搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

双光腔耦合下机械振子的基态冷却

刘妮 王建芬 梁九卿

引用本文:
Citation:

双光腔耦合下机械振子的基态冷却

刘妮, 王建芬, 梁九卿

Ground-state cooling of mechanical resonator in double optical cavity

Liu Ni, Wang Jian-Fen, Liang Jiu-Qing
PDF
HTML
导出引用
  • 机械振子的基态冷却是腔量子光力学中的基本问题之一. 所谓的基态冷却就是让机械振子的稳态声子数小于1. 本文通过光压涨落谱和稳态声子数研究双光腔光力系统(标准单光腔光力系统中引入第二个光腔, 并与第一个光腔直接耦合)的基态冷却. 首先得到系统的有效哈密顿量, 然后给出朗之万方程和速率方程, 最后分别给出空腔和原子腔的光压涨落谱、冷却率和稳态声子数. 通过光压涨落谱、冷却率和稳态声子数表达式, 重点讨论空腔时机械振子的基态冷却, 发现当满足最佳参数条件(机械振子的冷却跃迁速率对应光压涨落谱的最大值, 而加热跃迁速率对应光压涨落谱的最小值)时, 机械振子可以被冷却到稳态声子数足够少. 此外分析: 当辅助腔内注入原子系综时, 若参数选择恰当可能更利于基态冷却.
    The ground-state cooling of mechanical resonator is one of the fundamental problems in cavity quantum photomechanics. The so-called ground-state cooling is to make the number of steady-state phonons of the mechanical resonator less than one. In this paper, we first propose an electromagnetically-induced-transparency-like cooling mechanism in a double-cavity optomechanical system to cool a mechanical resonator. In the double-optical cavity optomechanical system, the right additional cavity, which is directly coupled to a standard optomechanical system, contains an ultra-cold two-level atomic ensemble. By selecting the optimal parameters to meet the cooling process of the mechanical resonator corresponding to the maximum value of the optical fluctuation spectrum and the heating process of the mechanical resonator corresponding to the minimum value of the optical fluctuation spectrum, the mechanical resonator can be cooled by monitoring the phonon number. We also exert the effects of the atomic additional cavity on the quantum Langevin equations and optical fluctuation spectrum. We find that the atomic double-cavity system may have a better ground-state cooling than the double-cavity in certain parameters.To date, the researchers have proposed a number of theoretical cooling schemes in order to achieve the ground-state cooling of mechanical resonator. As far as we know, the sideband cooling for just a standard optomechanical system is a most famous scheme and the mechanical resonator is coupled to the optical field via radiation pressure force. By the quantum theory of mechanical resonator’s sideband cooling, the optical fluctuation spectrum determines the transition rate of both cooling and heating process of the mechanical resonator. That’s to say, the optical fluctuation spectrum at a mechanical resonator frequency ωm is corresponding to the cooling transition, whereas the optical fluctuation spectrum at –ωm is corresponding to the heating transition. They respectively correspond to anti-Stokes and Stokes effect in physics. Under resolvable sideband conditions, the optical field’s decay rate (the half-width of the single Lorentzian peak of optical fluctuation spectrum) is less than the frequency of the mechanical resonator. So, the ground-state cooling of the mechanical resonator can be obtained by making the maximum and minimum value of the optical fluctuation spectrum respectively correspond to the cooling anti-Stokes process and heating Stokes process.In this paper, we mainly observe the electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system with an ensemble of two-level atoms. By adjusting the maximum and minimum value of the optical fluctuation spectrum at the position of ω = ωm and ω = –ωm, the mechanical resonator could be cooled down approximately to the ground state. Even when there exists an ensemble of two-level atoms in the right additional cavity, the mechanical resonator can be better cooled than just a cavity. These results may be conducive to the ground-state cooling of the mechanical resonator in the future experiment.
      通信作者: 刘妮, 317446484@qq.com
    • 基金项目: 国家级-约束动力学系统的保结构模型约化及保结构算法研究(11772177)
      Corresponding author: Liu Ni, 317446484@qq.com
    [1]

    Kippenberg T J, Vahala K J 2007 Opt. Express 15 17172Google Scholar

    [2]

    Aspelmeyer M, Meystre P, Schwab K 2012 Phys. Today 65 29Google Scholar

    [3]

    Metzger C H, Karrai K 2004 Nature 432 1002Google Scholar

    [4]

    Machnes S, Cerrillo J, Aspelmeyer M, Wieczorek W, Plenio M B, Retzker A 2012 Phys. Rev. Lett. 108 153601Google Scholar

    [5]

    O’Connell A D, Hofheinz M, Ansmann M, Bialczak R C, Lenander M, Lucero E, Neeley M, Sank D, Wang H, Weides M, Wenner J, Martinis J M, Cleland A N 2010 Nature 464 697Google Scholar

    [6]

    Teufel J D, Donner T, Li D, Harlow J W, Allmanet M S, Cicak K, Sirois A J, Whittaker J D, Lehnert K W, Simmonds R W 2011 Nature 475 359Google Scholar

    [7]

    Wilson-Rae I, Zoller P, Imamoglu A 2004 Phys. Rev. Lett. 92 075507Google Scholar

    [8]

    Liu Y C, Xiao Y F, Luan X, Wong C W 2013 Phys. Rev.Lett. 110 153606Google Scholar

    [9]

    Zhu J P, Li G X, Ficek Z 2012 Phys. Rev. A 85 033835Google Scholar

    [10]

    陈华俊, 米贤武 2011 物理学报 60 124206Google Scholar

    Chen H J, Mi X W 2011 Acta Phys. Sin. 60 124206Google Scholar

    [11]

    Wilson-Rae I, Nooshi N, Zwerger W, Kippenberg T J 2007 Phys. Rev. Lett. 99 093901Google Scholar

    [12]

    Marquardt F, Chen J P, Clerk A A, Girvin S M 2007 Phys. Rev. Lett. 99 093902Google Scholar

    [13]

    Liu Y C, Luan X, Li H K, Gong Q, Wong C W, Xiao Y F 2014 Phys. Rev. Lett. 112 213602Google Scholar

    [14]

    Jing H, Özdemir S K, Lü X Y, Zhang J, Yang L, Nori F 2014 Phys. Rev. Lett. 113 053604Google Scholar

    [15]

    Chen H J 2018 J. Appl. Phys. 124 153102Google Scholar

    [16]

    Zhang P, Wang Y D, Sun C P 2005 Phys. Rev. Lett. 95 097204Google Scholar

    [17]

    Xia K, Evers J 2009 Phys. Rev. Lett. 103 227203Google Scholar

    [18]

    EversJ, Keitel C H 2004 Europhys. Lett. 68 370Google Scholar

    [19]

    Harris S E 1997 Phys. Today 50 36Google Scholar

    [20]

    Fleischhauer M, Imamoglu A, Marangos J P 2005 Rev. Mod. Phys. 77 633Google Scholar

    [21]

    Genes C, Ritsch H, Drewsen M, Dantan A 2011 Phys. Rev. A 84 051801(R)Google Scholar

    [22]

    谷开慧, 严冬, 张孟龙, 殷景志, 付长宝 2019 物理学报 68 054201Google Scholar

    Gu K H, Yan D, Zhang M L, Yin J Z, Fu C B 2019 Acta Phys. Sin. 68 054201Google Scholar

    [23]

    Grudinin I S, Lee H, Painter O, Vahala K J 2010 Phys. Rev. Lett. 104 083901Google Scholar

    [24]

    Di K, Xie C, Zhang J 2011 Phys. Rev. Lett. 106 153602Google Scholar

    [25]

    Gu W J, Li G X 2013 Phys. Rev. A 87 025804Google Scholar

    [26]

    Ojanen T, Børkje K 2014 Phys. Rev. A 90 013824Google Scholar

    [27]

    Giovannetti V, Vitali D 2001 Phys. Rev. A 63 023812Google Scholar

    [28]

    Guo Y J, Li K, Nie W J, Li Y 2014 Phys. Rev. A 90 053841Google Scholar

    [29]

    Garrido Alzar C L, Martinez M A G, Nussenzeig P 2002 Am. J. Phys. 70 37Google Scholar

    [30]

    AnetsbergerG, Rivière R, Schliesser A, Arcizet O, Kippenberg T J 2008 Nat. Photonics 2 627Google Scholar

  • 图 1  可实现的双光腔光力系统的示意图

    Fig. 1.  Schematic diagram of an achievable double-cavity optomechanical system.

    图 2  双腔间耦合系数J影响下涨落谱$S\left( \omega \right)$随频率$\omega $的变化(左腔和右腔的有效失谐和对应的耗散率分别为${\varDelta _1} = {\omega _{\rm{m}}}, {\kappa _1} = 5{\omega _{\rm{m}}}$; ${\varDelta _2} = - {\omega _{\rm{m}}}, {\kappa _2} = 0.05{\omega _{\rm{m}}}$)

    Fig. 2.  Fluctuation spectrum $S\left( \omega \right)$ as a function of the frequency $\omega $ with different double-cavity coupling coefficient J. The effective detunings of the left cavity mode and right cavity mode and the corresponding decay rates are respectively are ${\varDelta _1} = {\omega _{\rm{m}}}, {\kappa _1} = 5{\omega _{\rm{m}}}$; ${\varDelta _2} = - {\omega _{\rm{m}}}, {\kappa _2} = 0.05{\omega _{\rm{m}}}$.

    图 3  不同衰减率${\kappa _2}$影响下的涨落谱(给定的参数分别为${\varDelta _1} = - {\omega _{\rm{m}}}, {\kappa _1} = 5{\omega _{\rm{m}}}$; ${\varDelta _2} = - {\omega _{\rm{m}}}, J = 2{\omega _{\rm{m}}}$)

    Fig. 3.  Optical fluctuation spectrum with different decay rates ${\kappa _2}$. The given parameters are ${\varDelta _1} = - {\omega _{\rm{m}}}, {\kappa _1} = 5{\omega _{\rm{m}}}$; ${\varDelta _2} = - {\omega _{\rm{m}}}, J = 2{\omega _{\rm{m}}}$.

    图 4  参数影响下空腔和原子腔涨落谱$S\left( \omega \right)$随频率$\omega $的变化(左腔和右腔的有效失谐和对应的耗散率分别为${\varDelta _1} = {\omega _{\rm{m}}},\; {\kappa _1} = 5{\omega _{\rm{m}}}$; ${\varDelta _2} = - {\omega _{\rm{m}}}, \;{\kappa _2} = 0.05{\omega _{\rm{m}}}$; 原子的有效失谐和相干衰减率是${\varDelta _{\rm{a}}} = {\omega _{\rm{m}}},\; {\gamma _{\rm{a}}} = 10{\omega _{\rm{m}}}$; 原子-场耦合系数${g_{\rm{a}}} = 0.62 \times {10^{ - 4}}{\omega _{\rm{m}}}$, 原子数$N = {10^8}$)

    Fig. 4.  Optical and atom-optical fluctuation spectrum $S\left( \omega \right)$ as a function of the frequency $\omega $ under the influence of parameters. The effective detunings of the left cavity mode and right cavity mode and the corresponding decay rates are respectively are ${\varDelta _1} = {\omega _{\rm{m}}},\; {\kappa _1} = 5{\omega _{\rm{m}}}$; ${\varDelta _2} = - {\omega _{\rm{m}}}, $${\kappa _2} = 0.05{\omega _{\rm{m}}} $. The atomic effective detuning and the coherent decay rates are respectively are ${\varDelta _{\rm{a}}} = {\omega _{\rm{m}}}, {\gamma _a} = 10{\omega _{\rm{m}}}$. The atom-field coupling strength is ${g_{\rm{a}}} = 0.62 \times {10^{ - 4}}{\omega _{\rm{m}}}$. The atomic number is $N = {10^8}$.

    图 5  衰减率${\kappa _2} = 0.05{\omega _{\rm{m}}}$影响下空腔和原子腔涨落谱(给定的参数分别为${\varDelta _1} = - {\omega _{\rm{m}}},\; {\kappa _1} = 5{\omega _{\rm{m}}}$; ${\varDelta _2} = - {\omega _{\rm{m}}}, J =$ $ 2{\omega _{\rm{m}}} $; ${\varDelta _{\rm{a}}} = {\omega _{\rm{m}}}, {\gamma _{\rm{a}}} = 10{\omega _{\rm{m}}}$; ${g_{\rm{a}}} \!=\! 0.62 \!\times\! {10^{ - 4}}{\omega _{\rm{m}}},$ $N \!=\! {10^8}$)

    Fig. 5.  Fluctuation spectrum and atom-optical fluctuation spectrum with given decay rates ${\kappa _2} = 0.05{\omega _{\rm{m}}}$. The given parameters are ${\varDelta _1} = - {\omega _{\rm{m}}}, \;{\kappa _1} = 5{\omega _{\rm{m}}}$, ${\varDelta _2} = - {\omega _{\rm{m}}}$, J = $ 2{\omega _{\rm{m}}} $, ${\varDelta _{\rm{a}}} = {\omega _{\rm{m}}}$, $ {\gamma _{\rm{a}}} = 10{\omega _{\rm{m}}} $; ${g_{\rm{a}}} = 0.62 \!\times\! {10^{ - 4}}{\omega _{\rm{m}}}$, $N \!= \!{10^8}$

    图 6  冷却速率${\gamma _{\rm{c}}}$在不同衰减率${\kappa _2}$影响下随光腔耦合系数J的函数(给定的参数是$g = 0.5{\omega _{\rm{m}}}, {\varDelta _2} = - {\omega _{\rm{m}}},\; {\kappa _1} = 5{\omega _{\rm{m}}}$, 最优失谐${\varDelta _1}$满足(66)式)

    Fig. 6.  Cooling rate ${\gamma _c}$ as a function of optical coupling coefficient J in the case of different decay rates ${\kappa _2}$. The given parameters are $g = 0.5{\omega _{\rm{m}}},\; {\varDelta _2} = - {\omega _{\rm{m}}}, \;{\kappa _1} = 5{\omega _{\rm{m}}}$, and the optimal detuning ${\varDelta _1}$ satisfied the Eq. (66).

    图 7  参数影响下平均声子数${n_{\rm{p}}}$随最佳光腔耦合系数J的变化(给定的参数是${\omega _{\rm{m}}} \!= \!1.55{\text{π}} \times 20\;{\rm{MHz}}$, $ {Q_{\rm{m}}} \!=\! {{{\omega _{\rm{m}}}} / {{\gamma _{\rm{m}}}}} =$ $ 6.2 \times {10^4}, {n_m} = 403 $, $g = 0.5{\omega _{\rm{m}}} $, ${\kappa _1} = 5{\omega _{\rm{m}}}$, ${\kappa _2} = 0.05{\omega _{\rm{m}}}$, ${\varDelta _2} = - {\omega _{\rm{m}}} $, 最优失谐${\varDelta _1}$满足(66)式)

    Fig. 7.  Mean phonon number ${n_{\rm p}}$ as a function of optical coupling coefficient J. The given parameters are ${\omega _{\rm{m}}} \!=\! 1.55{\text{π}} \times $$20\;{\rm{MHz}},\;{Q_{\rm{m}}} = {{{\omega _{\rm{m}}}} / {{\gamma _{\rm{m}}}}} = 6.2 \times {10^4} $, ${n_{\rm{m}}} = 403$, $g = 0.5{\omega _{\rm{m}}} $, ${\kappa _1} \!=\! 5{\omega _{\rm{m}}}, {\kappa _2} \!=\! 0.05{\omega _{\rm{m}}}, {\varDelta _2} \!=\! - {\omega _{\rm{m}}}$, and the optical detuning ${\varDelta _1}$ satisfied the Eq. (66).

    图 8  平均声子数${n_{\rm{p}}}$随有效初始温度T的变化(给定的参数是${\omega _{\rm{m}}} = 1.55{\text{π}} \times 20\;{\rm{MHz}}$, ${Q_{\rm{m}}} = {{{\omega _{\rm{m}}}} / {{\gamma _{\rm{m}}}}} = 6.2 \times {10^4} $, $J = 10{\omega _{\rm{m}}} $, $ g = 0.5{\omega _{\rm{m}}} $, ${\kappa _1} = 5{\omega _{\rm{m}}}$, ${\kappa _2} = 0.05{\omega _{\rm{m}}} $, ${\varDelta _2} =$$ - {\omega _{\rm{m}}} $, 最优失谐${\varDelta _1}$满足(66)式)

    Fig. 8.  Mean phonon number ${n_{\rm{p}}}$ as a function of effective initial temperature T. The given parameters are ${\omega _{\rm{m}}} =$ $ 1.55{\text{π}} \times 20\;{\rm{MHz}} $, $ {Q_{\rm{m}}} = {{{\omega _{\rm{m}}}} / {{\gamma _{\rm{m}}}}} = 6.2 \times {10^4} $, $ J = 10{\omega _{\rm{m}}} $, $ g = 0.5{\omega _{\rm{m}}} $, ${\kappa _1} = 5{\omega _{\rm{m}}}, {\kappa _2} = 0.05{\omega _{\rm{m}}}, {\varDelta _2} = - {\omega _{\rm{m}}}$ and the optical detuning ${\varDelta _1}$ satisfied the Eq. (66).

    图 9  冷却速率${\gamma _{\rm{c}}}$随最佳光腔耦合系数J的变化(给定的参数是${\omega _{\rm{m}}} = 1.55{\text{π}} \times 20\;{\rm{MHz}}$, ${Q_{\rm{m}}} = {{{\omega _{\rm{m}}}} / {{\gamma _{\rm{m}}}}} = 6.2 \times {10^4}$, ${n_{\rm{m}}} \!=\! 403$, $g \!=\! 0.5{\omega _{\rm{m}}} $, ${\kappa _1} \!=\! 5{\omega _{\rm{m}}}$, ${\kappa _2} \!=\! 0.05{\omega _{\rm{m}}} $, ${\varDelta _1} \!=\! {\varDelta _2} \!=\!$$ - {\omega _{\rm{m}}} $, ${\varDelta _{\rm{a}}} = {\omega _{\rm{m}}}$, $ {\gamma _{\rm{a}}} = 10{\omega _{\rm{m}}} $, $ {g_{\rm{a}}} = 0.62 \times {10^{ - 4}}{\omega _{\rm{m}}} $, $N = {10^8} $)

    Fig. 9.  Cooling rate ${\gamma _{\rm{c}}}$ as a function of optical coupling coefficient J. The given parameters are ${\omega _{\rm{m}}}\! =\! 1.55{\text{π}} \!\times \!20\;{\rm{MHz}}$, $ {Q_{\rm{m}}} = {{{\omega _{\rm{m}}}} / {{\gamma _{\rm{m}}}}} = 6.2\! \times \!{10^4} $, ${n_{\rm{m}}} = 403$, $g \!=\! 0.5{\omega _{\rm{m}}}$, ${\kappa _1} \!=\! 5{\omega _{\rm{m}}}$, ${\kappa _2} = 0.05{\omega _{\rm{m}}}$, $ {\varDelta _1} = {\varDelta _2} = - {\omega _{\rm{m}}}$, ${\varDelta _{\rm{a}}} = {\omega _{\rm{m}}} $, ${\gamma _{\rm{a}}} = 10{\omega _{\rm{m}}}$, $ {g_{\rm{a}}} = 0.62 \times {10^{ - 4}}{\omega _{\rm{m}}}$, $ N = {10^8} $.

    图 10  平均声子数${n_{\rm{p}}}$随最佳光腔耦合系数J的变化(给定的参数同图8)

    Fig. 10.  Mean phonon number ${n_{\rm{p}}}$ as a function of optical coupling coefficient J. The given parameters are same as the ones in Fig. 8.

  • [1]

    Kippenberg T J, Vahala K J 2007 Opt. Express 15 17172Google Scholar

    [2]

    Aspelmeyer M, Meystre P, Schwab K 2012 Phys. Today 65 29Google Scholar

    [3]

    Metzger C H, Karrai K 2004 Nature 432 1002Google Scholar

    [4]

    Machnes S, Cerrillo J, Aspelmeyer M, Wieczorek W, Plenio M B, Retzker A 2012 Phys. Rev. Lett. 108 153601Google Scholar

    [5]

    O’Connell A D, Hofheinz M, Ansmann M, Bialczak R C, Lenander M, Lucero E, Neeley M, Sank D, Wang H, Weides M, Wenner J, Martinis J M, Cleland A N 2010 Nature 464 697Google Scholar

    [6]

    Teufel J D, Donner T, Li D, Harlow J W, Allmanet M S, Cicak K, Sirois A J, Whittaker J D, Lehnert K W, Simmonds R W 2011 Nature 475 359Google Scholar

    [7]

    Wilson-Rae I, Zoller P, Imamoglu A 2004 Phys. Rev. Lett. 92 075507Google Scholar

    [8]

    Liu Y C, Xiao Y F, Luan X, Wong C W 2013 Phys. Rev.Lett. 110 153606Google Scholar

    [9]

    Zhu J P, Li G X, Ficek Z 2012 Phys. Rev. A 85 033835Google Scholar

    [10]

    陈华俊, 米贤武 2011 物理学报 60 124206Google Scholar

    Chen H J, Mi X W 2011 Acta Phys. Sin. 60 124206Google Scholar

    [11]

    Wilson-Rae I, Nooshi N, Zwerger W, Kippenberg T J 2007 Phys. Rev. Lett. 99 093901Google Scholar

    [12]

    Marquardt F, Chen J P, Clerk A A, Girvin S M 2007 Phys. Rev. Lett. 99 093902Google Scholar

    [13]

    Liu Y C, Luan X, Li H K, Gong Q, Wong C W, Xiao Y F 2014 Phys. Rev. Lett. 112 213602Google Scholar

    [14]

    Jing H, Özdemir S K, Lü X Y, Zhang J, Yang L, Nori F 2014 Phys. Rev. Lett. 113 053604Google Scholar

    [15]

    Chen H J 2018 J. Appl. Phys. 124 153102Google Scholar

    [16]

    Zhang P, Wang Y D, Sun C P 2005 Phys. Rev. Lett. 95 097204Google Scholar

    [17]

    Xia K, Evers J 2009 Phys. Rev. Lett. 103 227203Google Scholar

    [18]

    EversJ, Keitel C H 2004 Europhys. Lett. 68 370Google Scholar

    [19]

    Harris S E 1997 Phys. Today 50 36Google Scholar

    [20]

    Fleischhauer M, Imamoglu A, Marangos J P 2005 Rev. Mod. Phys. 77 633Google Scholar

    [21]

    Genes C, Ritsch H, Drewsen M, Dantan A 2011 Phys. Rev. A 84 051801(R)Google Scholar

    [22]

    谷开慧, 严冬, 张孟龙, 殷景志, 付长宝 2019 物理学报 68 054201Google Scholar

    Gu K H, Yan D, Zhang M L, Yin J Z, Fu C B 2019 Acta Phys. Sin. 68 054201Google Scholar

    [23]

    Grudinin I S, Lee H, Painter O, Vahala K J 2010 Phys. Rev. Lett. 104 083901Google Scholar

    [24]

    Di K, Xie C, Zhang J 2011 Phys. Rev. Lett. 106 153602Google Scholar

    [25]

    Gu W J, Li G X 2013 Phys. Rev. A 87 025804Google Scholar

    [26]

    Ojanen T, Børkje K 2014 Phys. Rev. A 90 013824Google Scholar

    [27]

    Giovannetti V, Vitali D 2001 Phys. Rev. A 63 023812Google Scholar

    [28]

    Guo Y J, Li K, Nie W J, Li Y 2014 Phys. Rev. A 90 053841Google Scholar

    [29]

    Garrido Alzar C L, Martinez M A G, Nussenzeig P 2002 Am. J. Phys. 70 37Google Scholar

    [30]

    AnetsbergerG, Rivière R, Schliesser A, Arcizet O, Kippenberg T J 2008 Nat. Photonics 2 627Google Scholar

  • [1] 李德彰, 卢智伟, 赵宇军, 杨小宝. 自旋半经典朗之万方程一般形式的探讨. 物理学报, 2023, 72(14): 140501. doi: 10.7498/aps.72.20230106
    [2] 乔亮, 羊富贵, 武永华, 柯友刚, 夏忠朝. Tm,Ho双掺调Q激光系统理论与实验研究. 物理学报, 2014, 63(21): 214205. doi: 10.7498/aps.63.214205
    [3] 李晨璞, 韩英荣, 展永, 谢革英, 胡金江, 张礼刚, 贾利云. 基于三磷酸腺苷调节的分子马达单向能量跃迁模型. 物理学报, 2013, 62(19): 190501. doi: 10.7498/aps.62.190501
    [4] 李晨璞, 韩英荣, 展永, 胡金江, 张礼刚, 曲蛟. 肌球蛋白Ⅵ分子马达周期势场下的弹性扩散模型. 物理学报, 2013, 62(23): 230501. doi: 10.7498/aps.62.230501
    [5] 蒋泽南, 房超, 孙立风. 朗之万方程及其在蛋白质折叠动力学中的应用. 物理学报, 2011, 60(6): 060502. doi: 10.7498/aps.60.060502
    [6] 林燕凤, 张戈, 朱海永, 黄呈辉, 李爱红, 魏勇. Nd:YAG调Q激光器双波长振荡机理分析. 物理学报, 2009, 58(6): 3909-3914. doi: 10.7498/aps.58.3909
    [7] 王同喜, 关宝璐, 郭霞, 沈光地. 载流子输运和寄生参数对隧道再生双有源区垂直腔面发射激光器调制特性的影响. 物理学报, 2009, 58(3): 1694-1699. doi: 10.7498/aps.58.1694
    [8] 樊华, 李理, 袁坚, 山秀明. 互联网流量控制的朗之万模型及相变分析. 物理学报, 2009, 58(11): 7507-7513. doi: 10.7498/aps.58.7507
    [9] 王浩, 刘国权, 岳景朝, 栾军华, 秦湘阁. MacPherson-Srolovitz晶粒长大速率方程的仿真验证. 物理学报, 2009, 58(13): 137-S140. doi: 10.7498/aps.58.137
    [10] 李小燕, 郑志强, 冯卓宏, 刘 璟, 姜翠华, 孔令凯, 明 海. 掺铒锆钛酸铅镧陶瓷的上转换动力学分析. 物理学报, 2008, 57(5): 3244-3248. doi: 10.7498/aps.57.3244
    [11] 张新陆, 王月珠, 李 立, 崔金辉, 鞠有伦. 端面抽运Tm,Ho∶YLF连续激光器的参数优化与实验研究. 物理学报, 2008, 57(6): 3519-3524. doi: 10.7498/aps.57.3519
    [12] 於海武, 徐美健, 段文涛, 隋 展. Yb离子抽运动力学及脉冲储能特性研究. 物理学报, 2007, 56(7): 4158-4168. doi: 10.7498/aps.56.4158
    [13] 张新陆, 王月珠, 李 立, 鞠有伦. 端面抽运Tm, Ho:YLF激光器热转换系数及热透镜效应的研究. 物理学报, 2007, 56(4): 2196-2201. doi: 10.7498/aps.56.2196
    [14] 金 哲, 聂秋华, 徐铁峰, 戴世勋, 沈 祥, 章向华. Tm3+/Yb3+共掺碲铅锌镧玻璃的能量传递和上转换发光. 物理学报, 2007, 56(4): 2261-2267. doi: 10.7498/aps.56.2261
    [15] 吴朝晖, 宋 峰, 刘淑静, 蔡 虹, 苏 静, 田建国, 张光寅. LD抽运Er3+,Yb3+共掺磷酸盐玻璃被动调Q激光器的理论分析和数值计算. 物理学报, 2006, 55(9): 4659-4664. doi: 10.7498/aps.55.4659
    [16] 张新陆, 王月珠. 能量传递上转换对Tm,Ho:YLF调Q激光器上能级寿命的影响. 物理学报, 2006, 55(3): 1160-1164. doi: 10.7498/aps.55.1160
    [17] 宋 峰, 苏瑞渊, 傅 强, 覃 斌, 田建国, 张光寅. 高浓度镱铒共掺磷酸盐光纤放大器增益特性. 物理学报, 2005, 54(11): 5228-5232. doi: 10.7498/aps.54.5228
    [18] 张新陆, 王月珠, 鞠有伦. 能量传递上转换对Tm,Ho:YLF激光器阈值的影响. 物理学报, 2005, 54(1): 117-122. doi: 10.7498/aps.54.117
    [19] 宋峰, 孟凡臻, 丁欣, 张潮波, 杨嘉, 张光寅. 1.54μmEr3+,Yb3+共掺玻璃激光器的速率方程及数值分析. 物理学报, 2002, 51(6): 1233-1238. doi: 10.7498/aps.51.1233
    [20] 周光召, 苏肇冰, 郝柏林, 于渌. 非平衡统计场论与临界动力学(Ⅰ)——广义朗之万方程. 物理学报, 1980, 29(8): 961-968. doi: 10.7498/aps.29.961
计量
  • 文章访问数:  6583
  • PDF下载量:  170
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-10-09
  • 修回日期:  2020-01-05
  • 刊出日期:  2020-03-20

/

返回文章
返回