三机械薄膜腔光力系统相互作用的研究

肖佳; 徐大海; 伊珍; 谷文举

doi:10.7498/aps.65.124202

摘要

本文主要研究了利用传输矩阵理论和共振透射条件详细地推导光腔中均匀放置三个机械薄膜构成的腔光力系统中系统本征模式随机械运动的色散关系. 计算结果发现系统的光学本征模式由一组四个的本征能级构成, 且不同的能级随不同的机械运动模式的变化曲线各不相同, 进而导致不同光学模式与不同机械运动模式之间的耦合也不相同. 此外, 利用微扰理论求解了当机械运动振幅远小于腔模波长、机械振子处于平衡位置附近时, 各种光学模式与不同机械振动模式间相互作用耦合强度的解析表达式. 研究结果能够为理论和实验上研究多模腔光力系统提供一定的参考.

关键词:

Abstract

Cavity optomechanics becomes a promising field in quantum and nano technologies. Motivated by the optomechancial experiment with the membrane located in a high-finesse optical cavity and theoretical treatment on two membranes cavity optomechanics, we here study the optomechanical interaction of the system consisting of triple membranes within an optical cavity. The increase of membranes will increase the normal modes of the cavity and mechanical fields, and thus enrich the forms of optomechanical interaction. Firstly, we use the transfer matrix and resonance transmission methods to obtain the dispersion relation between the eigen-frequencies of the optical modes and the mechanical motions. Owing to the existence of triple mechanical membranes, the system possesses different forms of collective mechanical motion, and here we focus on the center-of-mass (COM) motion and relative motion of the equally placed membranes. The numerical solutions of the dispersion relation show that the optical eigenmodes are comprised of a group of closely spaced avoided-crossing quaternion of wave numbers, which arise from the transmission and reflection of the optical field at the membranes and the tunneling couplings between subcavity modes. Moreover, the change of each eigen wave number along each form of the mechanical motion is different, which implies the different forms of optomechanical coupling between eigenmodes and mechanical motions. Then, to achieve the explicit expressions of the optomechanical coupling, it is sufficient to use the perturbation method under the equilibrium condition of the system, where the amplitude of mechanical motion is much smaller than the optical wavelength. With using the implicit function differentiation theorem, the optomechanical coupling strengths between the four optical modes and the COM and relative mechanical motions are obtained respectively. We find that the strong quadratic optomechanical coupling between the optical modes and COM motion can be achieved, and the linear and quadratic couplings between the optical modes and relative motion can both be realized. By tuning the laser to pump different optical modes, we can choose either the linear or the quadratic coupling to the relative motion. Our method is universal to multi-membrane system, and the results may provide some references to theoretical and experimental investigations on the multi-membrane cavity optomechanics.

Keywords:

作者及机构信息

1.
长江大学物理与光电工程学院, 荆州 434023

通信作者: 谷文举, guwenju@yangtzeu.edu.cn

基金项目: 国家自然科学基金(批准号: 11504031, 61505014)和长江大学长江青年科技创新团队基金(批准号: 2015cqt03)资助的课题.

Authors and contacts

1.
School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China

Corresponding author: Gu Wen-Ju, guwenju@yangtzeu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11504031, 61505014) and the Yangtze Fund for Youth Teams of Science and Technology Innovation, China (Grant No. 2015cqt03).

参考文献

[1]	Aspelmeyer M, Kippenberg T J, Marquardt F 2014 Rev. Mod. Phys. 86 1391
[2]	Kippenberg T J, Vahala K J 2007 Opt. Express 15 17172
[3]	Chen X, Liu X W, Zhang K Y, Yuan C H, Zhang W P 2015 Acta Phys. Sin. 64 164211 (in Chinese) [陈雪, 刘晓威, 张可烨, 袁春华, 张卫平 2015 物理学报 64 164211]
[4]	Teufel J D, Donner T, Li D, Harlow J W, Allman M S, Cicak K, Sirois A J, Whittaker J D, Lehnert K W, Simmonds R W 2011 Nature 475 359
[5]	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 464 697
[6]	Liu Y C, Hu Y W, Wong C W, Xiao Y F 2013 Chin. Phys. B 22 114213
[7]	Carmon T, Rokhsari H, Yang L, Kippenberg T J, Vahala K J 2005 Phys. Rev. Lett. 94 223902
[8]	Rokhsari H, Kippenberg T J, Carmon T, Vahala K J 2005 Opt. Express 13 5293
[9]	Thompson J D, Zwickl B M, Jayich A M, Marquardt F, Girvin S M, Harris J G E 2008 Nature 452 72
[10]	Anetsberger G, Arcizet O, Unterreithmeier Q P, Riviere R, Schliesser A, Weig E M, Kotthaus J P, Kippenberg T J 2009 Nat. Phys. 5 909
[11]	Lee D, Underwood M, Mason D, Shkarin A B, Hoch S W, Harris J G E 2015 Nat. Commun. 6 6232
[12]	Shkarin A B, Jacobs N E F, Hoch S W, Kashkanova A D, Deutsch C, Reichel J, Harris J G E 2014 Phys. Rev. Lett. 112 013602
[13]	Ludwig M, Hammerer K, Marquardt F 2010 Phys. Rev. A 82 012333
[14]	Komar P, Bennett S D, Stannigel K, Habraken S J M, Rabl P, Zoller P, Lukin M D 2013 Phys. Rev. A 87 013839
[15]	Verlot P, Tavernarakis A, Briant T, Cohadon P F, Heidmann A 2009 Phys. Rev. Lett. 102 103601
[16]	Tian L 2013 Phys. Rev. Lett. 110 233602
[17]	Andrews R W, Peterson R W, Purdy T P, Cicak K, Simmonds R W, Regal C A, Lehnert K W 2014 Nat. Phys. 10 321
[18]	Bui C H, Zheng J, Hoch S W, Lee L Y T, Harris J G E, Wong C W 2012 Appl. Phys. Lett. 100 021110
[19]	Sankey J C, Yang C, Zwickl B M, Jayich A M, Harris J G E 2010 Nature Phys. 6 707
[20]	Jacobs N E F, Hoch S W, Sankey J C, Kashkanova A, Jayich A M, Deutsch C, Reichel J, Harris J G E 2012 Appl. Phys. Lett. 101 221109
[21]	Underwood M, Mason D, Lee D, Xu H, Jiang L, Shkarin A B, Borkje K, Girvin S M, Harris J G E 2015 Phys. Rev. A 92 061801
[22]	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
[23]	Bhattacharya M, Meystre 2008 Phys. Rev. A 78 041801
[24]	Xuereb A, Genes C, Dantan A 2012 Phys. Rev. Lett. 109 223601
[25]	Tomadin A, Diehl S, Lukin M D, Rabl P, Zoller P 2012 Phys. Rev. A 86 033821
[26]	Ludwig M, Marquardt F 2013 Phys. Rev. Lett. 111 073603
[27]	Seok H, Buchmann L F, Wright E M, Meystre P 2013 Phys. Rev. A 88 063850
[28]	Xuereb A, Genes C, Pupillo G, Paternostro M, Dantan A 2014 Phys. Rev. Lett. 112 133604
[29]	Stannigel K, Komar P, Habraken S J M, Bennett S D, Lukin M D, Zoller P, Rabl P 2012 Phys. Rev. Lett. 109 013603
[30]	Bhattacharya M, Uys H, Meystre P 2008 Phys. Rev. A 77 033819
[31]	Hartmann M J, Plenio M B 2008 Phys. Rev. Lett. 101 200503
[32]	Zhang X, Zhang L 2015 Sci. Sin.: Phys. Mech. Astron. 45 044201 (in Chinese) [张旭, 张林 2015 中国科学: 物理学力学天文学 45 044201]
[33]	Fader W J 1985 IEEE J. Quantum Electron. 21 1838
[34]	Xu X W, Zhao Y J, Liu Y X 2013 Phys. Rev. A 88 022325
[35]	Xuereb A, Genes C, Dantan A 2013 Phys. Rev. A 88 053803
[36]	Deutsch I H, Spreeuw R J C, Rolston S L, Phillips W D 1995 Phys. Rev. A 52 1394
[37]	Ludwig M, Safavi-Naeini A H, Painter O, Marquardt F 2012 Phys. Rev. Lett. 109 063601
[38]	Gu W, Yi Z, Sun L, Xu D 2015 Phys. Rev. A 92 023811

施引文献

[1]	Aspelmeyer M, Kippenberg T J, Marquardt F 2014 Rev. Mod. Phys. 86 1391
[2]	Kippenberg T J, Vahala K J 2007 Opt. Express 15 17172
[3]	Chen X, Liu X W, Zhang K Y, Yuan C H, Zhang W P 2015 Acta Phys. Sin. 64 164211 (in Chinese) [陈雪, 刘晓威, 张可烨, 袁春华, 张卫平 2015 物理学报 64 164211]
[4]	Teufel J D, Donner T, Li D, Harlow J W, Allman M S, Cicak K, Sirois A J, Whittaker J D, Lehnert K W, Simmonds R W 2011 Nature 475 359
[5]	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 464 697
[6]	Liu Y C, Hu Y W, Wong C W, Xiao Y F 2013 Chin. Phys. B 22 114213
[7]	Carmon T, Rokhsari H, Yang L, Kippenberg T J, Vahala K J 2005 Phys. Rev. Lett. 94 223902
[8]	Rokhsari H, Kippenberg T J, Carmon T, Vahala K J 2005 Opt. Express 13 5293
[9]	Thompson J D, Zwickl B M, Jayich A M, Marquardt F, Girvin S M, Harris J G E 2008 Nature 452 72
[10]	Anetsberger G, Arcizet O, Unterreithmeier Q P, Riviere R, Schliesser A, Weig E M, Kotthaus J P, Kippenberg T J 2009 Nat. Phys. 5 909
[11]	Lee D, Underwood M, Mason D, Shkarin A B, Hoch S W, Harris J G E 2015 Nat. Commun. 6 6232
[12]	Shkarin A B, Jacobs N E F, Hoch S W, Kashkanova A D, Deutsch C, Reichel J, Harris J G E 2014 Phys. Rev. Lett. 112 013602
[13]	Ludwig M, Hammerer K, Marquardt F 2010 Phys. Rev. A 82 012333
[14]	Komar P, Bennett S D, Stannigel K, Habraken S J M, Rabl P, Zoller P, Lukin M D 2013 Phys. Rev. A 87 013839
[15]	Verlot P, Tavernarakis A, Briant T, Cohadon P F, Heidmann A 2009 Phys. Rev. Lett. 102 103601
[16]	Tian L 2013 Phys. Rev. Lett. 110 233602
[17]	Andrews R W, Peterson R W, Purdy T P, Cicak K, Simmonds R W, Regal C A, Lehnert K W 2014 Nat. Phys. 10 321
[18]	Bui C H, Zheng J, Hoch S W, Lee L Y T, Harris J G E, Wong C W 2012 Appl. Phys. Lett. 100 021110
[19]	Sankey J C, Yang C, Zwickl B M, Jayich A M, Harris J G E 2010 Nature Phys. 6 707
[20]	Jacobs N E F, Hoch S W, Sankey J C, Kashkanova A, Jayich A M, Deutsch C, Reichel J, Harris J G E 2012 Appl. Phys. Lett. 101 221109
[21]	Underwood M, Mason D, Lee D, Xu H, Jiang L, Shkarin A B, Borkje K, Girvin S M, Harris J G E 2015 Phys. Rev. A 92 061801
[22]	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
[23]	Bhattacharya M, Meystre 2008 Phys. Rev. A 78 041801
[24]	Xuereb A, Genes C, Dantan A 2012 Phys. Rev. Lett. 109 223601
[25]	Tomadin A, Diehl S, Lukin M D, Rabl P, Zoller P 2012 Phys. Rev. A 86 033821
[26]	Ludwig M, Marquardt F 2013 Phys. Rev. Lett. 111 073603
[27]	Seok H, Buchmann L F, Wright E M, Meystre P 2013 Phys. Rev. A 88 063850
[28]	Xuereb A, Genes C, Pupillo G, Paternostro M, Dantan A 2014 Phys. Rev. Lett. 112 133604
[29]	Stannigel K, Komar P, Habraken S J M, Bennett S D, Lukin M D, Zoller P, Rabl P 2012 Phys. Rev. Lett. 109 013603
[30]	Bhattacharya M, Uys H, Meystre P 2008 Phys. Rev. A 77 033819
[31]	Hartmann M J, Plenio M B 2008 Phys. Rev. Lett. 101 200503
[32]	Zhang X, Zhang L 2015 Sci. Sin.: Phys. Mech. Astron. 45 044201 (in Chinese) [张旭, 张林 2015 中国科学: 物理学力学天文学 45 044201]
[33]	Fader W J 1985 IEEE J. Quantum Electron. 21 1838
[34]	Xu X W, Zhao Y J, Liu Y X 2013 Phys. Rev. A 88 022325
[35]	Xuereb A, Genes C, Dantan A 2013 Phys. Rev. A 88 053803
[36]	Deutsch I H, Spreeuw R J C, Rolston S L, Phillips W D 1995 Phys. Rev. A 52 1394
[37]	Ludwig M, Safavi-Naeini A H, Painter O, Marquardt F 2012 Phys. Rev. Lett. 109 063601
[38]	Gu W, Yi Z, Sun L, Xu D 2015 Phys. Rev. A 92 023811

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