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Fabry-Perot腔与光学参量放大复合系统中实现可调谐的非常规光子阻塞

李宏 张斯淇 郭明 李美萱 宋立军

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Fabry-Perot腔与光学参量放大复合系统中实现可调谐的非常规光子阻塞

李宏, 张斯淇, 郭明, 李美萱, 宋立军

Tunable unconventional phonon blockade in Fabry-Perot cavity and optical parametric amplifier composite system

Li Hong, Zhang Si-Qi, Guo Ming, Li Mei-Xuan, Song Li-Jun
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  • 本文提出在Fabry-Perot腔和光学参量放大复合系统中实现非常规光子阻塞效应. 此系统包含可调谐的复合型驱动强度相位, 用二阶关联函数描述光子统计性质, 数值模拟不同参数下的光子阻塞效应, 研究发现通过调节复合型驱动强度相位可以控制非常规光子阻塞. 在弱驱动条件下, 计算得到了强光子反聚束的最优化条件, 并给出了二阶关联函数解析式, 研究发现数值模拟结果与解析结果相符合. 研究结果为光子阻塞的相干操作提供了平台, 在量子信息处理和量子光学器件等方面具有潜在的应用前景.
    In this paper, we present a scheme to realize an unconventional photon blockade effect in a Fabry-Perot cavity and optical parametric amplifier (OPA) composite system. The system includes a tunable phase of complex driving strength, the second-order correlation function is used to describe the photon statistical properties. The numerical simulation of the photon blockade effect is conducted with different parameters. Our calculations show that the unconventional photon blockade effect can be controlled by the tunable phase of complex driving strength. Under the weak driving condition, the exact optimal conditions for strong photon anti-bunching are analytically derived (i.e. the optimal nonlinear gain of optical parametric amplifier and the phase of the field driving for the strong photon anti-bunching are obtained), and obtain the analytic calculations of the second-order correlation function. Under the optimal conditions, we perform a numerical simulation with different parameters. The optimal conditions for strong photon anti-bunching are found by analytic calculations, which are in good agreement with the numerical results. The results provide a platform for coherently operating the photon blockade and have potential applications in quantum information processing and quantum optical devices.
      通信作者: 宋立军, songlj@jlenu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11347013)、吉林省教育厅科技规划项目(批准号: JJKH20190764KJ)、吉林工程技术师范学院博士科研启动经费专项(批准号: BSKJ201825)和吉林工程技术师范学院校级一般项目(批准号: XYB201820)资助的课题.
      Corresponding author: Song Li-Jun, songlj@jlenu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11347013), the Scientific Research Foundation of the Education Department of Jilin Province, China (Grant No. JJKH20190764KJ), the Specialized Fund for the Doctoral Research of Jilin Engineering Normal University, China (Grant No. BSKJ201825), and the General Program of of Jilin Engineering Normal University, China (Grant No. XYB201820).
    [1]

    Imamoglu A, Schmidt H, Woods G, Deutsch M 1997 Phys. Rev. Lett. 79 1467Google Scholar

    [2]

    Liew T C H, Savona V 2010 Phys. Rev. Lett. 104 183601Google Scholar

    [3]

    Cao C, Mi S C, Wang T, Zhang R, Wang C 2016 IEEE J. Quantum Electron. 52 7000205Google Scholar

    [4]

    Cao C, Mi S C, Gao Y P, He L Y, Yang D, Wang T J, Zhang R, Wang C 2016 Sci. Rep. 6 22920Google Scholar

    [5]

    Cao Cong, Chen Xi, Duan Y W, Fan L, Zhang R, Wang T J, Wang C 2017 Optik 130 659Google Scholar

    [6]

    张秀龙, 鲍倩倩, 杨明珠, 田雪松 2018 物理学报 67 104203Google Scholar

    Zhang X L, Bao Q Q, Yang M Z, Tian X S 2018 Acta Phys. Sin. 67 104203Google Scholar

    [7]

    廖庆洪, 叶杨, 李红珍, 周南润 2018 物理学报 67 40302Google Scholar

    Liao Q H, Ye Y, Li H Z, Zhou N R 2018 Acta Phys. Sin. 67 40302Google Scholar

    [8]

    Birnbaum K M, Boca A, Miller R, Boozer A D, Northup T E, Kimble H J 2005 Nature 436 87Google Scholar

    [9]

    Greentree A D, Tahan C, Cole J H, Hollenberg L C L 2006 Nat. Phys. 2 856Google Scholar

    [10]

    Angelakis D G, Santos M F, Bose S 2007 Phys. Rev. A 76 031805Google Scholar

    [11]

    Shen H Z, Zhou Y H, Yi X X 2015 Phys. Rev. A 91 063808Google Scholar

    [12]

    Shen H Z, Zhou Y H, Yi X X 2014 Phys. Rev. A 90 023849Google Scholar

    [13]

    Irvine W T M, Hennessy K, Bouwmeester D 2006 Phys. Rev. Lett. 96 057405Google Scholar

    [14]

    Zhou Y H, Shen H Z, Yi X X 2015 Phys. Rev. A 92 023838Google Scholar

    [15]

    Shen H Z, Zhou Y H, Liu H D, Wang G C, Yi X X 2015 Opt. Express 23 32835Google Scholar

    [16]

    Zhou Y H, Zhang S S, Shen H Z, Yi X X 2017 Opt. Lett. 42 1289Google Scholar

    [17]

    Shen H Z, Shang C, Zhou Y H, Yi X X 2018 Phys. Rev. A 98 023856Google Scholar

    [18]

    Shen H Z, Xu S, Zhou Y H, Wang G C, Yi X X 2018 J. Phys. B 51 035503Google Scholar

    [19]

    Zhou Y H, Shen H Z, Zhang X Y, Yi X X 2018 Phys. Rev. A 97 043819Google Scholar

    [20]

    Su S L, Tian Y Z, Shen H Z, Zang H P, Liang E J, Zhang S 2017 Phys. Rev. A 96 042335Google Scholar

    [21]

    Su S L, Gao Y, Liang E J, Zhang S 2017 Phys. Rev. A 95 022319Google Scholar

    [22]

    Su S L, Liang E J, Zhang S, Wen J J, Sun L L, Jin Z, Zhu A D 2016 Phys. Rev. A 93 012306Google Scholar

    [23]

    Zhou Y H, Shen H Z, Shao X Q, Yi X X 2016 Opt. Express 24 17332Google Scholar

    [24]

    Tang J, Geng W, Xu X 2015 Sci. Rep. 5 9252Google Scholar

    [25]

    Majumdar A, Bajcsy M, Rundquist A, Vuckovic J 2012 Phys. Rev. Lett. 108 183601Google Scholar

    [26]

    Zhang W, Yu Z, Liu Y, Peng Y 2014 Phys. Rev. A 8 043832

    [27]

    Flayac H, Savona V 2016 Phys. Rev. A 94 013815Google Scholar

    [28]

    Gerace D, Savona V 2014 Phys. Rev. A 89 031803Google Scholar

    [29]

    Lemonde M A, Didier N, Clerk A A 2014 Phys. Rev. A 90 063824Google Scholar

    [30]

    Xu X W, Li Y J 2013 J. Phys. B 46 035502Google Scholar

    [31]

    Wicz A, Li H R, Miranoao J Q, Nori F, Jing H 2018 Phys. Rev. Lett. 121 153601Google Scholar

    [32]

    石海泉, 谢智强, 徐勋卫, 刘念华 2018 物理学报 67 044203Google Scholar

    Shi H Q, Xie Z Q, Xu X W, Liu N H 2018 Acta Phys. Sin. 67 044203Google Scholar

    [33]

    Sarma B, Sarma A K 2017 Phys. Rev. A 96 053827Google Scholar

  • 图 1  (a) 用激光抽运OPA, 在腔内产生参量放大的腔结构示意图; (b) 量子干涉系统的跃迁路径

    Fig. 1.  (a) Schematic diagram of the cavity setup with an OPA which is pumped by a laser to produce parametric amplification in the cavity; (b) transition paths of the system for quantum interference.

    图 3  等时二阶关联函数$\lg \left[ {{g^{\left(2\right)}}\left(0\right)} \right]$数值结果随OPA非线性增益G和相位$\theta $的等高线图${\varOmega / {\kappa = 0.01}}$, ${\varDelta _a} = 1$, $\phi = 0.5\;{\rm{rad}}$

    Fig. 3.  Contour plot of the second-order correlation functions $\lg \left[ {{g^{\left(2\right)}}\left(0\right)} \right]$ vs. the nonlinear gain G of the OPA and phase $\theta $. Other parameters are ${\varOmega / {\kappa = 0.01}}$, ${\varDelta _a} = 1$, $\phi = 0.5\;{\rm{rad}}$.

    图 2  等时二阶关联函数${g^{\left(2\right)}}(0)$随OPA非线性增益G的变化${\varOmega / {\kappa = 0.01}}$, $\theta = - 0.0341{\text{π}}$, ${\varDelta _a} = 1$

    Fig. 2.  Variation curves of the zero-time-delay second-order correlation function ${g^{\left(2\right)}}(0)$ with the nonlinear gain G of the OPA. Other parameters are ${\varOmega / {\kappa = 0.01}}$, $\theta = - 0.0341{\text{π}}$, ${\varDelta _a} = 1$.

    图 4  等时二阶关联函数$\lg \left[ {{g^{\left(2\right)}}\left(0\right)} \right]$数值结果随相位$\theta $$\phi $的等高线图${\varOmega / {\kappa = 0.01}}$, ${\varDelta _a} = 1$, $G = {G_{\rm opt}}$

    Fig. 4.  Contour plot of the second-order correlation functions $\lg \left[ {{g^{\left(2\right)}}\left(0\right)} \right]$ vs. the phase $\theta $ and $\phi $. Other parameters are ${\varOmega / {\kappa = 0.01}}$, ${\varDelta _a} = 1$, $G = {G_{\rm opt}}$.

    图 5  等时二阶关联函数$\lg \left[ {{g^{\left(2\right)}}\left(0\right)} \right]$数值结果随OPA非线性增益$G$和相位$\phi $变化的等高线图${\varOmega / {\kappa = 0.01}}$, ${\varDelta _a} = 1$, $G = {G_{\rm opt}}$

    Fig. 5.  Contour plot of the second-order correlation functions $\lg \left[ {{g^{\left(2\right)}}\left(0\right)} \right]$ vs. the nonlinear gain of the optical parametric amplifier $G$ and phase $\phi $. Other parameters are ${\varOmega / {\kappa = 0.01}}$, ${\varDelta _a} = 1$, $G = {G_{\rm opt}}$.

    图 6  (a) 二阶关联函数${g^{\left(2\right)}}(0)$随OPA非线性增益$G$的变化, 其中蓝色实线由数值求解方程(3)得出, 红色菱形由(13)和(15)式解析得出; 其他参数为${\varDelta _a} = 1, \; \varOmega /\kappa = 0.01,$ $\phi = 0.5\;{\rm{rad}}, \; \theta = {\theta _{\rm opt}}$; (b) 二阶关联函数${g^{\left(2\right)}}(0)$随相位$\theta $的变化, 蓝色实线由数值求解方程(3)得出, 红色圆形由(13)和(15)式解析得出; 其他参数为${\varDelta _a} = 1, \;\varOmega /\kappa = 0.01,$ $\phi = 0.5\;{\rm{rad}}, \;G = {G_{\rm opt}}$

    Fig. 6.  (a) The second-order correlation functions ${g^{\left(2\right)}}(0)$ vs. the nonlinear gain of the optical parametric amplifier $G$; the blue solid line indicates the numerical results by numerically solving Eq. (3) and the red diamond corresponds to the analytical results of Eq. (13) and Eq. (15); other parameters are ${\varDelta _a} = 1, \; \varOmega /\kappa = 0.01, \; \phi = 0.5\;{\rm{rad}}, \; \theta = {\theta _{\rm opt}}$; (b) the second-order correlation functions ${g^{\left(2\right)}}(0)$ vs. the phase $\theta $; the blue solid line indicates the numerical results by numerically solving Eq. (3) and the red diamond corresponds to the analytical results of Eq. (13) and Eq. (15). Other parameters are ${\varDelta _a} = 1, \;\varOmega /\kappa = 0.01, \;\phi = 0.5\;{\rm{rad}},$ G = Gopt.

  • [1]

    Imamoglu A, Schmidt H, Woods G, Deutsch M 1997 Phys. Rev. Lett. 79 1467Google Scholar

    [2]

    Liew T C H, Savona V 2010 Phys. Rev. Lett. 104 183601Google Scholar

    [3]

    Cao C, Mi S C, Wang T, Zhang R, Wang C 2016 IEEE J. Quantum Electron. 52 7000205Google Scholar

    [4]

    Cao C, Mi S C, Gao Y P, He L Y, Yang D, Wang T J, Zhang R, Wang C 2016 Sci. Rep. 6 22920Google Scholar

    [5]

    Cao Cong, Chen Xi, Duan Y W, Fan L, Zhang R, Wang T J, Wang C 2017 Optik 130 659Google Scholar

    [6]

    张秀龙, 鲍倩倩, 杨明珠, 田雪松 2018 物理学报 67 104203Google Scholar

    Zhang X L, Bao Q Q, Yang M Z, Tian X S 2018 Acta Phys. Sin. 67 104203Google Scholar

    [7]

    廖庆洪, 叶杨, 李红珍, 周南润 2018 物理学报 67 40302Google Scholar

    Liao Q H, Ye Y, Li H Z, Zhou N R 2018 Acta Phys. Sin. 67 40302Google Scholar

    [8]

    Birnbaum K M, Boca A, Miller R, Boozer A D, Northup T E, Kimble H J 2005 Nature 436 87Google Scholar

    [9]

    Greentree A D, Tahan C, Cole J H, Hollenberg L C L 2006 Nat. Phys. 2 856Google Scholar

    [10]

    Angelakis D G, Santos M F, Bose S 2007 Phys. Rev. A 76 031805Google Scholar

    [11]

    Shen H Z, Zhou Y H, Yi X X 2015 Phys. Rev. A 91 063808Google Scholar

    [12]

    Shen H Z, Zhou Y H, Yi X X 2014 Phys. Rev. A 90 023849Google Scholar

    [13]

    Irvine W T M, Hennessy K, Bouwmeester D 2006 Phys. Rev. Lett. 96 057405Google Scholar

    [14]

    Zhou Y H, Shen H Z, Yi X X 2015 Phys. Rev. A 92 023838Google Scholar

    [15]

    Shen H Z, Zhou Y H, Liu H D, Wang G C, Yi X X 2015 Opt. Express 23 32835Google Scholar

    [16]

    Zhou Y H, Zhang S S, Shen H Z, Yi X X 2017 Opt. Lett. 42 1289Google Scholar

    [17]

    Shen H Z, Shang C, Zhou Y H, Yi X X 2018 Phys. Rev. A 98 023856Google Scholar

    [18]

    Shen H Z, Xu S, Zhou Y H, Wang G C, Yi X X 2018 J. Phys. B 51 035503Google Scholar

    [19]

    Zhou Y H, Shen H Z, Zhang X Y, Yi X X 2018 Phys. Rev. A 97 043819Google Scholar

    [20]

    Su S L, Tian Y Z, Shen H Z, Zang H P, Liang E J, Zhang S 2017 Phys. Rev. A 96 042335Google Scholar

    [21]

    Su S L, Gao Y, Liang E J, Zhang S 2017 Phys. Rev. A 95 022319Google Scholar

    [22]

    Su S L, Liang E J, Zhang S, Wen J J, Sun L L, Jin Z, Zhu A D 2016 Phys. Rev. A 93 012306Google Scholar

    [23]

    Zhou Y H, Shen H Z, Shao X Q, Yi X X 2016 Opt. Express 24 17332Google Scholar

    [24]

    Tang J, Geng W, Xu X 2015 Sci. Rep. 5 9252Google Scholar

    [25]

    Majumdar A, Bajcsy M, Rundquist A, Vuckovic J 2012 Phys. Rev. Lett. 108 183601Google Scholar

    [26]

    Zhang W, Yu Z, Liu Y, Peng Y 2014 Phys. Rev. A 8 043832

    [27]

    Flayac H, Savona V 2016 Phys. Rev. A 94 013815Google Scholar

    [28]

    Gerace D, Savona V 2014 Phys. Rev. A 89 031803Google Scholar

    [29]

    Lemonde M A, Didier N, Clerk A A 2014 Phys. Rev. A 90 063824Google Scholar

    [30]

    Xu X W, Li Y J 2013 J. Phys. B 46 035502Google Scholar

    [31]

    Wicz A, Li H R, Miranoao J Q, Nori F, Jing H 2018 Phys. Rev. Lett. 121 153601Google Scholar

    [32]

    石海泉, 谢智强, 徐勋卫, 刘念华 2018 物理学报 67 044203Google Scholar

    Shi H Q, Xie Z Q, Xu X W, Liu N H 2018 Acta Phys. Sin. 67 044203Google Scholar

    [33]

    Sarma B, Sarma A K 2017 Phys. Rev. A 96 053827Google Scholar

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出版历程
  • 收稿日期:  2019-01-27
  • 修回日期:  2019-04-04
  • 上网日期:  2019-06-01
  • 刊出日期:  2019-06-20

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