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Entanglement manipulation in various systems is one of the important problems in quantum information science. In this paper, the phase sensitivity and entanglement enhancement of the cascade four-wave mixing of hot atomic steam are studied. The results show that the quantum entanglement of the probe light and the conjugate light output at the second level of the cascade four-wave mixing process is significantly stronger than that at the first level, and the maximum increment can reach more than 5 dB, and the perfect entanglement can be achieved by increasing the intensity factor. The relations of quantum correlation type and the size of the entanglement with the pump phase and the nonlinear intensity factor are also discussed in this work. The results show that because of the enhancement of entanglement and the sensitivity of entanglement type to pump phase, the light field noise characteristics can be changed by controlling the phase and intensity factors thus realize the enhancement of entanglement between the probe and coupling light and the quantum manipulation of entanglement extent and quantum entanglement type. The theoretical study is of important significance for guiding the experimental implementation of optical parameter manipulation of entanglement enhancement, compression angle and compression degree of two-mode compression state.
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Keywords:
- phase sensitive amplifier /
- four-wave-mixing process /
- quantum entanglement /
- entanglement manipulation
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图 1 相位敏感的级联四波混频系统
Figure 1. Cascaded four-wave mixing process in hot vapor.
图 2 量子纠缠随强度因子
$G$ 的函数变化图, 其中红虚线为${S_{{a_1}{b_1}}}$ , 红实线为${S_{{a_2}{b_2}}}$ Figure 2. Two pair of quantum entanglement as a function of intensity factor
$G$ . Red dashed line corresponds to${S_{{a_1}{b_1}}}$ and red solid line corresponds to${S_{{a_2}{b_2}}}$ .
图 4 探针光
${\hat a_2}$ 与耦合光${\hat b_2}$ 的纠缠随相位${\theta _2}$ 的变化Figure 4. Entanglement of probe
${\hat a_2}$ conjugate${\hat b_2}$ beams as a function of the phase${\theta _2}$ for various values of the intensity gain.
图 3 不同强度因子下第二级四波混频过程产生的两束光纠缠
${S_{{a_2}{b_2}}}$ 的等值线图 (a)${G_1} = {G_2} = 1.5$ ; (b)${G_1} = {G_2} = 2$ ; (c)${G_1} = {G_2} = 2.5$ ; (d)${G_1} = {G_2} = 3$ Figure 3. Contour plots for
${S_{{a_2}{b_2}}}$ with different intensity gains: (a)${G_1} = {G_2} = 1.5$ ; (b)${G_1} = {G_2} = 2$ ; (c)${G_1} = {G_2} = 2.5$ ; (d)${G_1} = {G_2} = 3$ .
图 5 不同强度因子下第二级四波混频过程产生的两束光纠缠
${S_{{a_2}{b_2}}}$ 的等值线图 (a)${G_1} = {G_2} = 1.5$ ; (b)${G_1} = {G_2} = 2$ ; (c)${G_1} = {G_2} = 2.5$ ; (d)${G_1} = {G_2} = 3$ Figure 5. Contour plot for
${S_{{a_2}{b_2}}}$ with different intensity gains: (a)${G_1} = {G_2} = 1.5$ ; (b)${G_1} = {G_2} = 2$ ; (c)${G_1} = {G_2} = 2.5$ ; (d)${G_1} = {G_2} = 3$ .
图 6 探针光
${\hat a_2}$ 与耦合光${\hat b_2}$ 的纠缠随相位${\theta _2}$ 的变化Figure 6. Entanglement of probe
${\hat a_2}$ conjugate${\hat b_2}$ beams as a function of the phase${\theta _2}$ for various values of the intensity gain.
图 7 相位
${\theta _1}$ 对两对量子纠缠的影响 (a)${\theta _2} = 0/2{\text{π}}$ ,${G_1} = {G_2} = 1.5$ ; (b)${\theta _2} = {\text{π}}$ ,${G_1} = {G_2} = 1.5$ Figure 7. Two pair of quantum entanglement versus phase
${\theta _1}$ : (a)${\theta _2} \!= 0/2{\text{π}}$ ,${G_1} \!= {G_2}\! = 1.5$ ; (b)${\theta _2} \!= {\text{π}}$ ,${G_1} \!= {G_2} \!= 1.5$ -
[1] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777
Google Scholar
[2] Davidovich L 1996 Rev. Mod. Phys. 68 127
Google Scholar
[3] Lvovsky A I, Raymer M G 2009 Rev. Mod. Phys. 81 299
Google Scholar
[4] Polkinghorne R E S, Ralph T C 1999 Phys. Rev. Lett. 83 2095
Google Scholar
[5] Jing J T, Zhang J, Yan Y, Zhao F G, Xie C D, Peng K C 2003 Phys. Rev. Lett. 90 167903
Google Scholar
[6] Wu L A, Kimble H J, Hall J L, Wu H 1986 Phys. Rev. Lett. 57 2520
Google Scholar
[7] Ou Z Y, PereiraS F, KimbleH J, Peng K C 1992 Phys. Rev. Lett. 68 3663
Google Scholar
[8] Maeda M W, Kumar P, Kimble H J, Shapiro J H 1987 Opt. Lett. 12 161
Google Scholar
[9] Hsu M T L, Hétet G, Peng K, Harb C C, Bachor H A, Johnsson M T, Hope J J, Lam P K, Dantan A, Cviklinski J, Bramati A, Pinard M 2006 Phys. Rev. A 73 023806
Google Scholar
[10] Tang R, Devgan P S, Grigoryan V S, Kumar P, Vasilyev M 2008 Opt. Express 16 9046
Google Scholar
[11] Tong Z, Lundstrm C, Andrekson P A, Mckinstrie C J, Karlsson M, Blessing D J, Tipsuwannakul E, Puttnam B J, Toda H, Grner-Nielsen L 2011 Nat. Photon. 5 430
Google Scholar
[12] Slusher R E, Hollberg L, Yurke B, Mertz J C, Valley J F 1985 Phys. Rev. A 31 3512
Google Scholar
[13] McCormick C F, Boer V, Arimondo E, Lett P D 2007 Opt. Lett. 32 178
Google Scholar
[14] Pooser R, Jing J T 2014 Phys. Rev. A 90 043841
Google Scholar
[15] Kong J, Jing J T, Wang H J, Hudelist F, Liu C J, Zhang W P 2013 Appl. Phys. Lett. 102 011130
Google Scholar
[16] Qin Z Z, Cao L M, Wang H L, Marino A M, Zhang W P, Jing J T 2014 Phys. Rev. Lett. 113 023602
Google Scholar
[17] Cao L M, Qi J, Du J J, Jing J T 2017 Phys. Rev. A 95 023803
Google Scholar
[18] Fang Y M, Jing J T 2015 New J. Phys. 17 023027
Google Scholar
[19] Wang L, Wang H L, Li S J, Wang Y X, Jing J T 2017 Phys. Rev. A 95 013811
Google Scholar
[20] Wang L, Jing J T 2017 Appl. Opt. 56 2398
Google Scholar
[21] Boyer V, Marino A M, Pooser R C, Lett P D 2008 Science 321 544
Google Scholar
[22] Pooser R C, Lawrie B 2015 Optica 2 393
Google Scholar
[23] Embrey C S, Turnbull M T, Petrov P G, Boyer V 2015 Phys. Rev. X 5 031004
Google Scholar
[24] Marino A M, Pooser R C, Boyer V, Lett P D 2009 Nature 457 859
Google Scholar
[25] Pooser R C, Marino A M, Boyer V, Jones K M, Lett P D 2009 Phys. Rev. Lett. 103 010501
Google Scholar
[26] Clark J B, Glasser R T, Glorieux Q, Vogel U, Li T, Jones K M, Lett P D 2014 Nat. Photonics 8 515
Google Scholar
[27] Wang H L, Fabre C, Jing J T 2017 Phys. Rev. A 95 051802
Google Scholar
[28] Xin J, Qi J, Jing J T 2017 Opt. Lett. 42 366
Google Scholar
[29] Chen H, Zhang J 2009 Phys. Rev. A 79 063826
Google Scholar
[30] McCormick C F, Marino A M, Boyer V, Lett P D 2008 Phys. Rev. A 78 043816
Google Scholar
[31] Duan L M, Giedke G, Cirac J I, Zoller P 2000 Phys. Rev. Lett. 84 2722
Google Scholar
[32] Shaked Y, Michael y, Vered R Z, Bello L, Rosenbluh M, Pe’er A 2018 Nat. Commun. 9 609
Google Scholar
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