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双光腔光机械系统的动力学相变和选择性能量交换

刘妮 张小芳 梁九卿

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双光腔光机械系统的动力学相变和选择性能量交换

刘妮, 张小芳, 梁九卿

Dynamical phase transition and selective energy exchange in dual-cavity optochanical systems

Liu Ni, Zhang Xiao-Fang, Liang Jiu-Qing
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  • 本文探究了单腔和双腔光机械装置的动力学相变和选择性能量交换. 发现系统会经历类似于Dicke-Hepp-Lieb超辐射型的动力学相变, 且两光场间的正交动量耦合出现一个新的动力学临界点. 两光场间的正交动量耦合等价于单(双)模光机械系统的外场驱动. 通过耦合参数的调控, 系统可以实现任意两模间的选择性能量交换, 且临界耦合点与选择性能量交换对应. 模压缩是能量转换的标志, 且任何两模的正交压缩由特定玻色模间的能量交换决定.
    In recent years, the cavity quantum photomechanics has been developed rapidly, and played a very important role in quantum information processing, quantum basic principle verification, and high-precision measurement. The kinds of quantum mechanical behaviors have also been explored and discovered in the study of cavity mechanics. By placing the Kerr medium in the system, quantum nonlinearity is introduced into the optomechanical system. Quantum phase transition is a relatively important part in the research of condensed matter physics. Since Dicke quantum phase transition was successfully observed experimentally, the problem of quantum phase transition in the optical cavity has attracted more attention. The spin-coherent-state variation method and the Holstein-Primakoff transformation are used to theoretically calculate the ground state energy functional, and the rich structure of the macroscopic multi-particle quantum state is given by adjusting the parameters. The quantum phase transition evolution equation describes the relationship between each phase and the time of generating a new phase when reaching the critical phase transition point. At the same time, the mode squeezing of multi-mode hybrid optomechanical system has also became one of the basic problems of quantum mechanical behavior in cavity quantum dynamics. In this article, we explore the quantum dynamics of optomechanical devices including single-cavity and dual-cavities. We find that the system will undergo a dynamic phase transition, which is similar to the Dicke-Hepp-Lieb superradiant type phase transition, and a new dynamic critical point appears in the coupling between the momentum quadratures of the two optical fields. By manipulating the coupling parameters, we can achieve selective energy exchange between any two modes and the critical coupling point corresponds to selective energy exchange. Mode squeezing, which is easy to measure by applying the quantum uncertainty relationship, is also revealed and consistent with selective energy exchange. The study of coordinate and momentum variances gives us the revelation that the compressed orthogonal variables are the most suitable for measurement because of the small quantum noise. In fact, phononic modes can store energy in a longer duration, while photonic modes can transfer energy in a long distance. This phenomenon makes the hybrid optomechanical cavities useful in the next-generation quantum communications and quantum information processing units.
      通信作者: 刘妮, 317446484@qq.com
    • 基金项目: 国家自然科学基金(批准号: 11772177, 12047571)和山西省高等学校科技创新项目(批准号: 2019L0069) 资助的课题
      Corresponding author: Liu Ni, 317446484@qq.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11772177, 12047571) and the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi Province (STIP), China (Grant No. 2019L0069)
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    Stannigel K, Komar P, Habraken S J M, Bennett S D, Lukin P, Zoller P, Rabl P 2012 Phys. Rev. Lett. 109 013603Google Scholar

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    Chang D E, Safavi-Naeini A H, Hafezi M, Painter O 2011 New Journal of Physics 13 023003Google Scholar

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    刘妮, 王建芬, 梁九卿 2020 物理学报 69 064202Google Scholar

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    Yan B, Chernyak V Y, Zurek W H, Sinitsyn N A 2021 Phys. Rev. Lett. 126 070602Google Scholar

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    Lerose A, Marino J, Zunkovic B, Gambassi A, Silva A 2018 Phys. Rev. Lett. 120 130603Google Scholar

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    Nicola S, Michailidis A, Serbyn M 2021 Phys. Rev. Lett 126 040602Google Scholar

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    Korolkova N, Perina J 1997 Optics Communications 136 135Google Scholar

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    Korolkova N, Perina J 1997 Journal of Modern Optics 44 1525

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    Gröblacher S, Hammerer K, Vanner M R, Aspelmeyer M 2009 Nature 460 724Google Scholar

  • 图 1  光机械腔系统, 由频率为${\omega _{\rm{0}}}$的光学模(用运算符a表示), 频率为${\omega _{\rm{m}}}$的机械模(用运算符b表示)和频率为${\omega _{\rm{L}}}$(振幅为μ)的驱动场组成, 光腔与机械振子之间的耦合系数为g

    Fig. 1.  An optomechanical cavity consisting of the optical mode (the frequency ${\omega _{\rm{0}}}$) denoted by a, the mechanical mode b (the frequency ${\omega _{\rm{m}}}$) and an pair of optical drivings (the frequency ${\omega _{\rm{L}}}$ and the amplitude μ) with the coupling strength g.

    图 2  在给定条件$\omega = {\omega _{\rm{m}}}$下, 激发能量${\varepsilon _i}/{\omega _{\rm{m}}}$随耦合参数$\eta /{\omega _{\rm{m}}}$的变化

    Fig. 2.  Variation of the excitation energy ${\varepsilon _i}/{\omega _{\rm{m}}}$ with respect to the coupling parameter $\eta /{\omega _{\rm{m}}}$ in the case of $\omega = {\omega _{\rm{m}}}$.

    图 3  双光腔光机械系统, 由频率分别为${\omega _{\rm{1}}}$${\omega _{\rm{2}}}$的光学模(用运算符${a_1}$${a_2}$表示), 频率为${\omega _{\rm{m}}}$的机械模(用运算符b表示)和频率为${\omega _{\rm{L}}}$(振幅为${\mu _i}$)的两束对打的驱动场组成, 两模光腔与机械振子之间的耦合系数分别为${g_1}$${g_2}$

    Fig. 3.  A double-optical cavtiy optomechanical system consisting of two optical mode (the frequencies ${\omega _{\rm{1}}}$ and ${\omega _{\rm{2}}}$) denoted by ${a_1}$ and ${a_2}$, the mechanical mode b (the frequency ${\omega _{\rm{m}}}$) and an pair of optical drivings (the frequency ${\omega _{\rm{L}}}$ and the amplitude ${\mu _i}$) with the coupling strength ${g_1}$ and ${g_2}$.

    图 4  激发能量${\varepsilon _i}/{\omega _{\rm{m}}}$随耦合参数 (a)${G_1}/{\omega _{\rm{m}}}$和(b)${G_2}/{\omega _{\rm{m}}}$的变化, 给定的参数是${\varOmega _1} = {\varOmega _2} = {\omega _{\rm{m}}}$

    Fig. 4.  Variation of the excitation energy ${\varepsilon _i}/{\omega _{\rm{m}}}$ with respect to the coupling parameters (a) ${G_1}/{\omega _{\rm{m}}}$ and (b)${G_2}/{\omega _{\rm{m}}}$. The given parameters are ${\varOmega _1} = {\varOmega _2} = {\omega _{\rm{m}}}$.

    图 5  双光腔光机械系统, 由频率分别为${\omega _{\rm{1}}}$${\omega _{\rm{2}}}$的光学模(用运算符${a_1}$${a_2}$表示)和频率为${\omega _{\rm{m}}}$的机械模(用运算符b表示)组成, 两模光腔与机械振子之间的耦合系数分别为${g_1}$${g_2}$, 两腔间与机械振子的耦合系数为J

    Fig. 5.  A double-optical cavtiy optomechanical system consisting of two optical mode (the frequencies ${\omega _{\rm{1}}}$ and ${\omega _{\rm{2}}}$) denoted by ${a_1}$ and ${a_2}$ and the mechanical mode b with the coupling strength ${g_1}$, ${g_2}$ andJ.

    图 6  激发能量${\varepsilon _i}/{\omega _{\rm{m}}}$随耦合参数 (a)$\delta /{\omega _{\rm{m}}}$, (b)${J_1}/{\omega _{\rm{m}}}$和(c)${J_2}/{\omega _{\rm{m}}}$的变化, 给定的参数是${\varOmega _1} = {\varOmega _2} = {\omega _{\rm{m}}}$

    Fig. 6.  Variation of the excitation energy ${\varepsilon _i}/{\omega _{\rm{m}}}$ with respect to the coupling parameters (a)$\delta /{\omega _{\rm{m}}}$, (b) ${J_1}/{\omega _{\rm{m}}}$ and (c)${J_2}/{\omega _{\rm{m}}}$. The given parameters are ${\varOmega _1} = {\varOmega _2} = {\omega _{\rm{m}}}$.

    图 7  $ \omega = {\omega _{\rm{m}}}$下, 压缩方差$ {\left( {\Delta \alpha } \right)^2}{\omega _{\rm{m}}}$$ {\left( {\Delta {p_{\alpha} }} \right)^2}/{\omega _{\rm{m}}}$随耦合参数$ \eta /{\omega _{\rm{m}}}$的变化

    Fig. 7.  Plot of the squeezing variances ${\left( {\Delta \alpha } \right)^2}{\omega _{\rm{m}}}$(solid line) and ${\left( {\Delta {p_{\alpha} }} \right)^2}/{\omega _{\rm{m}}}$(dashed line) as a function of $\eta /{\omega _{\rm{m}}}$ in the case of $\omega = {\omega _{\rm{m}}}$.

    图 8  ${\left( {\Delta \alpha } \right)^2}{\omega _{\rm{m}}}$下, 压缩方差${\left( {\Delta \alpha } \right)^2}{\omega _{\rm{m}}}$${\left( {\Delta {p_{\alpha} }} \right)^2}/{\omega _{\rm{m}}}$随耦合参数(a)${G_1}/{\omega _{\rm{m}}}$和(b)${G_2}/{\omega _{\rm{m}}}$的变化

    Fig. 8.  Plot of the squeezing variances ${\left( {\Delta \alpha } \right)^2}{\omega _{\rm{m}}}$(solid line) and ${\left( {\Delta {p_{\alpha} }} \right)^2}/{\omega _{\rm{m}}}$(dashed line) as a function of (a) ${G_1}/{\omega _{\rm{m}}}$ and (b) ${G_2}/{\omega _{\rm{m}}}$.

    图 9  $\omega = {\omega _{\rm{m}}}$下, 压缩方差${\left( {\Delta \alpha } \right)^2}{\omega _{\rm{m}}}$(实线)和${\left( {\Delta {p_{\alpha} }} \right)^2}/{\omega _{\rm{m}}}$(虚线)随耦合参数 (a)$\delta /{\omega _{\rm{m}}}$, (b)${J_1}/{\omega _{\rm{m}}}$和(c)${\left( {\Delta \alpha } \right)^2}{\omega _{\rm{m}}}$的变化

    Fig. 9.  Plot of the squeezing variances ${\left( {\Delta \alpha } \right)^2}{\omega _{\rm{m}}}$(solid line) and ${\left( {\Delta {p_{\alpha} }} \right)^2}/{\omega _{\rm{m}}}$(dashed line) as a function of (a)$\delta /{\omega _{\rm{m}}}$, (b)${J_1}/{\omega _{\rm{m}}}$, (c)${J_2}/{\omega _{\rm{m}}}$ in the case of $\omega = {\omega _{\rm{m}}}$.

  • [1]

    Marquardt F, Girvin S M 2009 Physics 2 40Google Scholar

    [2]

    Brennecke F, Ritter S, Donner T, Esslingert T 2008 Science 322 235Google Scholar

    [3]

    Safavi-Naeini A H, Mayer Alegre T P, Chan J, Eichenfield M, Winger M, Lin Q, Hill J T, Chang D E, Painter O 2011 Nature 478 89Google Scholar

    [4]

    Verhagen E, Deléglise S, Weis S, Schliesser A, Kippenberg T J 2012 Nature 482 63Google Scholar

    [5]

    Kumar T, Bhattacherjee A, ManMohan 2010 Physical Review A 81 013835Google Scholar

    [6]

    Thompson J D, Zwickl B M, Jayich A M, Marquardt F, Girvin S M, Harris J G E 2008 Nature 452 900

    [7]

    Antonio D, Czaplewski D A, Guest J R, López D 2015 Phys. Rev. Lett. 114 034103Google Scholar

    [8]

    Stannigel K, Komar P, Habraken S J M, Bennett S D, Lukin P, Zoller P, Rabl P 2012 Phys. Rev. Lett. 109 013603Google Scholar

    [9]

    Chang D E, Safavi-Naeini A H, Hafezi M, Painter O 2011 New Journal of Physics 13 023003Google Scholar

    [10]

    Emary C, Brandes T 2003 Phys. Rev. E 67 066203Google Scholar

    [11]

    刘妮, 王建芬, 梁九卿 2020 物理学报 69 064202Google Scholar

    Liu N, Wang J F, Liang J Q 2020 Acta Phys. Sin. 69 064202Google Scholar

    [12]

    Zhao X Q, Liu N, Bai X M, Liang J Q 2017 Ann. Phys 378 448Google Scholar

    [13]

    Xuereb A, Barbieri M, Paternostro M 2012 Physical Review A 86 013809Google Scholar

    [14]

    Xu K, Sun Z, Liu W, Zhang Y, Li H, Dong H, Ren W, Zhang P, Nori F, Zheng D, Fan H, Wang H 2020 Science Advances 6 eaba4935Google Scholar

    [15]

    Yan B, Chernyak V Y, Zurek W H, Sinitsyn N A 2021 Phys. Rev. Lett. 126 070602Google Scholar

    [16]

    Lerose A, Marino J, Zunkovic B, Gambassi A, Silva A 2018 Phys. Rev. Lett. 120 130603Google Scholar

    [17]

    Nicola S, Michailidis A, Serbyn M 2021 Phys. Rev. Lett 126 040602Google Scholar

    [18]

    Korolkova N, Perina J 1997 Optics Communications 136 135Google Scholar

    [19]

    Korolkova N, Perina J 1997 Journal of Modern Optics 44 1525

    [20]

    Gröblacher S, Hammerer K, Vanner M R, Aspelmeyer M 2009 Nature 460 724Google Scholar

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出版历程
  • 收稿日期:  2021-01-25
  • 修回日期:  2021-03-02
  • 上网日期:  2021-06-07
  • 刊出日期:  2021-07-20

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