Amplification of entangled beam based on four-wave mixing process *

The two-mode entangled state is an important quantum resource for quantum information. In this paper, the amplification of a single mode of two-mode entangled state (single-mode amplification scheme) and two modes of two-mode entangled state (two-mode amplification scheme) are theoretically proposed. Here, the optical beam splitter model is used to simulate the vacuum noise introduced by the loss in the optical transmission process. By utilizing the positivity under partial transpose criterion, we analyze the effect of the gain of the four-wave mixing process on the entanglement degree of the initial two-mode entangled state in two different amplification schemes. In these two schemes, we set the gain of the initial two-mode entangled state generation process to be 1.5, 2.5 and 50 respectively, and then change the gain of the amplification process in a certain range. We also set the transmission efficiency of the amplified beams in the two schemes to a definite value. The results show that the entanglement of the initial two-mode entangled state


Abstract
The two-mode entangled state is an important quantum resource for quantum information.In this paper, the amplification of a single mode of two-mode entangled state (single-mode amplification scheme) and two modes of two-mode entangled state (two-mode amplification scheme) are theoretically proposed.Here, the optical beam splitter model is used to simulate the vacuum noise introduced by the loss in the optical transmission process.By utilizing the positivity under partial transpose criterion, we analyze the effect of the gain of the four-wave mixing process on the entanglement degree of the initial two-mode entangled state in two different amplification schemes.In these two schemes, we set the gain of the initial two-mode entangled state generation process to be 1.5, 2.5 and 50 respectively, and then change the gain of the amplification process in a certain range.We also set the transmission efficiency of the amplified beams in the two schemes to a definite value.The results show that the entanglement of the initial two-mode entangled state decreases with the increase of the gain under the condition of specific transmission loss in two schemes.When the gain does not exceed a certain value, the entanglement of the initial two-mode entangled state can be maintained.Then, with the increase of the gain, the entanglement of the initial two-mode entangled state will disappear.Moreover, the entanglement of the initial two-mode entangled state of the two-mode amplification scheme disappears faster than that of the single-mode amplification scheme.Our theoretical results pave the way for the experimental realization of the amplification of two-mode entangled state based on four-wave mixing process.

Fig. 1 .
Fig. 1.A scheme for single-mode amplification of EPR beams: (a) Simplified diagram of

Fig. 2 .
Fig. 2. The relationship between the smallest symplectic eigenvalue and 2G of the single-mode

Fig. 3 .
Fig. 3.A scheme for two-mode amplification of EPR beams

Fig. 4 .
Fig. 4. The relationship between the smallest symplectic eigenvalue and 2 G of the two-mode Keywords: four-wave mixing, quantum entanglement, two-mode entangled state, optical parametric amplifier PACS: 03.65.Ud, 03.67.Mn, 42.50.-p* Project supported by the National Natural Science Foundation of China (Grant No. 11874155, 91436211, 11374140), the National Basic Research Program of China (Grant No. 2016YFA0302103), the Natural Science Foundation of Shanghai (Grant No. 17ZR1442900), the Innovation Program of Shanghai Municipal Education Commission (Grant No. 2021-01-07-00-08-E00100), the Basic Research Project of Shanghai Science and Technology Commission (Grant No. 20JC1416100), the Program of Scientific and Technological Innovation of Shanghai (Grant No. 17JC1400401), the Shanghai Municipal Science and Technology Major Project (Grant No. 2019SHZDZX01), the Shanghai Sailing Program (Grant No. 21YF1410800), the Minhang Leading Talents (Grant No. 201971), and the Programme of Introducing Talents of Discipline to Universities (Grant No. B12024).† Corresponding author.E-mail: ssliu@lps.ecnu.edu.cn‡ Corresponding author.E-mail: jtjing@phy.ecnu.edu.cn Phys.Rev. Applied 7 014023 [29] Li C B, Li W, Zhang D, Zhang Z Y, Gu B L, Li K K, Zhang Y P 2019 Laser Phys.