| The dissertation presents the researches in quantum optics in my Ph. D. study. The content includes four components, a. the related investigations of the generation of the entangled state of the light in FWM. b. the intracavity FWM process, c. the multi-normal mode splitting of the EIT-cavity system under the superstrong coupling condition, d. the study and work when I visit Vladan group at MIT.a. The squeezed and entangled states of the light are the important resource of the quantum information process. The FWM has been attracted many attentions since the realization of the first squeezed state of the light in FWM. Specially, the recent researches in the non-degenerate FWM in the atomic vapor make it a hot study area in quantum optics. We will present our works on the entangled state of the light in the non-degenerate FWM in the rubidium vapor in the chapter one. In our experiment, the new detection system is composed of two pairs of self-balanced detection system, it is convenient for us to measure the SNL, squeezed intensity difference and intensity sum noise spectra simultaneously. And we also study the influence of the extra noise of the input signal field. We find the ways which can cancel the extra noise or maximize the squeezing.b. The high power is need in the hot atom medium or under the large detuning condition. The coherence can enhance the conversion efficiency of the FWM in the low power regime. We can also resort to the cavity. In chapter two, we demonstrate the triply-resonant optical parametric oscillator theoretically. By means of the large dispersion due to the two-photon transitions and the enhancement of tha cavity, the above-threshold oscillations of the Stokes and anti-Stokes fields together with the single pumping beam are realized in the experiment. The OPO efficiency is20%, and the threshold is35mW.c. The quantum non-demolition measurement, the single atom laser, the photon Fock state filter, etc. can just be realized under the strong coupling condition that is the key problem in cavity QED. We discuss the multi-normal-mode splitting in the EIT medium and cavity system under the super-strong coupling condition when the large number of atoms are in the cavity. The resonant cavity mode splits into three parts and the other modes near the resonant mode can also split into three parts. In addition, the linewidth of the central peaks are narrowed because of the large sleep of the dispersion in the EIT window.d. In chapter four, I present the study and the work about the cavity-based single atom detection at Vladan group during my visiting. Vladan group design a cavity of13.7mm, the finesse is6x104. Because of the novel design, the atoms can be loaded into the cavity directly. The technique of trapping the atoms in the free space and in the micro-cavity can be applied to the experiment. So it open the potential application in quantum optics. The very weak pump laser is used to excite a single atom or several atoms into the measured state. And by removing the background atoms, the system can distinguish two atoms in the cavity.
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