Entangled State From Cascaded Second-harmonic Generation

Since entanglement had been defined as "the representative characteristics of quantum mechanics" by Schrodinger, people have done a lot of work to study it. Facts proved that the entanglement has played a very important role in quantum communication, quantum metrology, quantum computation and quantum network. Entangled state could generally be divided into two categories:discrete-variable and continuous-variable. By contrast, CV entanglement is of the most significance in quantum dense coding and quantum cloning. Especially, multicolor CV entanglement not only could be available applied in the quantum key distribution as well as quantum teleportation, but also might be used as the quantum network nodes for storaging, encoding and transmitting. Therefore, how to prepare multicolor entangled light is very imperative. Using the cascaded nonlinear physical system as the main physical system, we theoretically investigated the generating process of multipartite entanglement. By means of Langevin equations of motion, we calculated the steady-state solution and the quadrature fluctuations of the output state, then provided the variation of quantum noise spectrum depended on system parameters. Thus, we proved that the cascaded nonlinear system was able to generate CV multicolor entanglement.This article focus on using the cascaded nonlinear systems to obtain the CV entanglement, the main works are as follows:(1) A system to generate CV quadripartite entangled state based on a type Ⅱ phase-matched Second-Harmonic Generation(SHG) cavity cascaded with a type Ⅰ phase-matched SHG cavity was investigated in chapter two. This proposal was different from the one that only utilized a nonlinear cavity to produce entangled state of light, we put two nonlinear crystal respectively in two different SHG cavity. Due to the experimental technology of SHG is comparatively mature, this was a easy way to implement the manipulation of each SHG cavities independently. This type of quadripartite entangled state is suitable for the quantum information storaging and processing, which crossed the gap between the optical systems of different wavelength and bridged the frequency octave of communication windows and multi-level atomic system.(2) A system to generate CV tripartite entangled state based on two cascaded type I phase-matched SHG cavities was investigated in chapter three. Based on the above idea, the output field of the first cavity was used as the pump field of the second cavity in the simplified system. Through this protocol, we realized the transformation of entanglement during the cascaded process, and get the well tripartite entangled state. This type of tripartite entangled state of light linked up two physical systems with different frequency, which was able to applicate in quantum information storaging and processing.(3) A system to generate CV quadripartite entangled state based on an optical parametric oscillator cascaded with a type I phase-matched SHG cavity was investigated in chapter four. As is well-known, due to the predominant tunable feature of the Optical Parametric Oscillator(OPO), it was one of the effective ways to produce bright entangled state of light. What is more, the SHG process was also a good generation source of entanglement. As a result, we effectively combined both of them as a new generation source to get quadripartite entangled state which had extremely practical value in application.