Theoretical Investigation Of Multipartite Entanglement And Optimization Of SNR Based On Four-wave Mixing Process

Four-wave mixing (FWM) process is an effective way to generate quantum state and has many potential applications. In this paper, we theoretically construct two systems based on FWM process in rubidium vapor. One is used to realize multipartite quantum entanglement and the other is used to optimize the signal-to-noise ratio (SNR) of optical beams.We theoretically investigate a system based on four-wave mixing processes in hot ru-bidium vapor to generate genuine quadripartite quantum entanglement. The number of output beams of this system is exponentially proportional to the number of rubidium va-por cells and the quantum correlation between the output beams increases as the number of rubidium vapor cells increases. In this paper, we investigate quantum entanglement in this system using several criteria related to homodyne detection. We firstly analyze bipartite quantum entanglement between any pair of output beams using Duan and Si-mon criteria and then quadripartite quantum entanglement between the four output beams using three-condition criterion and single-condition criteria proposed by Loock and Fu-rusawa. At last, we deduce an optimized single-condition criterion which can be used to characterize genuine quadripartite quantum entanglement by introducing different co-efficients of quadratures to maximally cancel the quantum noise between output beams. Using the optimized single-condition criterion, the degree of genuine quadripartite quan-tum entanglement increases as the gains of the FWM processes increase simultaneously when the gains are greater than 1.5 (the gains are equal). The optimized single-condition criterion is experimentally feasible and can be easily generalized to the case of genuine multipartite quantum entanglement.We theoretically investigate a system based on four-wave mixing process in hot rubid-ium vapor to realize the optimization of SNR. We analyze the change of SNR of probe beam in phase-insensitive amplifier, i.e. when the input probe is coherent state and the input conjugate is vacuum state, and find that the noise figure (NF) is greater than 1.i.e. the SNR of probe beam reduces in the process of amplification. Then we analyze the change of SNR of probe beam in phase-sensitive amplifier, i.e. when the input probe and conjugate are both coherent states, and find that the NF is less than 1 under certain condi-tions, i.e. the SNR of probe beam increases in the process of amplification. We find that when the relative phase between input beams ((?)) is 2kπ (k is integer), the effective gain of probe beam is maximum and the NF is minimum. Under the condition of (?)=2kπ (k is integer), as long as the intensity of input conjugate beam is greater than 17.2% of the intensity of input probe beam, the SNR of probe beam increases in the process of amplification. Particularly, when the intensity of input conjugate beam is less than the intensity of input probe beam at the same time, the optimization of SNR of strong beams by weak beams is realized.