非简并四波混频体系中连续变量双模光场的纠缠特性
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摘要
纠缠反映的是一个多体量子系统中各子系统之间所存在的非局域的量子关联,它是量子力学有别于经典力学的基本概念。近年来有关连续变量纠缠态的制备及其在量子信息处理中的应用是量子光学和量子信息科学的前沿研究领域。这不仅是因为对于连续变量纠缠态性质的研究可以用于验证量子力学的基本原理,而且还由于连续变量纠缠态是量子信息处理的基本资源,因此如何制备连续变量纠缠态受到人们的广泛关注。另一方面,由于体系与周围的环境的相互作用而导致的退相干的影响,使得所制备的纠缠态十分脆弱而难于保存。因此,基于现有的实验条件和技术,如何制备出抗环境干扰能力强、稳定的、高纠缠度的纠缠源是人们感兴趣的问题之一。
首先,在三能级中,采用四波混频的方法制备出连续变量的量子纠缠态。分析得出此模型在强抽运光的作用下相当于一个参量放大器。满足一定的条件下纠缠在任何时候都存在,随着时间的延长,纠缠由零逐渐增大,最后达到稳态,并且纠缠的程度和双模光子数与抽运光强度I_2,合作参量C以及失谐频率Δ′有关。
接下来主要讨论了光腔中囚禁的双梯形四能级原子来制备纠缠光,并且在修饰态表象中分析了如何来提高光场的纠缠。我们首先通过标准的二阶微扰理论求出腔模运动的主方程,利用段路明提出的双模高斯态的纠缠判据来分析激光场的纠缠性质。接下来讨论如何来提高光场的纠缠。主要是通过大失谐绝热消除能级|α>,用强激光场去驱动原子使原子的一阶修饰态稳态布居发生变化,使四波混频过程中的两个通道被加强,与之干涉相消的另外的两个通道被削弱,从而提高了纠缠的程度。分析发现,为了得到高明亮的强压缩和纠缠光系统必须要有失谐量Δ,同时要工作在阈值以上。
In addition to being of fundamental interest in quantum mechanics, entanglement as quantum correlations among quantum systems is a key element in rapid developing quantum informatics. Now, continuous variable entanglement has attracted a lot of attention in quantum optics and quantum information due to the experimental realization of quantum information processings in continuous variable regime. Any attempt to exploit the entanglement have to, however, face the corruption of the entanglement by unavoidable decoherence. As a result, how to produce the robust, steady, and high entanglement is an interesting research issue. In this thesis, we focus mainly on the preparation of bright and high continuous variable entanglement.
We apply nondegenerate four-wave mixing processes to the generation of stable continuous variable entangled light and study the evolution of continuous variable entangled light with time. We analytically get the characteristic function of the two-mode field and find that the system is an optical parametric amplifier. We also show that the two-mode cavity field exhibits stable continuous variable entanglement under some conditions. The degree of the entanglement is dependent upon the two photon intensity I_2 , the coopera-tivity parameter C and the side-mode detuning△'.
Next, We have investigated a double-ladder atom trapped in a non-degenerate doubly resonant cavity. We obtain the master equation of the cavity modes and consider further the dynamics of this physical system under suitable conditions. It is found that employing these conditions the physical system is a nondegenerate parametric oscillatorin in NDFWM. the large detuning A is necessary for improving squeezing and entanglement. In order to get bright and strong entangled field, the system should operate above threshold.
首先,在三能级中,采用四波混频的方法制备出连续变量的量子纠缠态。分析得出此模型在强抽运光的作用下相当于一个参量放大器。满足一定的条件下纠缠在任何时候都存在,随着时间的延长,纠缠由零逐渐增大,最后达到稳态,并且纠缠的程度和双模光子数与抽运光强度I_2,合作参量C以及失谐频率Δ′有关。
接下来主要讨论了光腔中囚禁的双梯形四能级原子来制备纠缠光,并且在修饰态表象中分析了如何来提高光场的纠缠。我们首先通过标准的二阶微扰理论求出腔模运动的主方程,利用段路明提出的双模高斯态的纠缠判据来分析激光场的纠缠性质。接下来讨论如何来提高光场的纠缠。主要是通过大失谐绝热消除能级|α>,用强激光场去驱动原子使原子的一阶修饰态稳态布居发生变化,使四波混频过程中的两个通道被加强,与之干涉相消的另外的两个通道被削弱,从而提高了纠缠的程度。分析发现,为了得到高明亮的强压缩和纠缠光系统必须要有失谐量Δ,同时要工作在阈值以上。
In addition to being of fundamental interest in quantum mechanics, entanglement as quantum correlations among quantum systems is a key element in rapid developing quantum informatics. Now, continuous variable entanglement has attracted a lot of attention in quantum optics and quantum information due to the experimental realization of quantum information processings in continuous variable regime. Any attempt to exploit the entanglement have to, however, face the corruption of the entanglement by unavoidable decoherence. As a result, how to produce the robust, steady, and high entanglement is an interesting research issue. In this thesis, we focus mainly on the preparation of bright and high continuous variable entanglement.
We apply nondegenerate four-wave mixing processes to the generation of stable continuous variable entangled light and study the evolution of continuous variable entangled light with time. We analytically get the characteristic function of the two-mode field and find that the system is an optical parametric amplifier. We also show that the two-mode cavity field exhibits stable continuous variable entanglement under some conditions. The degree of the entanglement is dependent upon the two photon intensity I_2 , the coopera-tivity parameter C and the side-mode detuning△'.
Next, We have investigated a double-ladder atom trapped in a non-degenerate doubly resonant cavity. We obtain the master equation of the cavity modes and consider further the dynamics of this physical system under suitable conditions. It is found that employing these conditions the physical system is a nondegenerate parametric oscillatorin in NDFWM. the large detuning A is necessary for improving squeezing and entanglement. In order to get bright and strong entangled field, the system should operate above threshold.
引文
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[5]R.Simon,Phys.Rev.Lett.84,2726(2000).
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[7]S.L.Branustein,Phys.Rev.Lett.80,4084(1998).
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[9]S.Lloyd and J.J.E.Slotine,Phys.Rev.Lett.80,4088(1998).
[10]U.Leonhardt,Measuring the Quantum State of Light(Cambridge University Press).
[11]S.L.Braunstein and P.van Loock,Rev.Mod.Phys.77,513(2005).
[12]R.F.Werner,Phys.Rev.A 40,4277(1989).
[13]A.Peres,Phys.Rev.Lett.77,1413(1996).
[14]M.C.de.Oliveira,Phys.Rev.A 70,034303(2004).
[15]L.M.Duan et al.,Phys.Rev.Lett.84,2722(2000).
[16]G.Adesso,A.Serafini,and F.Illuminati Phys.Rev.Lett.92,087901(2004).
[17]G.Giedke et al.,Phys.Rev.Lett.91,107901(2003).
[18]M.M.Wolf et al.,Phys.Rev.A 69,052320(2004).
[19]G.Vidal and R.F.Werner Phys.Rev.A 65,032314(2002).
[20]P.Van Loock and A.Furusawa,Phys.Rev.A 67,052315(2003).
[21]A.S.Bradley et al.,Phys.Rev.A 72,053805(2005).
[22]A.S.Villar et al.,Phys.Rev.Lett.97,140504(2006).
[23]Cassemiro et al.,Opt.Lett.32,695(2007).
[24]J.Jing et al.,Phys.Rev.Lett.90,167903(2003).
[25]T.Aoki et al,,Phys.Rev.Lett.,91,080404(2003).
[26]J.Guo et al.,Phys.Rev.A 71,034305(2005).
[27]Yu et al.,Phys.Rev.A 74,042332(2006).
[28]M.K.Olsen and A.S.Bradley,Phys.Rev.A 74,063809(2006).
[29]A.Ferraro et al.,J.Opt.Soc.Am.B 21,1241(2004).
[30]Y.Wu et al.,Phys.Rev.A 69,063803(2004).
[31]O.Pfister et al.,Phys.Rev.A 70,020302(2004);R.C.Pooser and O.Pfister,Opt.Lett.30,2635(2005).
[32]Ch.Silberhorn et al.,Phys.Rev.Lett.86,4267(2001).
[33]D.A.Hollm and M.Ⅲ.Sargent,Phys.Rev.A 33,4001(1986).
[34]A.Sunghyuck and M.Ⅲ.Sargent,Phys.Rev.A 39,1841(1989).
[35]M.Ⅲ.Sargent,D.A.Hollm and M.S.Zubairy,Phys.Rev.A 31,3112(1985).
[36]N.A.Ansari,Phys.Rev.A 46,1560(1992).
[37]S.M.Barnett and P.M.Radmore,Methods in Theoretical Quantum Optics(Oxford:Clarendon Press,1997).
[38]J.S.Peng,G.X.Li,Introduction to Modern Quantum Optics(Singapore:Word Scientific,1998).
[39]C.J.Villas and M.H.Moussa,Eur.Phys.J.D 32,147(2004).
[40]M.Kiffner,M.S.Zubairy,J.Evers and C.H.Keitel,Phys.Rev.A 75,033816(2007).
[41]X.Y.Lv,J.B.Liu,L.G.Si and X.X.Yang,J.Phys.B 41,035501(2008).
[42]Y.P.Zhang et al.,Phys.Rev.A 74,053813(2006).
[43]M.O.Scully and M.S.Zubairy,Quantum Optics(Cambridge:Cambridge University Press,1997).
[44]L.M.Duan,G.Giedke,J.I.Cirac and P.Zoller,Phys.Rev.Lett.84 2722(2000).
[45]A.Furusawa et al.,Science 282,706(1998).
[46]Z.Y.Ou et al.,Phys.Rev.Lett.68,3663(1992).
[47]V.Balic et al.,Phys.Rev.Lett.98,183601(2005).
[48]J.Zhang,C.Xie,and K.Peng Phys.Rev.A 73,042315(2006).
[49]X.L.Su,Phys.Rev.Lett.98,070502(2007).
[50]F.Casagrande,A.Lulli,and M.G.A.Paris Phys.Rev.A 75,032336(2007).
[51]A.Ourjoumtsev et al.,Phys.Rev.Lett.98,030502(2007).
[52]A.Biswas and D.A.Lidar,Phys.Rev.A 74,062303(2006).
[53]E.Shchukin and W.Vogel,Phys.Rev.Lett.95,230502(2005).
[54]M.Hillery and M.S.Zubairy,Phys.Rev.Lett.96,050503(2006).