Optical nonreciprocity with blue-detuned driving in two-cavity optomechanics

Zhang Li-Wei; Li Xian-Li; Yang Liu

doi:10.7498/aps.68.20190205

Abstract

Radiation pressure in an optomechanical system can be used to generate various quantum phenomena. Recently, one paid more attention to the study of optical nonreciprocity in an optomechanical system, and nonreciprocal devices are indispensable for building quantum networks and ubiquitous in modern communication technology. Here in this work, we study how to realize the perfect optical nonreciprocity in a two-cavity optomechanical system with blue-detuned driving. Our calculations show that the optical nonreciprocity comes from the quantum interference of signal transmission between two possible paths corresponding to the two interactions in this system, i.e. optomechanical interaction and linearly-coupled interaction. According to the standard input-output relation of optical field in cavity optomechanics, we obtain the expression of output optical field, from which we can derive the essential conditions to achieve the perfect optical nonreciprocity, and find there are two sets of coupling strengths both of which can realize the perfect optical nonreciprocal transmission. Because the system is driven by blue-detuned driving, the system is stable only under some conditions which we can obtain according to the Routh-Hurwitz criterion. Due to the blue-detuned driving, there will be transmission gain (transmission amplitude is greater than 1) in the nonreciprocal transmission spectrum. We also find that the bandwidth of nonreciprocal transmission spectrum is in proportion to mechanical decay rate if mechanical decay rate is much less than the cavity decay rate. In other words, in a realistic optomechanical parameter regime, where mechanical decay rate is much less than cavity decay rate, the bandwidth of nonreciprocal transmission spectrum is very narrow. Our results can also be applied to other parametrically coupled three-mode bosonic systems and may be used to realize the state transfer process and optical nonreciprocal transmission in an optomechanical system.

Keywords:

Authors and contacts

1.
College of Electronic Science, Northeast Petroleum University, Daqing 163318, China
2.
College of Automation, Harbin Engineering University, Harbin 150001, China

Corresponding author: Li Xian-Li, lxl7158@163.com ; Yang Liu, lyang@hrbeu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 41472126, 11804066), the China Postdoctoral Science Foundation (Grant No. 2018M630337), the Fundamental Research Fund for the Central Universities, China (Grant No. 3072019CFM0405), the Natural Science Foundation of Heilongjiang Province, China (Grant No. LH2019A005), and the Heilongjiang Postdoctoral Sustentation Fund, China (Grant No. LBH-Z18062).

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References

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Cited By

图 1 双腔光力学系统示意图, 两光学腔通过光力相互作用与一个力学振子相耦合, 振幅为$\varepsilon_{\rm c}$和 $\varepsilon_{\rm d}$($\varepsilon_{\rm L}$和$\varepsilon_{\rm R}$)的强耦合场 (探测场)分别从左右两侧驱动腔模$c_{1}$和$c_{2}$, 同时两腔模之间存在线性耦合相互作用J

Figure 1. A two-cavity optomechanical system with a mechanical resonator interacted with two cavities. Two strong coupling fields (probe fields) with amplitudes $\varepsilon_{\rm c}$ and $\varepsilon_{\rm d}$ ($\varepsilon_{\rm L}$ and $\varepsilon _{\rm R}$) are used to drive cavity $c_{1}$ and $c_{2}$ respectively. Meanwhile, the two cavities are linearly coupled to each other with coupling strength J

DownLoad: Full-Size Img PowerPoint

图 2 传输振幅$T_{\rm {LR}}$(红线)和$T_{\rm {RL}}$(黑线)在不同力学振子耗散速率下随着标准化失谐$x/\kappa$的变化曲线　(a) $\gamma/\kappa$=1/100; (b) $\gamma/\kappa$=1/10; (c) $\gamma/\kappa$=1; (d) $\gamma/\kappa$=2; 其他参数: $\theta=-\dfrac{{\text{π}}}{2}$, $G =G_{+}$和$J=J_{+}$(见(16)式)

Figure 2. Transmission amplitudes $T_{\rm {LR}}$ (red line) and $T_{\rm {RL}}$ (black line) are plotted vs normalized detuning $x/\kappa$ for different cavity damping rate: (a) $\gamma/\kappa$=1/100; (b) $\gamma/\kappa$=1/10; (c) $\gamma/\kappa$=1; (d) $\gamma/\kappa$=2. Other parameters: $\theta=-\dfrac{{\text{π}}}{2}$, $G =G_{+}$ and $J=J_{+}$ according to Eq. (16)

DownLoad: Full-Size Img PowerPoint

图 3 传输振幅$T_{\rm {LR}}$(红线)和$T_{\rm {RL}}$(黑线)在不同力学振子耗散速率下随着标准化失谐$x/\kappa$的变化曲线　(a) $\gamma/\kappa$=1/100; (b) $\gamma/\kappa$=1/10; (c) $\gamma/\kappa$=1; (d) $\gamma/\kappa$=10. 其他参数: $\theta=-\dfrac{{\text{π}}}{2}$, $G =G_{-}$和$J=J_{-}$(见(16)式)

Figure 3. Transmission amplitudes $T_{\rm {LR}}$ (red line) and $T_{\rm {RL}}$ (black line) are plotted vs normalized detuning $x/\kappa$ for different mechancial damping rate: (a) $\gamma/\kappa$=1/100; (b) $\gamma/\kappa$=1/10; (c) $\gamma/\kappa$=1; (d) $\gamma/\kappa$=10. Other parameters: $\theta=-\dfrac{{\text{π}}}{2}$, $G =G_{-}$ and $J=J_{-}$ according to Eq. (16)

DownLoad: Full-Size Img PowerPoint

图 4 传输振幅$T_{\rm {LR}}$(红线)和$T_{\rm {RL}}$(黑线)在不同非互易相位差θ和耦合强度G时随着标准化失谐$x/\gamma$的变化曲线　(a) $\theta=-\dfrac{{\text{π}}}{4}$和$G=G_{-}$; (b) $\theta=-\dfrac{{\text{π}}}{4}$和$G=G_{+}$; (c) $\theta=-\dfrac{3{\text{π}}}{4}$和$G=G_{-}$; (d) $\theta=-\dfrac{3{\text{π}}}{4}$和$G=G_{+}$; 其他参数: $\gamma/\kappa=10^{-3}$, $J=J_{\pm}$和$G=G_{\pm}$(见(19)式)

Figure 4. Transmission amplitudes $T_{\rm {LR}}$ (red line) and $T_{\rm {RL}}$ (black line) are plotted vs normalized detuning $x/\gamma$ for different nonreciprocal phase θ and coupling strength G: (a) $\theta=-\dfrac{{\text{π}}}{4}$ and $G=G_{-}$; (b) $\theta=-\dfrac{{\text{π}}}{4}$ and $G=G_{+}$; (c) $\theta=-\dfrac{3{\text{π}}}{4}$ and $G=G_{-}$; (d) $\theta=-\dfrac{3{\text{π}}}{4}$ and $G=G_{+}$. Other parameters: $\gamma/\kappa=10^{-3}$, coupling strengths $J=J_{\pm}$ and $G=G_{\pm}$ according to Eq. (19)

DownLoad: Full-Size Img PowerPoint

map

[1]	Jalas D, Petrov A, Eich M, et al. 2013 Nat. Photonics 7 579 Google Scholar
[2]	Aplet L J, Carson J W 1964 Appl. Opt. 3 544 Google Scholar
[3]	Aspelmeyer M, Kippenberg T J, Marquardt F 2014 Rev. Mod. Phys. 86 1391 Google Scholar
[4]	陈雪, 刘晓威, 张可烨, 袁春华, 张卫平 2015 64 164211 Google Scholar Chen X, Liu X W, Zhang K Y, Yuan C H, Zhang W P 2015 Acta Phys. Sin. 64 164211 Google Scholar
[5]	陈华俊, 方贤文, 陈昌兆, 李洋 2016 65 194205 Google Scholar Chen H J, Fang X W, Chen C Z, Li Y 2016 Acta Phys. Sin. 65 194205 Google Scholar
[6]	严晓波, 杨柳, 田雪冬, 刘一谋, 张岩 2014 63 204201 Google Scholar Yan X B, Yang L, Tian X D, Liu Y M, Zhang Y 2014 Acta Phys. Sin. 63 204201 Google Scholar
[7]	班章, 梁静秋, 吕金光, 梁中翥, 冯思悦 2018 67 070701 Google Scholar Zhang B, Liang J Q, Lü J G, Liang Z Z, Feng S Y 2018 Acta Phys. Sin. 67 070701 Google Scholar
[8]	Chen R X, Shen L T, Yang Z B, Wu H Z, Zheng S B 2014 Phys. Rev. A 89 023843 Google Scholar
[9]	Liao J Q, Wu Q Q, Nori F 2014 Phys. Rev. A 89 014302 Google Scholar
[10]	Yan X B 2017 Phys. Rev. A 96 053831 Google Scholar
[11]	He Q Y, Ficek Z 2014 Phys. Rev. A 89 022332 Google Scholar
[12]	张秀龙, 鲍倩倩, 杨明珠, 田雪松 2018 67 104203 Google Scholar Zhang X L, Bao Q Q, Yang M Z, Tian X S 2018 Acta Phys. Sin. 67 104203 Google Scholar
[13]	Kiesewetter S, He Q Y, Drummond P D, Reid M D 2014 Phys. Rev. A 90 043805 Google Scholar
[14]	Lin Q, He B, Ghobadi R, Simon C 2014 Phys. Rev. A 90 022309 Google Scholar
[15]	He Q Y, Reid M D 2013 Phys. Rev. A 88 052121 Google Scholar
[16]	Yan X B, Deng Z J, Tian X D, Wu J H 2019 Opt. Express 27 024393 Google Scholar
[17]	He B, Yang L, Lin Q, Xiao M 2017 Phys. Rev. Lett. 118 233604 Google Scholar
[18]	Li Y, Wu L A, Wang Z D 2011 Phys. Rev. A 83 043804 Google Scholar
[19]	Deng Z J, Li Y, Gao M, Wu C W 2012 Phys. Rev. A 85 025804 Google Scholar
[20]	Liu Y C, Wen H Y, Wei W C, Xiao Y F 2013 Chin. Phys. B 22 114213 Google Scholar
[21]	Huang S M, Agarwal G S 2009 Phys. Rev. A 79 013821 Google Scholar
[22]	Agarwal G S, Huang S M 2010 Phys. Rev. A 81 041803(R)Google Scholar
[23]	Shu J 2011 Chin. Phys. Lett. 28 104203 Google Scholar
[24]	陈华俊, 米贤武 2011 60 124206 Google Scholar Chen H J, Mi X W 2011 Acta Phys. Sin. 60 124206 Google Scholar
[25]	Han Y, Cheng J, Zhou L 2011 J. Phys. B 44 165505 Google Scholar
[26]	Zhang J Q, Li Y, Feng M, Xu Y 2012 Phys. Rev. A 86 053806 Google Scholar
[27]	Lü X Y, Zhang W M, Ashhab S, Wu Y, Nori F 2013 Sci. Rep. 3 2943 Google Scholar
[28]	Zhou L, Cheng J, Han Y, Zhang W P 2013 Phys. Rev. A 88 063854 Google Scholar
[29]	He B 2012 Phys. Rev. A 85 063820 Google Scholar
[30]	Cao C, Mi S C, Gao Y P, He L Y, Yang D, Wang T J, Zhang R, Wang C 2016 Sci. Rep. 6 22920 Google Scholar
[31]	Cao C, Mi S C, Wang T J, Zhang R, Wang C 2016 IEEE J. Quantum Electron. 52 1
[32]	Cao C, Chen X, Duan Y W, Fan L, Zhang R, Wang T J, Wang C 2017 Optik 130 659 Google Scholar
[33]	Xiong X R, Gao Y P, Liu X F, Cao C, Wang T J, Wang C 2018 Sci. China-Phys. Mech. Astron. 61 090322 Google Scholar
[34]	石海泉, 谢智强, 徐勋卫, 刘念华 2018 67 044203 Google Scholar Shi H Q, Xie Z Q, Xu X W, Liu N H 2018 Acta Phys. Sin. 67 044203 Google Scholar
[35]	Manipatruni S, Robinson J T, Lipson M 2009 Phys. Rev. Lett. 102 213903 Google Scholar
[36]	Hafezi M, Rabl P 2012 Opt. Express 20 7672 Google Scholar
[37]	Wang Z, Shi L, Liu Y, Xu X, Zhang X 2015 Sci. Rep. 5 8657 Google Scholar
[38]	Shen Z, Zhang Y L, Chen Y, Zou C L, Xiao Y F, Zou X B, Sun F W, Guo G C, Dong C H 2016 Nat. Photonics 10 657 Google Scholar
[39]	Peterson G A, Lecocq F, Cicak K, Simmonds R W, Aumentado J, Teufel J D 2017 Phys. Rev. X 7 031001
[40]	Barzanjeh S, Wulf M, Peruzzo M, Kalaee M, Dieterle P B, Painter O, Fink J M 2017 Nat. Commun. 8 953 Google Scholar
[41]	Fang K, Luo J, Metelmann A, Matheny M H, Marquardt F, Clerk A A, Painter O 2017 Nat. Phys. 13 465 Google Scholar
[42]	Maayani S, Dahan R, Kligerman Y, Moses E, Hassan A U, Jing H, Nori F, Christodoulides D N, Carmon T 2018 Nature (London) 558 569 Google Scholar
[43]	Xu X W, Li Y 2015 Phys. Rev. A 91 053854 Google Scholar
[44]	Xu X W, Li Y, Chen A X, Liu Y 2016 Phys. Rev. A 93 023827 Google Scholar
[45]	Tian L, Li Z 2017 Phys. Rev. A 96 013808 Google Scholar
[46]	Malz D, Tóth L D, Bernier N R, Feofanov A K, Kippenberg T J, Nunnenkamp A 2018 Phys. Rev. Lett. 120 023601 Google Scholar
[47]	Jiang Y, Maayani S, Carmon T, Nori F, Jing H 2018 Phys. Rev. Applied 10 064037 Google Scholar
[48]	Li Y, Huang Y Y, Zhang X Z, Tian L 2017 Opt. Express 25 18907 Google Scholar
[49]	Huang R, Miranowicz A, Liao J Q, Nori F, Jing H 2018 Phys. Rev. Lett. 121 153601 Google Scholar
[50]	Xu X W, Zhao Y J, Wang H, Jing H, Chen A X 2018 arXiv: 1809.07596
[51]	Lü H, Jiang Y, Wang Y Z, Jing H 2017 Photonics Res. 5 367 Google Scholar
[52]	Habraken S J M, Stannigel K, Lukin M D, Zoller P, Rabl P 2012 New J. Phys. 14 115004 Google Scholar
[53]	Seif A, DeGottardi W, Esfarjani K, Hafezi M 2018 Nat. Commun. 9 1207 Google Scholar
[54]	Thompson J D, Zwickl B M, Jayich A M, Marquardt F, Girvin S M, Harris J G E 2008 Nature (London) 452 72 Google Scholar
[55]	Jayich A M, Sankey J C, Zwickl B M, Yang C, Thompson J D, Girvin S M, Clerk A A, Marquardt F, Harris J G E 2008 New J. Phys. 10 095008 Google Scholar
[56]	Sankey J C, Yang C, Zwickl B M, Jayich A M, Harris J G E 2010 Nat. Phys. 6 707 Google Scholar
[57]	Agarwal G S, Huang S 2014 New J. Phys. 16 033023 Google Scholar
[58]	Yan X B, Cui C L, Gu K H, Tian X D, Fu C B, Wu J H 2014 Opt. Express 22 4886 Google Scholar
[59]	DeJesus E X, Kaufman C 1987 Phys. Rev. A 35 5288 Google Scholar

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