For the first time, we study the parametric amplification process of multi-wave mixing (PA-MWM) signal and cascaded-nonlinearity process (CNP) in sodium vapors both theoretically and experimentally, based on a conventional phase-conjugate MWM and a self-diffraction four-wave mixing (SD-FWM) processes, which are pumped by laser or amplified spontaneous emission (ASE), respectively. For laser pumping case, SD-FWM process serves as a quantum linear amplifier (a CNP) out (inside) of the resonant absorption region. While for ASE case, only the CNP occurs and the output linewidth is much narrower than that of the MWM signal due to the second selected effect of its electromagnetically induced transparency window. In addition, the phase-sensitive amplifying process seeded by two MWM processes is discussed for the first time. Theoretical fittings agree well with the experiment. The investigations have important potential applications in quantum communication.
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