference and diffraction effect can also be controlled by modulating the optical field phase.Constructive interference or destructive interference is decided by the phases relationship of light waves, as long as having the same phase optical field interacted with atom, constructive interference can be achieved, thus the weaker light field can realize the large stimulated efficiency.Based on the second order perturbation theory, we get the analytic expression of the excited state population probability and study the two-photon processes under the controllable chirp pulse. The bigger two-photon transition probability can be obtained by choosing the best shaping function under the resonance case.The results have certain reference value by using spectroscopy to explore material structure and other areas in theory and experiment. Through studying in-depth we find that the amplitude of the two-photon transition probability is actually the Fraunhofer diffraction process in frequency domain when the light goes through crystal and the results depend on the width of the slit. Based on the mature shaped pulse technology, we can realize the compression of the multiple-slit interference by cropping the optical field or modulating the phase.After compressing the the transition probability is greatly enhanced and quantum focused effect can be relized. Consequently the design idea is of great practical significance for quantum control,information processing and so on. Also the significance of this work is guiding the experiment in the lab environment and providing demonstration for teaching. This paper is composed of the following three parts.The first part is perturbation theoryIn this part, it mainly introduces the fundamental theories of the interaction. Under electric dipole approximation, we get Hamiltonian H, of the whole system between atoms and radiation field. Through solving the Schrodinger equation, using iterative method and the perturbation theory related with time, we discuss the every term of HI contributes to the transition probability and get the expression of the excited state probability amplitude and transition probability. It introduces two-photon process and discusses transition probability of the two-photon processes based on the second-order perturbation theory, and finally we gain the evolution of population probability of the excited state, which is the basic theory for later chapters and also has significant meaning for research work.The second part is that pulse shaping and two-photon transition controlIn this part, based on the second-order perturbation theory,the two-photon processes in the atom system excited by a shaped pulse are analyzed.The evolution of the two-photon transition probability is studied detailedly under two cases of nonresonance and resonance.It's shown that the transition probabilities disappeared at some corresponding frequencies under the nonresonance case, and thus the laser pulse can get through the medium without loss.Meanwhile,the bigger two-photon transition probability is obtained by choosing the best shaping function under the resonance case.It's proved that chirped effect has great advantages in some coherent quantum modulation of physical process research, The results has certain reference value when using spectroscopy to explore material structure and other areas in theory and experiment.The third part is quantum focused effectIn this part, the evolution of the two-photon transition rules under the chirp pulse light field are analyzed using the current laser coherent quantum control method. Based on the second order perturbation theory, we get the analytic expression of the population probability of the excited state. It's shown that the amplitude of the two-photon transition probability is actually Fraunhofer diffraction process in frequency domain when the light goes through crystal.The results of the diffraction depend on the width of the slit. It is just a single slit diffraction when the slit (the frequency width of the pump field) is narrower.When the slit is wider, the evolution of the population probability of the excited state is similar to the adding of two straight edge diffraction together. Based on the mature shaped pulse technology, we can realize the compression of the multiple-slit interference by cropping the optical field or modulating the phase. After compressing the the transition probability is greatly enhanced and the quantum focused effect can be relized. Consequently the design idea is of great practical significance for quantum control,information processing and so on.