| Quantum optics is a subject based on the quantum theory, for study of light transmission, detection and interaction between light and matter. The theory of quantum optics has been developed for more than a century, early in 1900, Max Planck put forward the quantum theory of radiation field, successfully explain blackbody radiation problems. In 1905, Einstein put the quantum theory throughout the entire radiation and the quantum physics of light absorption process, to successfully explain photoelectric effect and to be confirmed by the later Compton experiments. He explains the Max Planck blackbody radiation formula, put forward the three physical process about light and atomic interaction, the spontaneous radiation, stimulated radiation, stimulated absorption. And these provided the foundation for the 1960s laser production. Lasers can provide the coherent beam that is different from ordinary hot field. The existence of laser opens a new way for the development of quantum optics experiment. Today, the theoretical and experimental research of quantum optics respectively obtain remarkable achievements and considerable development in separated variable and continuous variable fields, especially in the production and application for nonclassical field.Generally speaking, the nonclassic fields contain squeezed state and entangled state, the noises of these fields can beyond shot noise limit and exist quantum correlation. They can be widely used in many fields, such as the gravitational waves detection and quantum communications. In recent years, spatial quantum optics and spatial quantum information have been also studied. They can provide spatial quantum correlation, which is different from the general TEM00 mode based on time scales. It can be used in spatial information transmission, ultra-high precision measurement, quantum imaging, image transmission, quantum holography, image amplification without noise. These quantum properties make people consider entanglement as the most important and the most foundational quantum resource.At present, the squeezed and entangled state are the hot topics in the field of quantum optics. In this thesis, we mainly studied theoretically about the generation of tripartite entanglement by frequency doubling in a dual-port cavity, the theoretical design to construct periodically poled KTiOP04 (PPKTP) producing bi-entanglement of cesium atom absorption line and communication wave, the generation of Rb atomic absorption line multicolor entanglement lights by simultaneous quasi phase matching, the generation of the TEMoo squeezed field and TEM01 squeezed and entangled field by using an optical parametric amplifier.The main content is divided into the following five parts:1) Quantum mechanics and quantum optics are briefly reviewed. Two kinds of the nonclassical field containing the squeezed entanglement state and spatial entangled state are introduced. Quantum property and application are also introduced.2) Birefringence phase matching, quasi-phase matching and 532-1064nm PPKTP crystal are briefly introduced. The classical and quantum properties of squeezed state are investigated by the Lanngevin equation. The scheme of entanglement by combining two squeezed beams with a beam splitter is also introduced.3) We calculate the quantum fluctuations of the fundamental frequency pump beam and second harmonic beams in a two-port Frequency Doubling Resonator, and investigate the tripartite continuous-variable entanglement generated by this device for the first time.4) The design and construction of PPKTP which can be used to produce entanglement of 852.3742 nm and 1550.42 nm are theoretically investigated. The structure of PPKTP is designed for generating multicolor entanglement lights of one atomic transition line by simultaneous quasi phase matching. Discussion is made on simultaneous phase matching for two different optical parametric process at the same period in PPKTP.5) The content about high-order hermite-gaussian modes and the generation methods in experiment is briefly introduced. We demonstrated experimentally the squeezed TEM01 mode is generated in a degenerate optical parametric amplifier with the nonlinear crystal of PPKTP. The level of 2.2dB squeezing is measured using a spatial balance homodyne detection system.2.8dB squeezing corresponds to TEM00 mode. Further more, we combine two squeezed TEM01 fields with a beam splitter to produce entanglement for TEM01 mode. The sum of the beams amplitudes is -1.5 dB, and the difference of the beams phases is -1.2dB below the standard quantum limit.The innovative work is listed as below:1) We proposed that tripartite continuous-variable entanglement can be produced in a two-port frequency doubling resonator, The quantum correlation is studied using a necessary and sufficient criterion for Gaussian entanglement states, the positivity under partial transposition (PPT).2) We theoretically proposed that tricolor entangled fields by simultaneous quasi phase matching in a crystal of PPKTP.3) The TEM01 mode entanglement was produced in our experiment.4) We reconstructed Wigner quasi-probability distribution function of squeezed TEM01 state using quantum tomography.Key Words:Optical parameters process; Squeezed entanglement state; Quasi-phase matching;Multicolor Multipartite entanglement; High order transverse mode...
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