The Photon Statistic Of The Single Molecule

As the development of the science and technology,the concept of the single molecule technology was arisen in the science field.Less than 20 years from the detected the signal of the single dye molecule in 1989,the technology of single molecule developed very fast in past decade years,has become an important tool of the study physics,chemistry, biology and material science.Compared with the conventional spectroscopy technology, the merit of the single molecule technology is that the single molecule technology can detect the fluctuation of the system which in the conventional spectroscopy are ensemble averaged out.Carefully analyze the fluorescence data emission from the system,we can obtain the distribution information of the surrounding matrix of the single molecule and the dynamics of the single molecule.This provides a new method to study the biology, such as,used the single molecule spectroscopy to study thc protein's fold and unfold processes, and so on.But the signal we obtain from the single nano-system always included many noise,not only the unperfect of the experiment technic but also caused by the instinct of the single nano-system itself.So how to extract the information from the signal obtained from the single molecule is very important.Some theory methods are used to analyze the single molecule signals.Master equation(Rate equation)method,which neglected the coherence and spectral diffusiou and non-Markovian effect,is a straight forward method.The Quantum Jump method,the defects of this method is,firstly, the single molecule should have more complex behavior than the simple two-level atom system,for example,the energy level should not just two levels.Secondly,the single molecule is not the isolated system,which should interacted with the bath or reservoir, the parameters of the system should fluctuate with the time for the interaction between single molecule and the bath existence,this is different with the isolated atom system. The generalized Wiener-Khintchine approach,this method deal the photon counting with the semi-classical method,which caused the anti-bunching can not be captured by this method.The Levy walk method,which was used to deal the non-stationary processes.The generating function approach,this method not only can capture the bunching phenomenon but also can capture the anti-bunching phenomenon,and for the concrete system,the generating function become the like-optical Bloch equations,we called it Generalized Bloch Optical equatious(GBE),using the mathematical method to deal with the GBE is straight froward and easily.In this thesis,we use this method discussed the three level system interact with the continual wave laser and pulse laser, demonstrated the absorption transparent and the quantum beats phenomenon in the V type system,the electromagnetical induced transparent in the A type system also discussed in this thesis.This thesis composed with four chapters.In the chapter 1,we introduced the background of the single molecule spectroscopy and it caused the revolution of the physics,chemistry,biology and material science.An example is present to demonstrate the difference of the single molecule spectroscopy's Line-shape and the convenient Line-shape.In the chapter 2,The definition of the density matrix is given,from the Schr(o|¨)dinger equation,we obtained the density matrix evolution equation,which is the Liouville equation.Then we introduced the reduced density matrix,used the reduced density matrix to describe the three level system,obtained the reduced evolution equation, consequently we introduced the generating function method to deal with the photon statistics problems.In the chapter 3,the generating function use to discuss the typical three level systems such as∨,∧,(?)type three-level systems.For the∨type system we investigated the line-shape and Mandel's Q parameter as the system driven by single continuous wave external field,the average photon number of the different kinds photon emission from the system and the corresponding Mandel's Q parameters,the photon's joint probabilities and marginal probabilities as the system driven by one and two pulses.For the∧type system,we investigated the line-shape and Mandel's Q parameter as the system driven by single continuous wave external field and the electromagnetic induce transparency as the system driven by two continuous wave field,one is the laser field and the other is the electromagnetic filed.For the(?)system,we just discussed the line-shape and Mandel's Q parameter as the system driven by single continuous wave field.In the chapter 4,a briefly summary is presented in this chapter.