The Generating Function Approach For Emission Photon Counting Statistics Of Single Quantum Systems

Observation and operation of the single quantum systems (such as single atom, single molecule and single nanoparticles) is a dream of the scientists. As the devel-opment of the science and technology, specially the invention of scanning tunneling microscopy in 1982, with the help of the scanning tunneling microscope scientists almost have observed the image of the atoms of the surface and operated the atoms on the surface, in other words, the scanning tunneling microscope helps the sci-entists to realize the dream. Until 1989, Moerner and his coworkers archived the first optical single molecule experiment through observing the single molecule's ab-sorption signals, then Orrit and his coworkers through observing the fluorescence of the single molecule obtained high signal-to-noise ratio signals, which opens up the optical study the single quantum systems' door.The property of single quantum systems is that the single quantum systems are very sense to its surround environment changes, the properties of the photons emit-ted from the single quantum systems always reflect the changes. So the single quan-tum systems are always used as a detector or as a fluorphore in bio-macromolecule, then through investigating the statistical properties of emission photons from the single quantum systems which as a detector put in bio-macromolecule, one can obtain the bio-macromolecule's conformation changes with time in the biology pro-cesses, which would help us to understand some confusing problems. In the other hand, the single quantum systems experiments can observe the fluctuation of the emission photons in very short time scale, in the same order with the lifetime of ex-cited state of single quantum systems. So, the statistical properties of the emission photons from the single quantum systems also reflect the dynamics which occurred in the single quantum systems themselves.This thesis organized as followsIn chapter?, we give an introduction to the single quantum systems and some potential applications of the single quantum systems, and some experimental meth- ods and theoretical methods are also introduced. Then, we give a brief introduction to serval different kinds of generating functions, at the end of this chapter, we give an example to demonstrate how to use the generating function approach in the counting problem.In chapter?, some basic quantum concepts are introduced, which are needed in the next chapters. Firstly, we briefly introduced how to quantized the electro-magnetic field, because the interaction between quantized electromagnetic field and the single quantum systems caused the excited states of the single quantum sys-tems damping or relaxing with respect to time. Then, we introduced the definition of the density matrix operator, and obtained the motion equation of the density matrix operator from the Schrodinger equation. Then, we shows how to calculate the spontaneous emission rates of the single quantum systems. The spontaneous emission rates are separated in four parts in the calculating process, the second, and third parts are very important for the photon emission processes. At the end of this chapter, we demonstrated how to obtain the rate equation from the motion equation of density matrix operator as the coherent damping very fast.In the chapter?, we discussed the photon statistics of the?type three level system using generating function approach. According to the direction of the tran-sition dipole moment of?type three level systems, we can sort the?type three level systems into two sorts, one is the transition dipole moments are parallel to each other, the other is the transition dipole moments are orthogonal to each other, we call them parallel system and orthogonal system. The photons emitted from the two different systems show different behavior, for the orthogonal system, we discussed the emission photon number <N> and Mandel Q parameter as a function of the angle between the direction of the external laser field and the direction of the transition dipole moment between ground state?g> and excited state?y>. In the weak driven field case, the expectation value of emission photons <N> and Mandel Q show sine or cosine behavior with respect to the angle?. Then we the beats of the envelope of the photons emitted from?type three level system driven by two pulses field with the delay time td between two pulses. In the parallel system, we discussed a coherent population trapping phenomenon as the system driven by two cw external laser fields.In the chapter?, we discussed the blinking phenomenon occurred in single terrylene molecule through two models, in model I, the waiting time distribution of the ON and OFF are demonstrated. The waiting time distribution of the OFF state shows bi-exponential decaying behavior, as the OFF state composed with two substates OFF1 and OFF2. The other model is used to discuss the photon statistics of the single molecule, the <N> and Mandel Q parameter are linear relation with the evolution time, at the last we give the analytical expression of the <N> and Mandel Q at long time limit.In the chapter?, we give a brief summary and an outlook also given in this chapter.