Please wait a minute...
Chin. Phys. B, 2018, Vol. 27(2): 024204    DOI: 10.1088/1674-1056/27/2/024204
Special Issue: TOPICAL REVIEW — Solid-state quantum information processing
TOPICAL REVIEW—Solid-state quantum information processing Prev   Next  

Cavity optomechanics: Manipulating photons and phonons towards the single-photon strong coupling

Yu-long Liu(刘玉龙)1,2, Chong Wang(王冲)1,2, Jing Zhang(张靖)2,3, Yu-xi Liu(刘玉玺)1,2
1. Institute of Microelectronics, Tsinghua University, Beijing 100084, China;
2. Tsinghua National Laboratory for Information Science and Technology(TNList), Beijing 100084, China;
3. Department of Automation, Tsinghua University, Beijing 100084, China
Abstract  

Cavity optomechanical systems provide powerful platforms to manipulate photons and phonons, open potential applications for modern optical communications and precise measurements. With the refrigeration and ground-state cooling technologies, studies of cavity optomechanics are making significant progress towards the quantum regime including nonclassical state preparation, quantum state tomography, quantum information processing, and future quantum internet. With further research, it is found that abundant physical phenomena and important applications in both classical and quantum regimes appeal as they have a strong optomechanical nonlinearity, which essentially depends on the single-photon optomechanical coupling strength. Thus, engineering the optomechanical interactions and improving the single-photon optomechanical coupling strength become very important subjects. In this article, we first review several mechanisms, theoretically proposed for enhancing optomechanical coupling. Then, we review the experimental progresses on enhancing optomechanical coupling by optimizing its structure and fabrication process. Finally, we review how to use novel structures and materials to enhance the optomechanical coupling strength. The manipulations of the photons and phonons at the level of strong optomechanical coupling are also summarized.

Keywords:  optomechanical systems      single-photon strong coupling      controllable photons and phonons transport  
Received:  24 September 2017      Revised:  23 November 2017      Accepted manuscript online: 
PACS:  42.50.Wk (Mechanical effects of light on material media, microstructures and particles)  
  42.82.Fv (Hybrid systems)  
  42.65.Sf (Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics)  
  42.79.Nv (Optical frequency converters)  
Fund: 

Project supported by the National Basic Research Program of China (Grant No. 2014CB921401), the Tsinghua University Initiative Scientific Research Program, and the Tsinghua National Laboratory for Information Science and Technology (TNList) Cross-discipline Foundation.

Corresponding Authors:  Yu-xi Liu     E-mail:  yuxiliu@mail.tsinghua.edu.cn
About author:  42.50.Wk; 42.82.Fv; 42.65.Sf; 42.79.Nv

Cite this article: 

Yu-long Liu(刘玉龙), Chong Wang(王冲), Jing Zhang(张靖), Yu-xi Liu(刘玉玺) Cavity optomechanics: Manipulating photons and phonons towards the single-photon strong coupling 2018 Chin. Phys. B 27 024204

[1] Kippenberg T J and Vahala K J 2008 Science 321 5893
[2] Aspelmeyer M and Painter O J 2012 Physics Today 65 29
[3] Aspelmeyer M, Kippenberg T J and Marquardt F 2013 Rev. Mod. Phys. 86 1391
[4] Liu Y C, Hu Y W, Wong C W and Xiao Y F 2014 Chin. Phys. B 22 114213
[5] Rogers B, Gullo N L, Chiara G D, Palma G M and Paternostro M 2014 Quantum Meas. Quantum Metrol. 2 11
[6] Yin Z Q, Zhao N and Li T C 2015 Sci. China-Phys. Mech. Astron. 58 1
[7] Wallquist M, Hammerer K, Rabl P, Lukin M and Zoller P 2009 Phys. Scr. 137 014001
[8] Li P B, Liu Y C, Gao S Y, Xiang Z L, Rabl P, Xiao Y F and Li F L 2015 Phys. Rev. Appl. 4 044003
[9] Agarwal G S and Huang S M 2010 Phys. Rev. A 81 041803
[10] Fan L, Fong K Y, Poot M and Tang H X 2015 Nat. Commun. 6 5850
[11] Massel F, Cho S U, Pirkkalainen J M, Heikkilä T T and Sillanpää M A 2012 Nat. Commun. 3 987
[12] Safavi-Naeini A H, Alegre T P M, Chan J, Eichenfield M, Winger M, Lin Q, Hill J T, Chang D E and Painter O 2011 Nature 472 69
[13] Singh V, Bosman S J, Schneider B H, Blanter Y M, Castellanos-Gomez A and Steele G A 2014 Nat. Nanotechnol. 9 820
[14] Jia W Z, Wei L F, Li Y and Liu Y X 2015 Phys. Rev. A 91 043843
[15] Xu X W and Li Y X 2015 Phys. Rev. A 92 023855
[16] Jiang C, Cui Y, Bian X, Li X and Chen G 2016 Chin. Phys. B 25 054204
[17] Dong C H, Shen Z, Zou C L, Zhang Y L, Fu W and Guo G C 2015 Nat. Commun. 6 6193
[18] Ruesink F, Miri M A, Alú A and Verhagen E 2016 Nat. Commun. 7 13662
[19] Manipatruni S, Robinson J T and Lipson M 2009 Phys. Rev. Lett. 102 213903
[20] Liu L, Yue J and Li Z 2017 IEEE Photon. J. 9 1
[21] Kim J H, Kim S and Bahl G 2017 Sci. Rep. 7 1647
[22] Qiu H, Dong J, Liu L and Zhang X 2017 Opt. Express 25 8975
[23] Shen Z, Zhang Y L, Chen Y, Zou C L, Xiao Y F, Zou X B, Sun F W, Guo G C and Dong C H 2016 Nat. Photon. 10 657
[24] Shakeri S, Zandi M H and Bahrampour A 2017 J. Mod. Opt. 64 507
[25] Kim J H, Kuzyk M C, Han K, Wang H and Bahl G 2015 Nat. Phys. 11 275
[26] Xu X W, Li Y, Chen A X and Liu Y X 2016 Phys. Rev. A 93 023827
[27] Li Y, Huang Y Y, Zhang X Z and Tian L 2017 Opt. Express 25 18907
[28] Xu X W and Li Y 2015 Phys. Rev. A 91 053854
[29] Miri M A, Ruesink F, Verhagen E and Alú A 2017 Phys. Rev. Appl. 7 064014
[30] Wang Z, Shi L, Liu Y, Xu X and Zhang X 2015 Sci. Rep. 5 8657
[31] Hafezi M and Rabl P. 2012 Opt. Express 20 7672
[32] Potton R J 2004 Rep. Prog. Phys. 67 717
[33] Liu Y C, Li B B and Xiao Y F 2017 Nanophotonics 10 1515
[34] Liu L, Yang Y, Li Z, Jin X, Mo W and Liu X 2017 Opt. Express 25 960
[35] Liu L, Chen Z, Jin X, Yang Y, Yu Z, Zhang J, Zhang L and Wang H 2017 Opt. Express 25 17329
[36] Peterson G A, Lecocq F, Cicak K, Simmonds R W, Aumentado J and Teufel J D 2017 Phys. Rev. X 7 031001
[37] Hossein-Zadeh M and Vahala K J 2007 Opt. Lett. 32 1611
[38] Lin Q, Rosenberg J, Chang D, Camacho R, Eichenfield M, Vahala K J and Painter O 2010 Nat. Photon. 4 236
[39] Shkarin A B, Flowers-Jacobs N E, Hoch S W, Kashkanova A D, Deutsch C, Reichel J and Harris J G E 2014 Phys. Rev. Lett. 112 013602
[40] Spethmann N, Kohler J, Schreppler S, Buchmann L and Stamper-Kurn D M 2016 Nat. Phys. 12 27
[41] Fang K, Matheny M H, Luan X and Painter O 2015 arXiv preprint arXiv:1508.05138
[42] Xu X W, Liu Y, Sun C P and Li Y 2015 Phys. Rev. A 92 013852
[43] Habraken S J M, Stannigel K, Lukin M D, Zoller, P and Rabl P 2012 New J. Phys. 14 115004
[44] Zhang J, Peng B, Özdemir Ş K, Liu Y X, Jing H, Lü X, Liu Y L, Yang L and Nori F 2015 Phys. Rev. B 92 115407
[45] Kim S, Xu X, Taylor J M and Bahl G 2017 Nat. Commun. 8 205.
[46] Fang K, Matheny M H, Luan X and Painter, O 2016 Nat. Photon. 10 489
[47] Fleury R, Sounas D L, Sieck C F, Haberman M R and Alú A 2014 Science 343 516
[48] Gavartin E, Verlot P and Kippenberg T J 2012 Nat. Nanotechnol. 7 509
[49] Balram K C, Davanço M I, Song J D and Srinivasan K 2016 Nat. Photon. 10 346
[50] Hill J T, Safavi-Naeini A H, Chan J and Painter O 2012 Nat. Commun. 3 1196
[51] Liu Y X, Davanço M, Aksyuk V and Srinivasan K 2013 Phys. Rev. Lett. 110 223603
[52] Zhao C, Fang Q, Susmithan S, Miao H, Ju L, Fan Y, Blair D, Hosken D J, Munch J, Veitch P J and Slagmolen B J J 2011 Phys. Rev. A 84 063836
[53] Bagci T, Simonsen A, Schmid S, Villanueva L G, Zeuthen E, Appel J, Taylor J M, Sorensen A, Usami K, Schliesser A and Polzik E S 2014 Nature 507 81
[54] Tian L and Wang H 2010 Phys. Rev. A 82 053806
[55] Dong C, Fiore V, Kuzyk M C, Tian L and Wang H 2015 Ann. Phys. 527 100
[56] Notomi M, Taniyama H, Mitsugi S and Kuramochi E 2006 Phys. Rev. Lett. 97 023903
[57] Ockeloen-Korppi C F, Damskägg E, Pirkkalainen J M, Heikkilä, T T, Massel F and Sillanpää M A 2016 Phys. Rev. X 6 041024
[58] Braginsky V B and Khalili F Y 1965 Quantum Measurement (England:Cambridge University Press) 1992
[59] Ockeloen-Korppi C F, Damskägg E, Pirkkalainen J M, Clerk A A, Woolley M J and Sillanpää M A 2016 Phys. Rev. Lett. 117 140401
[60] Caves C M 1981 Phys. Rev. D 23 1693
[61] Unruh W G 1982 Quantum Optics, Experimental Gravitation and Measurement Theory, eds. Meystre P and Scully M O (New York:Plenum), p. 647
[62] Jaekel M T and Reynaud S 1990 Europhys. Lett. 13 301
[63] Kimble H J, Levin Y, Matsko A B, Thorne K S and Vyatchanin S P 2001 Phys. Rev. D 65 022002
[64] Harms J, Chen Y, Chelkowski S, Franzen A, Vahlbruch H, Danzmann K and Schnabel R 2003 Phys. Rev. D 68 042001
[65] Corbitt T, Chen Y, Khalili F, Ottaway D, Vyatchanin S, Whitcomb S and Mavalvala N 2006 Phys. Rev. A 73 023801
[66] Gong Z R, Ian H, Liu Y, Sun C P and Nori F 2009 Phys. Rev. A 80 065801
[67] Aldana S, Bruder C and Nunnenkamp A 2013 Phys. Rev. A 88 043826
[68] Brooks D W C, Botter T, Schreppler S, Purdy T P, Brahms N and Stamper-Kurn D M 2012 Nature 488 476
[69] Kilda D and Nunnenkamp A 2016 J. Opt. 18 014007
[70] Safavi-Naeini A H, Gröblacher S, Hill J T, Chan J, Aspelmeyer M and Painter O 2013 Nature 500 185
[71] Purdy T P, Yu P L, Peterson R W, Kampel N S and Regal C A 2013 Phys. Rev. X 3 031012
[72] Fabre C, Pinard M, Bourzeix S, Heidmann A, Giacobino E and Reynaud S 1994 Phys. Rev. A 149 1337
[73] Mancini S and Tombesi P 1994 Phys. Rev. A 49 4055
[74] Wollman E E, Lei C U, Weinstein A J, Weinstein A J, Suh J, Kronwald A, Marquardt F, Clerk A A and Schwab K C 2015 Science 349 952
[75] Safavi-Naeini A H, Chan J, Hill J T, Alegre T P M, Krause A and Painter O 2012 Phys. Rev. Lett. 108 033602
[76] Tan H, Li G and Meystre P 2013 Phys. Rev. A 87 033829
[77] Pirkkalainen J M, Damskägg E, Brandt M, Brandt M, Massel F and Sillanpää M A 2015 Phys. Rev. Lett. 115 243601
[78] Marquardt F, Chen J P, Clerk A A and Girvin S M 2007 Phys. Rev. Lett. 99 093902
[79] Wilson-Rae I, Nooshi N, Zwerger W and Kippenberg T J 2007 Phys. Rev. Lett. 99 093901
[80] Wilson-Rae I, Nooshi N, Dobrindt J, Kippenberg T J and Zwerger W 2008 New J. Phys. 10 095007
[81] Grajcar M, Ashhab S, Johansson J R and Nori F 2008 Phys. Rev. B 78 035406
[82] Bhattacharya M and Meystre P 2007 Phys. Rev. Lett. 99 073601
[83] Alkan S S and Braun D G 2011 Phys. Rev. Lett. 107 273601
[84] Genes C, Vitali D, Tombesi P, Gigan S and Aspelmeyer M 2008 Phys. Rev. A 77 033804
[85] Xue F, Wang Y D and Liu Y X and Nori F 2007 Phys. Rev. B 76 205302
[86] Li Y, Wang Y D, Xue F and Bruder C 2008 Phys. Rev. B 78 134301
[87] Li Y, Wu L A and Wang Z D 2011 Phys. Rev. A 83 043804
[88] Gröblacher S, Hertzberg J B, Vanner M R, Cole G D, Gigan S, Schwab K C and Aspelmeyer M 2009 Nat. Phys. 5 485
[89] Park Y S and Wang H 2009 Nat. Phys. 5 489
[90] Schliesser A, Arcizet O, Riviére R, Anetsberger G and Kippenberg T J 2009 Nat. Phys. 5 509
[91] Schliesser A, Riviére R, Anetsberger G, Arcizet O and Kippenberg T J 2008 Nat. Phys. 4 415
[92] Liu Y C, Xiao Y F, Luan X and Wong C W 2013 Phys. Rev. Lett. 110 153606
[93] Liu Y C, Shen Y F, Gong Q Gong and Xiao Y F 2014 Phys. Rev. A 89 053821
[94] Liu Y L and Liu Y X 2017 Phys. Rev. A 96 023812
[95] Guo Y, Li K, Nie W and Li Y 2014 Phys. Rev. A 90 053841
[96] Li Y, Wu L A, Wang Y D and Yang L P 2011 Phys. Rev. B 84 094502
[97] Poot M, Fong K Y, Bagheri M, Pernice W H P and Tang H X 2012 Phys. Rev. A 86 1844
[98] Zhang L and Kong H Y 2014 Phys. Rev. A 89 023847
[99] Gao M, Lei F C, Du C G and Long G L 2015 Phys. Rev. A 91 013833
[100] Grudinin I S, Lee H, Painter O and Vahala K J 2010 Phys. Rev. Lett. 104 083901
[101] Wu H, Heinrich G and Marquardt F 2013 New J. Phys. 15 123022
[102] Lörch N and Hammerer K 2015 Phys. Rev. A 91 061803
[103] Cohen J D, Meenehan S M, Maccabe G S, Gröblacher S, Safavi-Naeini A H, Marsili F, Shaw M D and Painter O 2015 Nature 520 522
[104] Hong S, Riedinger R, Marinkovié I, Wallucks A, Hofer S G, Norte R A, Aspelmeyer M and Gröblacher S 2017 Science 358 203
[105] Palomaki T A, Teufel J D, Simmonds R W and Lehnert K W 2013 Science 342 710
[106] Riedinger R, Hong S, Norte R A, Slater J A, Shang J, Krause A G, Anant V, Aspelmeyer M and Gröblacher S 2016 Nature 530 313
[107] Purdy T P, Grutter K E, Srinivasan K and Taylor J M 2017 Science 356 1265
[108] Palomaki T A, Harlow J W, Teufel J D, Simmonds R W and Lehnert K W 2013 Nature 495 210
[109] Bochmann J, Vainsencher A, Awschalom D D and Cleland A N 2013 Nat. Phys. 9 712
[110] McGee S A, Meiser D, Regal C A, Lehnert K W and Holland M J 2013 Phys. Rev. A 87 053818
[111] Andrews R W, Peterson R W, Purdy T P, Cicak K, Simmonds R W, Regal C A and Lehnert K W 2014 Nat. Phys. 10 321
[112] Tian L 2012 Phys. Rev. Lett. 108 153604
[113] Jing H, Cheng J and Meystre P 2007 Phys. Rev. Lett. 99 133002
[114] Singh S, Jing H, Wright E M and Meystre P 2012 Phys. Rev. A 86 021801
[115] Sete E A and Eleuch H 2015 Phys. Rev. A 91 032309
[116] Sete E A, Eleuch H and Ooi C H R 2014 J. Opt. Soc. Am. B 31 002821
[117] Tian L 2015 Ann. Phys. 527 1
[118] Rakhubovsky A A and Filip R 2017 Sci. Rep. 7 46764
[119] Safavi-Naeini A H and Painter O 2011 New J. Phys. 13 013017
[120] De Moraes Neto G D, Andrade F M, Montenegro V and Bose S 2016 Phys. Rev. A 93 062339
[121] Barzanjeh S, Abdi M, Milburn G J, Tombesi P and Vitali D 2012 Phys. Rev. Lett. 109 130503
[122] Wang Y D and Clerk A A 2012 Phys. Rev. Lett. 108 153603
[123] Dong C, Wang Y and Wang H 2015 Natl. Sci. Rev. 2 510
[124] Xiong H, Si L G, Lv X Y, Yang X X and Wu Y 2015 Sci. China-Phys. Mech. Astron. 58 050302
[125] Zhang W Z, Cheng J, Liu J Y and Zhou L 2015 Phys. Rev. A 91 063836
[126] Brennecke F, Ritter S, Donner T and Esslinger T 2008 Science 322 235
[127] Liu Y L, Liu Z P and Zhang J 2015 J. Phys. B 48 105501
[128] Xu X W and Li Y J 2013 J. Phys. B 46 035502
[129] Kyriienko O, Liew T C H and Shelykh I A 2014 Phys. Rev. Lett. 112 076402
[130] Liu Y L, Wu R, Zhang J, Özdemir Ş K, Yang L, Nori F and Liu Y X 2017 Phys. Rev. A 95 013843
[131] Marquardt F, Harris J G E and Girvin S M 2006 Phys. Rev. Lett. 96 103901
[132] Mueller F, Heugel S and Wang L J 2009 Phys. Rev. A 79 031804
[133] Dong Y, Ye J and Pu H 2011 Phys. Rev. A 83 031608
[134] Ludwig M, Kubala B and Marquardt F 2008 New J. Phys. 10 095013
[135] Chang Y, Shi T, Liu Y X, Sun, C P and Nori F 2011 Phys. Rev. A 83 063826
[136] Mueller F, Heugel S and Wang L J 2008 Phys. Rev. A 77 031802
[137] Carmon T, Cross M C and Vahala K J 2007 Phys. Rev. Lett. 98 167203
[138] Bakemeier L, Alvermann A and Fehske H 2015 Phys. Rev. Lett. 114 013601
[139] Lü X Y, Jing H, Ma J Y and Wu Y 2015 Phys. Rev. Lett. 114 253601
[140] Xiong H, Si L G, Zheng A S, Yang X and Wu Y 2012 Phys. Rev. A 86 013815
[141] Li W, Jiang Y, Li C and Song H 2016 Sci. Rep. 6 31095
[142] Cao C, Mi S C, Gao Y P, He L Y, Yang D, Wang T J, Zhang R and Wang C 2016 Sci. Rep. 6 22920
[143] Jing H, Özdemir Ş K, Geng Z, Geng Z, Zhang J, Lü X Y, Peng B, Yang L and Nori Franco 2015 Sci. Rep. 5 9663
[144] Wang C, Chen H J and Zhu K D 2015 Appl. Opt. 54 4623
[145] Schönleber D W, Eisfeld A and El-Ganainy R 2016 New J. Phys. 18 045014
[146] Lemonde M A, Didier N and Clerk A A. 2013 Phys. Rev. Lett. 111 053602
[147] Borkje K, Nunnenkamp A, Teufel J D and Girvin S M 2013 Phys. Rev. Lett. 111 053603
[148] Kronwald A and Marquardt F 2013 Phys. Rev. Lett. 111 133601
[149] Ma J, You C, Si L G, Xiong H, Li J, Yang X and Wu Y 2015 Sci. Rep. 5 11278
[150] Xiong H, Si L G, Lü X Y, Yang X and Wu Y 2014 Ann. Phys. 349 43
[151] Xiong H, Si L G, Lü X Y, Yang X and Wu Y 2013 Opt. Lett. 38 353
[152] Jiao Y, Lü H, Qian J, Li Y and Jing H 2016 New J. Phys. 18 083034
[153] Monifi F, Zhang J, Özdemir Ş K, Peng B, Liu Y X, Bo F, Nori F and Yang L 2016 Nat. Photon. 10 399
[154] Li W, Li C and Song H 2015 J. Phys. B 48 035503
[155] Heinrich G, Ludwig M, Qian J, Kubala B and Marquardt F 2011 Phys. Rev. Lett. 107 043603
[156] Zhang M, Wiederhecker G S, Manipatruni S, Barnard A, McEuen P and Lipson M 2012 Phys. Rev. Lett. 109 233906
[157] Bagheri M, Poot M, Fan L, Marquardt F and Tang H X 2013 Phys. Rev. Lett. 111 213902
[158] Weiss T, Kronwald A and Marquardt F 2016 New J. Phys. 18 013043
[159] Ludwig M and Marquardt F 2013 Phys. Rev. Lett. 111 073603
[160] Shlomi K, Yuvaraj D, Baskin I, Suchoi O, Winik R and Buks E 2015 Phys. Rev. E 91 032910
[161] Li W, Li C and Song H 2016 Phys. Rev. E 93 062221
[162] Walter S, Nunnenkamp A and Bruder C 2014 Phys. Rev. Lett. 112 094102
[163] Zhang M, Shah S, Cardenas J and Lipson M 2015 Phys. Rev. Lett. 115 163902
[164] Li T, Bao T Y, Zhang Y L, Zou C L, Zou X B and Guo G C 2016 Opt. Express 24 12336
[165] Gil-Santos E, Labousse M, Baker C, Goetschy A, Hease W, Gomez C, Lematre A, Leo G, Ciuti C and Favero I 2017 Phys. Rev. Lett. 118 063605
[166] Li W, Li C and Song H 2017 Phys. Rev. E 95 022204
[167] Holmes C A, Meaney C P and Milburn G J 2012 Phys. Rev. E 85 066203
[168] Yin X F, Zhang W Z and Zhou L 2017 J. Mod. Opt. 64 578
[169] Liao J Q and Law C K 2013 Phys. Rev. A 87 043809
[170] Liao J Q, Cheung H K and Law C K 2012 Phys. Rev. A 85 025803
[171] Liao J Q, Jacobs K, Nori F and Simmonds R W 2014 New J. Phys. 16 072001
[172] Liao J Q and Nori F 2014 Phys. Rev. A 90 023851
[173] Marshall W, Simon C, Penrose R and Bouwmeester D 2003 Phys. Rev. Lett. 91 130401
[174] Xu X W, Wang H, Zhang J and Liu Y X 2013 Phys. Rev. A 88 063819
[175] Xu X W, Zhao Y J and Liu Y X 2013 Phys. Rev. A 88 022325
[176] Wang H, Wang Z, Zhang J, Özdemir Ş K, Yang L and Liu Y X 2014 Phys. Rev. A 90 053814
[177] Jing H, Özdemir Ş K, Lü X Y, Zhang J, Yang L and Nori F 2014 Phys. Rev. Lett. 113 053604
[178] Xu X W, Li Y J and Liu Y X 2013 Phys. Rev. A 87 025803
[179] Komar P, Bennett S D, Stannigel K, Habraken S J M, Rabl P, Zoller P and Lukin M D 2013 Phys. Rev. A 87 013839
[180] Wang H, Gu X, Liu Y X, Miranowicz A and Nori F 2015 Phys. Rev. A 92 033806
[181] Wang H, Gu X, Liu Y X, Miranowicz A and Nori F 2014 Phys. Rev. A 90 023817
[182] Xu X W and Li Y 2014 Phys. Rev. A 90 033809
[183] Xu X W and Li Y 2014 Phys. Rev. A 90 033832
[184] Ramos T, Sudhir V, Stannigel K, Zoller P and Kippenberg T J 2013 Phys. Rev. Lett. 110 193602
[185] Miranowicz A, Bajer J, Lambert N, Liu Y X and Nori F 2016 Phys. Rev. A 93 013808
[186] Soykal Ö O and Tahan C. 2013 Phys. Rev. B 88 134511
[187] Wang X, Miranowicz A, Li H R and Nori F 2016 Phys. Rev. A 93 063861
[188] Xie H, Liao C G, Shang X, Ye M Y and Lin X M 2017 Phys. Rev. A 96 013861
[189] Gao M, Lei F, Du C and Long G 2016 Sci. China-Phys. Mech. Astron. 59 610301
[190] Macrí V, Garziano L, Ridolfo A, Stefano O D and Savasta S 2016 Phys. Rev. A 94 013817
[191] Liao J, Law C K, Kuang L and Nori F 2015 Phys. Rev. A 92 013822
[192] Galland C, Sangouard N, Piro N, Gisin N and Kippenberg T J 2014 Phys. Rev. Lett. 112 143602
[193] Ren X, Li H, Yan M, Liu Y, Xiao Y and Gong Q 2013 Phys. Rev. A 87 033807
[194] Ng K H and Law C K 2016 Phys. Rev. A 93 043834
[195] Ridolfo A, Leib M, Savasta S and Hartmann M J, Photon Blockade in the Ultrastrong Coupling Regime 2012 Phys. Rev. Lett. 109 193602
[196] Shakeri S, Mahmoudi Z, Zandi M H, Bahrampour A R 2016 Opt. Commun. 370 55
[197] Yan Y, Zhu J and Li G 2016 Opt. Express 24 13590
[198] Garziano L, Stassi R, Macrí V, Savasta S and Stefano O D 2015 Phys. Rev. A 91 023809
[199] Mahmoudi Z, Shakeri S, Hamidi O, Zandi M H and Bahrampour A 2015 J. Mod. Opt. 62 1685
[200] Damskägg E, Pirkkalainen J and Sillanpää M A 2016 J. Opt. 18 104003
[201] Gangat A A, Stace T M and Milburn G J 2011 New J. Phys. 13 043024
[202] Basiri-Esfahani S, Akram U and Milburn G J 2012 New J. Phys. 14 085017
[203] Clerk A A, Marquardt F and Harris J G E 2010 Phys. Rev. Lett. 104 213603
[204] Barzanjeh S and Vitali D 2016 Phys. Rev. A 93 033846
[205] Xu X W, Chen A X and Liu Y X 2017 Phys. Rev. A 96 023832
[206] Law C K 1995 Phys. Rev. A 51 2537
[207] Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243
[208] Bender C M, Gianfreda M, Özdemir Ş K, Peng B and Yang L 2013 Phys. Rev. A 88 062111
[209] El-Ganainy R, Makris K G, Christodoulides D N and Musslimani Z H 2007 Opt. Lett. 32 2632
[210] Ramezani H, Kottos T, El-Ganainy R and Christodoulides D N 2010 Phys. Rev. A 82 043803
[211] Li G and Ramy E G 2016 Sci. Rep. 6 24889
[212] Peng B, Özdemir Ş K, Rotter S, Yilmaz H, Liertzer M, Monifi F, Bender C M, Nori F and Yang L 2014 Science 346 328
[213] Peng B, Özdemir Ş K, Lei F, Monifi F, Gianfreda M, Long G L, Fan S, Nori F, Bender C M and Yang L 2014 Nat. Phys. 10 394
[214] Bender C M, Brody D C and Jones H F 2002 Phys. Rev. Lett. 89 270401
[215] Bender C M, Brody D C and Jones H F and Meister B K 2007 Phys. Rev. Lett. 98 040403
[216] Liu Z P, Zhang J, Özdemir Ş K, Peng B, Jing H, Lü X Y, Li C W, Yang L, Nori F and Liu Y X 2016 Phys. Rev. Lett. 117 110802
[217] Lü X Y, Wu Y, Johansson J R, Jing H, Zhang J and Nori F 2015 Phys. Rev. Lett. 114 093602
[218] Huang S and Agarwal G S 2009 Phys. Rev. A 79 013821
[219] Degenfeld-Schonburg P, Abdi M, Hartmann M J and Navarrete-Benlloch C 2016 Phys. Rev. A 93 023819
[220] Shahidani S, Naderi M H and Soltanolkotabi M 2013 Phys. Rev. A 88 053813
[221] Li Ling, Nie W J and Chen A X 2016 Sci. Rep. 6 35090
[222] Yang R G, Li N, Zhang J, Li J and Zhang T C 2017 J. Phys. B:At. Mol. Opt. Phys. 50 085502
[223] Zhang D and Zheng Q 2013 Chin. Phys. Lett. 30 024213
[224] Lemonde M A, Didier N and Clerk A A 2014 Phys. Rev. A 33 2230
[225] Poot M, Fong K Y and Tang H X 2014 Phys. Rev. A 90 063809
[226] Koashi M, Kono K, Hirano T and Matsuoka M 1993 Phys. Rev. Lett. 71 1164
[227] Lu Y J and Ou Z Y 2001 Phys. Rev. Lett. 88 023601
[228] Grosse N B, Symul T, Stobińska M, Ralph T C and Lam P K 2007 Phys. Rev. Lett. 98 153603
[229] Li P B, Li H R and Li F L 2016 Sci. Rep. 6 19065
[230] Cirac J I, Parkins A S, Blatt R and Zoller P 1993 Phys. Rev. Lett. 70 556
[231] Rabl P, Shnirman A and Zoller P 2004 Phys. Rev. B 70 205304
[232] Parkins A S, Solano E and Cirac J I 2006 Phys. Rev. Lett. 96 053602
[233] Dalla Torre E G, Otterbach J, Demler E, Vuletic V and Lukin M D 2013 Phys. Rev. Lett. 110 120402
[234] Didier N, Qassemi F and Blais A 2014 Phys. Rev. A 89 013820
[235] Kronwald A, Marquardt F and Clerk A A 2013 Phys. Rev. A 88 063833
[236] Lemonde M A, Didier N, Clerk A A 2016 Nat. Commun. 7 11338
[237] Pirkkalainen J -M, Cho S U, Massel F, Tuorila J, Heikkilä T T, Hakonen P J and Sillanpää M A 2015 Nat. Commun. 6 6981
[238] Wang H, Sun H, Zhang J and Liu Y X 2012 Sci. China-Phys. Mech. Astron. 55 2264
[239] Heikkilä T T, Massel F, Tuorila J, Khan R and Sillanpää M A 2014 Phys. Rev. Lett. 112 203603
[240] Rimberg A J, Blencowe M P, Armour A D and Nation P D 2014 New J. Phys. 16 055008
[241] Sun C P, Wei L F, Liu Y X and Nori F 2006 Phys. Rev. A 73 022318
[242] Buks E, Zaitsev S, Segev E, Abdo B and Blencowe M P 2007 Phys. Rev. E 76 026217
[243] Zhang J, Liu Y X and Nori F 2009 Phys. Rev. A 79 052102
[244] Pirkkalainen J M, Cho S U, Li J, Paraoanu G S, Hakonen P J and Sillanpää M A 2013 Nature 494 211
[245] Kim E, Johansson J R and Nori F 2015 Phys. Rev. A 91 033835
[246] Johansson J R, Johansson G and Nori F 2014 Phys. Rev. A 90 053833
[247] Georgescu I M, Ashhab S and Nori F 2014 Rev. Mod. Phys. 86 153
[248] Gu X, Kockum A F, Miranowicz A, Liu Y X and Nori F 2017 Phys. Rep. 718 1
[249] Forn-Díaz P, García-Ripoll J J, Peropadre B, Orgiazzi J L, Yurtalan M A, Belyansky R, Wilson C M and Lupascu A 2017 Nat. Phys. 13 39
[250] Beaudoin F, Gambetta J M and Blais A 2011 Phys. Rev. A 84 043832
[251] Garziano L, Macrí V, Stassi R, Di Stefano O, Nori F and Savasta S 2016 Phys. Rev. Lett. 117 043601
[252] Di Stefano O, Stassi R, Garziano L, Kockum A F, Savasta S and Nori F 2017 New J. Phys. 19 053010
[253] Garziano L, Stassi R, Macrí V, Kockum A F, Savasta S and Nori F 2015 Phys. Rev. A 92 063830
[254] Garziano L, Ridolfo A, Stassi R, Di Stefano O and Savasta S 2013 Phys. Rev. A 88 063829
[255] Cirio M, Debnath K, Lambert N and Nori F 2017 Phys. Rev. Lett. 119 053601
[256] Johansson J R, Johansson G, Wilson C M and Nori F 2009 Phys. Rev. Lett. 103 147003
[257] Johansson J R, Johansson G, Wilson C M and Nori F 2010 Phys. Rev. A 82 052509
[258] Wilson C M, Johansson G, A Pourkabirian, Simoen M, Johansson J R, Duty T, Nori F, Delsing P 2011 Nature 479 376
[259] Liu X F, Li Y and Jing H 2016 Sci. Rep. 6 27102
[260] Nie W, Lan Y, Li Y and Zhu S 2013 Phys. Rev. A 88 063849
[261] Nie W, Lan Y, Li Y and Zhu S 2012 Phys. Rev. A 86 063809
[262] Xuereb A, Genes C and Dantan A 2012 Phys. Rev. Lett. 109 223601
[263] Xuereb A, Genes C and Dantan A 2013 Phys. Rev. A 88 053803
[264] García P D, Bericat-Vadell R, Arregui G, Navarro-Urrios D, Colombano M, Alzina F and Sotomayor-Torres C M 2017 Phys. Rev. B 95 115129
[265] Xia K and Twamley J 2015 arXiv preprint arXiv:1506.06315
[266] Nation P D, Suh J and Blencowe M P 2016 Phys. Rev. A 93 022510
[267] Hu D, Huang S, Liao J, Tian L and Goan H 2015 Phys. Rev. A 91 013812
[268] Blencowe M P and Buks E 2007 Phys. Rev. B 76 014511
[269] Nation P D, Blencowe M P and Buks E 2008 Phys. Rev. B 78 104516
[270] Etaki S, Poot M, Mahboob I, Onomitsu K, Yamaguchi H and Van der Zant H S J 2008 Nat. Phys. 4 785
[271] Poot M, Etaki S, Mahboob I, Onomitsu K, Yamaguchi H, Blanter Y M and Van der Zant H S J 2010 Phys. Rev. Lett. 105 207203
[272] Via G, Kirchmair G and Romero-Isart O 2015 Phys. Rev. Lett. 114 143602
[273] Lü X Y, Zhang W M, Ashhab S, Wu Y and Nori F 2013 Sci. Rep. 3 2943
[274] Genes C, Xuereb A, Pupillo G and Dantan A 2013 Phys. Rev. A 88 033855
[275] Li G, Wang T and Song H S 2014 Phys. Rev. A 90 013827
[276] Ludwig M, Safavi-Naeini A H, Painter O and Marquardt F 2012 Phys. Rev. Lett. 109 063601
[277] Stannigel K, Komar P, Habraken S J M, Bennett S D, Lukin M D, Zoller P and Rabl P 2012 Phys. Rev. Lett. 109 013603
[278] Liu Y L, Wang G Z, Liu Y X and Nori F 2016 Phys. Rev. A 93 013856
[279] Dorsel A, McCullen J D, Meystre P, Vignes E and Walther H 1983 Phys. Rev. Lett. 51 1550
[280] Hadjar Y, Cohadon P F, Aminoff C G, Pinard M and Heidmann A 1999 Europhys. Lett. 47 545
[281] Cohadon P F, Heidmann A and Pinard M 1999 Phys. Rev. Lett. 83 3174
[282] Tittonen I, Breitenbach G, Kalkbrenner T, Müller T, Conradt R, Schiller S, Steinsland E, Blanc N and de Rooij N F 1999 Phys. Rev. A 59 1038
[283] Arcizet O, Cohadon P F, Briant T, Pinard M and Heidmann A 2006 Nature 444 71
[284] Gigan S, Böhm H R, Paternostro M, Blaser F, Langer G, Hertzberg J B, Schwab K C, Bäuerle D, Aspelmeyer M and Zeilinger A 2006 Nature 444 67
[285] Kleckner D and Bouwmeester D 2006 Nature 444 75
[286] Corbitt T, Chen Y, Innerhofer E, Müller-Ebhardt H, Ottaway D, Rehbein H, Sigg D, Whitcomb S, Wipf C and Mavalvala N 2007 Phys. Rev. Lett. 98 150802
[287] Groeblacher S, Gigan S, Böhm H R, Zeilinger A and Aspelmeyer M 2008 Europhys. Lett. 81 54003
[288] Gröblacher S, Hertzberg J B, Vanner M R, Cole G D, Gigan S, Schwab K C and Aspelmeyer M 2009 Nat. Phys. 5 485
[289] Gröblacher S, Hammerer K, Vanner M R and Aspelmeyer M 2009 Nature 460 724
[290] Vanner M R, Pikovski I, Cole G D, Kimb M S, Brukner Č, Hammererc K, Milburne G J and Aspelmeyer M 2011 Proc. Natl. Acad. Sci. 108 16182
[291] Vanner M R, Hofer J, Cole G D and Aspelmeyer M 2013 Nat. Commun. 14 115018
[292] Wieczorek W, Hofer S G, Hoelscherobermaier J, Riedinger R, Hammerer K and Aspelmeyer M 2015 Phys. Rev. Lett. 114 223601
[293] Thompson J D, Zwickl B M, Jayich A M, Marquardt F, Girvin S M and Harris J G E 2008 Nature 452 72
[294] Sankey J C, Yang C, Zwickl B M, Jayich A M and Harris J G 2010 Nat. Phys. 6 707
[295] Jayich A M, Sankey J C, Borkje K, Lee D, Yang C, Underwood M, Childress L, Petrenko A, Girvin S M and Harris J G E 2012 New J. Phys. 14 115018
[296] Underwood M, Mason D, Lee D, Xu H, Jiang L, Shkarin A B, Borkje K, Girvin S M and Harris J G E 2015 Phys. Rev. A 92 061801
[297] Peterson R W, Purdy T P, Kampel N S, Andrews R W, Yu P L, Lehnert K W and Regal C A 2016 Phys. Rev. Lett. 116 063601
[298] Camerer S, Korppi M, Jöckel A, Hunger D, Hänsch T W and Treutlein P 2011 Phys. Rev. Lett. 107 223001
[299] Jöckel A, Faber A, Kampschulte T, Korppi M, Rakher M T and Treutlein P 2015 Nat. Nanotechnol. 10 55
[300] Karuza M, Biancofiore C, Bawaj M, Molinelli C, Galassi M, Natali R, Tombesi P, Giuseppe G Di and Vitali D 2013 Phys. Rev. A 88 013804
[301] Xu H, Mason D, Jiang L, Xu and Harris J G E 2016 Nature 537 80
[302] Brückner F, Friedrich D, Clausnitzer T, Britzger M, Burmeister O, Danzmann K, Kley E B, Tünnermann A and Schnabel R 2010 Phys. Rev. Lett. 104 163903
[303] Kuhn A G, Bahriz M, Ducloux O, Chartier C, Le Traon O, Briant T, Cohadon P F, Heidmann A, Michel C, Pinard L and Flaminio R 2011 Appl. Phys. Lett. 99 121103
[304] Tsvirkun V, Surrente A, Raineri F, Beaudoin G, Raj R, Sagnes I, Robert-Philip I and Braive R 2011 Sci. Rep. 5 16526
[305] Woolf D, Hui P C, Iwase E, Khan M, Rodriguez A W, Deotare P, Bulu I, Johnson S G, Capasso F and Loncar M 2013 Opt. Express 21 7258
[306] Shimizu W, Nagai N, Kohno K, Hirakawa K and Nomura M 2013 Opt. Express 21 21961
[307] Weaver M J, Pepper B, Luna F, Buters M, Eerkens H J, Welker G, Perock B, Heeck K, de Man S and Bouwmeester D 2015 Appl. Phys. Lett. 108 033501
[308] Kleckner D, Pepper B, Jeffrey E, Sonin P, Thon S M and BouwmeesterD 2011 Opt. Express 19 19708
[309] Reinhardt C, Müller T, Bourassa A and Sankey J C 2016 Phys. Rev. X 6 021001
[310] Norte R A, Moura J P and Gröblacher S 2016 Phys. Rev. Lett. 116 147202
[311] Kippenberg T J, Rokhsari H, Carmon T, Scherer A and Vahala K J2005 Phys. Rev. Lett. 95 033901
[312] Verhagen E, Deléglise S, Weis S, Schliesser A and Kippenberg T J 2012 Nature 482 63
[313] Anetsberger G, Rivière R, Schliesser A, Arcizet O and Kippenberg T J 2008 Nat. Photon. 2 627
[314] Jiang X, Lin Q, Rosenberg J, Vahala K and Painter O 2009 Opt. Express 17 20911
[315] Zhang M, Luiz G, Shah S, Wiederhecker G and Lipson M 2014 Appl. Phys. Lett. 105 051904
[316] Shah S Y, Zhang M, Rand R and Lipson M 2015 Phys. Rev. Lett. 114 113602
[317] Wiederhecker G S, Manipatruni S, Lee S and Lipson M 2011 Opt. Express 19 2782
[318] Wiederhecker G S, Chen L, Gondarenko A and Lipson M 2009 Nature 462 633
[319] Bahl G, Kim K H, Lee W, Liu J, Fan X and Carmon T 2013 Nat. Commun. 4 1994
[320] Li H, Chen Y, Noh J, Tadesse S and Li M 2012 Nat. Commun. 3 1091
[321] Santos F G S, Espinel Y A V, Luiz G O, Benevides R S, WiederheckerG S and Alegre T P M 2017 Opt. Express 25 508
[322] Mitchell M, Khanaliloo B, Lake D P, Masuda T, Hadden J P and Barclay P E 2016 Optica 3 963
[323] Chan J, Alegre T M, Safavi-Naeini A H, Hill J T, Krause A, Gröblacher S, Aspelmeyer M and Painter O 2011 Nature 478 89
[324] Eichenfield M, Camacho R, Chan J, Vahala K J and Painter O 2009 Nature 459 550
[325] Eichenfield M, Chan J, Camacho R M, Vahala K J and Painter O 2009 Nature 462 78
[326] Davancço M, Chan J, Safavi-Naeini A H, Painter O and Srinivasan K2012 Opt. Express 20 24394
[327] Safavi-Naeini A H, Hill J T, Meenehan S, Chan J, Gröblacher S and Painter O 2014 Phys. Rev. Lett. 112 153603
[328] Mohammadi S, Eftekhar A A, Khelif A and Adibi A 2010 Opt. Express 18 9164
[329] Chan J, Safavi-Naeini A H, Hill J T, Meenehan S and Painter O 2012 Appl. Phys. Lett. 101 081115
[330] Burek M J, Cohen J D, Meenehan S M, El-Sawah N, Chia C, RuelleT, Meesala S, Rochman J, Atikian H A, Markham M, Twitchen D J,Lukin M D, Painter O and Lončar M 2016 Optica 3 1404
[331] Regal C A, Teufel J D and Lehnert K W 2008 Nat. Phys. 4 555
[332] Hertzberg J B, Rocheleau T, Ndukum T, Savva M, Clerk A A andSchwab K C 2010 Nat. Phys. 6 213
[333] Sulkko J, Sillanpää M A, Häkkinen P, Lechner L, Helle M, Fefferman A, Parpia J and Hakonen P J 2010 Nano Lett. 10 4884
[334] Teufel J D, Li D, Allman M S, Cicak K, Sirois A J, Whittaker J D andSimmonds R W 2011 Nature 471 204
[335] Dieterle P B, Kalaee M, Fink J M and Painter O 2016 Phys. Rev. Appl. 6 014013
[336] Fink J M, Kalaee M, Pitanti A, Norte R, Heinzle L, Davanço M, Srinivasan K and Painter O 2016 Nat. Commun. 7 12396
[337] Kerckhoff J, Andrews R W, Ku H S, Kindel W F, Cicak K, SimmondsR W and Lehnert K W 2013 Phys. Rev. X 3 021013
[338] Clark J B, Lecocq F, Simmonds R W, Aumentado J and Teufel J D2016 Nat. Phys. 12 683
[339] Zhang L and Yang C 2017 arXiv preprint arXiv:1705.04936v3
[340] Asjad M, Zippilli S and Vitali D 2016 Phys. Rev. A 94 051801
[341] Clark J B, Lecocq F, Simmonds R W, Aumentado J and Teufel J D2017 Nature 541 191
[342] Singh V, Bosman S J, Schneider B H, Blanter Y M, Castellanos-GomezA and Steele G A 2014 Nat. Nanotechnol. 9 820
[343] Zhang X, Zou C L, Jiang L, Tang H X 2016 Sci. Adv. 2 e1501286
[344] Roelli P, Galland C, Piro N and Kippenberg T J 2016 Nat. Nanotechnol. 11 164
[345] Kiesel N, Blaser F, Delić U, Grass D, Kaltenbaek R and Aspelmeyer M 2013 Proc. Natl. Acad. Sci. 110 14180
[346] Kashkanova A D, Shkarin A B, Brown C D, Flowers-Jacobs N E, Childress L, Hoch S W, Hohmann L, Ott K, Reichel J and Harris J G E 2017 Nat. Phys. 13 74
[347] Kashkanova A D, Shkarin A B, Brown C D, Flowers-Jacobs N E, Childress L, Hoch S W, Hohmann L, Ott K, Reichel J and Harris J G E 2017 J. Opt. 19 034001
[348] Fong K Y, Poot M and Tang H X 2015 Nano Lett. 15 6116
[349] Harris G I, McAuslan D L, Sheridan E, Sachkou Y, Baker C and BowenW P 2016 Nat. Phys. 12 788
[350] Baker C G, Harris G I, McAuslan D L, Sachkou Y, He X and BowenW P 2016 New J. Phys. 18 123025
[351] Agarwal G S 2014 Phys. Rev. A 90 023812
[352] De Lorenzo L A and Schwab K C 2014 New J. Phys. 16 113020
[353] De Lorenzo L A and Schwab K C 2017 J. Low Temp. Phys. 186 233
[354] Singh S, De Lorenzo L A, Pikovski I and Schwab K C 2017 New J. Phys. 19 073023
[355] Souris F, Christiani H and Davis J P 2017 Appl. Phys. Lett. 111 172601
[356] Souris F, Rojas X, Kim P H and Davis J P 2017 Phys. Rev. Appl. 7 044008
[1] Optomechanical state transfer between two distant membranes in the presence of non-Markovian environments
Jiong Cheng(程泂), Xian-Ting Liang(梁先庭), Wen-Zhao Zhang(张闻钊), Xiangmei Duan(段香梅). Chin. Phys. B, 2018, 27(12): 120302.
No Suggested Reading articles found!