Statistical Properties Of Single Molecule Photon Emission In Solid Matrix

Since the 90s of last century, the single molecule technology has developed rapidly and has become the important tool on the study of physics, chemistry, biology and mate-rial science. The development of single molecule science is based on the molecular scale study of Scanning Probe Microscopy (SPM), laser tweezers, single molecule manipula-tion and single molecule fluorescence spectrum and so on. The research contents of single molecule science primary contains single molecule detection, single molecule chemical physics, single molecule dynamics, physical properties of single molecule, and the corre-sponding study methods of single molecule. The development of single molecule science brings the observation and discovery of physical phenomenons and impels to manipulate the physical world on the level of single molecule. The past observation technologies fo-cus on the overall average of some parameters about the numerous molecular assembly, and hardly cover the special information of single molecule. However, the observation on the scale of single molecule can discover the time-varying molecular characterization, such as, the quantum transition between the singlet state and triple state of the excited single molecule, forming the two statuses of "yes" and "no", as well as the blinking effect of enzyme catalyze.An important feature of single molecule technology is closely related the fluctuation of environment. Through the observation of single molecule, the analysis of environ-ment can offer the vital dynamical process in the condensed matter and some distribu-tion on the nano-environment, such as the single molecule spectrum, studying the effect of environment on the molecule parameters and some statistical relevance. The ordi-nary spectrum shows the average features of numerous molecules. But single molecule spectrum is the spectrum of single molecule and usually is a spectral analysis on the dynamical behavior of single biology molecule, basing on the properties of optics, elec-tronics and mechanics about single molecule. Single molecule spectrum primarily studies macromolecule (including DNA and protein), carbon nano-tube, nano-particle and dye molecules and∞on. The conventional spectrum technology shows the colony statis-tical average, i.e., average response and average value of ensemble, which covers some special information and which is rejected by the single molecule spectrum. Through the emission signal of single molecule fluorescence, the got information of environment and dynamical behaviors give a hand on the study about material science and biology. The change information of biology macromolecule can show the relevant message about the microenvironment. We have further realized the dynamical process and details of biol-ogy and material science on the single molecule level, and have comprehensively knew the relation of the system and environment.The studies on fluorescence molecule in solid matrix become more and more. The existence of solid matrix makes the movement of fluorescence under restriction, weakens the intermolecular interaction, decreases the quenching by the collision and increases the stiffness of molecule structure, which come near to the single molecule. So, the research on the statistical properties of single molecule reflects the structure characters of solid matrix environment. However, when the luminescence molecular in the solution, there is strong intermolecular interaction, and hardly photon emission due to the inter-system energy transduction after being excited state. Taking the fluorescence molecule for example, we study the statistical properties of single molecule photon emission.It is very strong that the effect of environment fluctuation on the single molecule and this "hot noise" almost submerges the experimental signals, so it becomes very dif-ficult to extract some useful information from the experimental signals. The analysis of single molecule data is more difficult than the analysis of ensemble average data, which need look for better theory method in order to extract useful information from the data about the fluorescence strength and fluctuation. There are some developed methods: Master equation method, Wiener-Khintchine method, quantum jumping method, gen-erating function and Levy-walk method and so on. These methods can be used for the analysis of single molecule fluorescence signals and give the theoretical result, but these methods cut both ways. We use the recently developed generating function method to analysis the single molecule fluorescence signal. This method can calculate some statistical properties of single molecule emission photon, not only analytically but also numerically. Using this method, not only the high moments of emission photon can be got, but also the bunching effect and antibunching effect for the distribution of single molecule emission photon. Taking the DBATT molecule as the example, we discuss the statistical behaviors of two level system using the generating function method, showing the conditions for enhancement and suppression of fluorescence emission. Further, we provide other statistical information, such as, the waiting time of photon emission, the probabilities of one and double photons and so on. Finally, we talk over the blinking phenomenon ubiquitous in the biology molecules using the generating function method, discussing the statistical properties of photon emission and jumping in different direc-tions in fluorescence blinking process.This article is divided into five chapters:In the chapter 1, we introduce the background and current situation about the development of single molecule and simply present the single molecule technologies. Single molecule science caused the revolution and promotion of the physics, chemistry, biology and life science.In the chapter 2, we give the theory methods. First, introduce the all theory methods researching the single molecule systems, their advantages and disadvantages, as well as the applicable scope for every method. We show the definition of density matrix theory and derive its evolution. Then, simply discuss the generating function method.In the chapter 3, the statistical properties of two level system under external fields are given. Firstly, give the detailed derivation and get kinematic equation of density matrix for the two level system under laser and rf fields, so as to extract the statistical physical quantities for single molecule systems. Then, we respectively discuss the sta-tistical properties under continue external fields and pulse external fields. While under continue external fields, there is divided into the absentee and present of spectral diffu-sion and the result about emission photon is very according with the experiment. While under pulse external fields, we show the different situations about statistical properties of emission photon.In the chapter 4, we deal with the fluorescence blinking process using the generating function method. Extract the statistical information from the emission photon of single molecule system under two different models and get the first order moment and other high order moment about emission photon in this process, aiming to show the moder-ating effect of external field on the single molecule systems. Furthermore, we introduce two variables to respectively get the relevant information about ON state jumping and OFF state jumping, such as, the waiting time and its distribution, the correlation func-tion about the two direction jumping, the probabilities of different direction jumping and joint probability of the two directions jumping. The good description of blinking phenomenon widens the application of generating function method.In the chapter 5, a summary and outlook are presented in this chapter. We sum-marize the study and bring a further development about the statistical properties using generating function method and about the other application of generating function.