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A model describing optomechanical dynamics via radiation-pressure coupling with a driven optical cavity is investigated by a linearized quantum Langevin equation. The spectrum of the oscillator presents normal mode splitting with the increase of the input laser power in strong coupling regime and our results are in good agreement with the experimental results. The effective mechanical damping and the resonance frequency shift are derived. The redshifted sideband leads to the cooling of the mechanical oscillator, and the blueshifted motional sideband results in amplification. Furthermore, an approximate mechanism is introduced to analyze the cooling of the mechanical oscillator. Since both the normal mode splitting and cooling require working in the resolved sideband regime, whether the normal mode splitting influences the cooling of the mirror is considered. Meanwhile, we give three key factors influencing the cooling of mechanical oscillator, these being initial bath temperature, input laser power and mechanical quality factor.
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Keywords:
- cavity optomechanics /
- radiation pressure /
- normal mode splitting /
- cooling
[1] Aspelmeyer M, Groblacher S, Hammerer K, Kiesel N 2010 J. Opt. Soc. Am. B 27 A189
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[3] [4] Ekinci K L, Yang Y T, Roukes M L 2004 J. Appl. Phys. 95 2682
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[8] Schwab K C, Roukes M L 2005 Phys. Today 58 36
[9] [10] Leggett A J 2002 J. Phys: Condens. Matter 14 R415
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[14] Kippenberg T J, Vahala K J 2008 Science 321 1172
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[28] [29] Wilson-Rae I, Nooshi N, Zwerger W, Kippenberg T J 2007 Phys. Rev. Lett. 99 093901
[30] Marquardt F, Chen J P, Clerk A, Girvin S M 2007 Phys. Rev. Lett. 99 093902
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[36] [37] Wilson-Rae I, Nooshi N, Dobrindt J, Kippenberg T J, Zwerger W 2008 New J. Phys. 10 095007
[38] Metzger C H, Karrai K 2004 Nature 432 1002
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[44] [45] Park Y S, Wang H L 2009 Nat. Phys. 5 489
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[48] Tian L 2009 Phys. Rev. B 79 193407
[49] [50] [51] Grlacher S, Hammerer K, Vanner M R, Aspelmeyer M 2009 Nature 460 724
[52] Dobrindt J M, Wilson-Rae I, Kippenberg T J 2008 Phys. Rev. Lett. 101 263602
[53] [54] Huang S M, Agarwal G S 2009 Phys. Rev. A 80 033807
[55] [56] Paternostro M, Gigan S, Kim M S, Blaser F, Bohm H R, Aspelmeyer M 2006 New J. Phys. 8 107
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[64] [65] DeJesus E X, Kaufman C 1987 Phys. Rev. A 35 5288
[66] Teufel J D, Regal C A, Lehnert K W 2008 New J. Phys. 10 095002
[67] [68] [69] Genes C, Vitali D, Tombesi P, Gigan S, Aspelmeyer M 2008 Phys. Rev. A 77 033804
[70] Wallraff A, Schuster D I, Blais A, Frunzio L, Huang R S, Majer J, Kumar S, Girvin S M, Schoelkopf R J 2004 Nature 431 162
[71] [72] [73] Thompson R J, Rempe G, Kimble H J 1992 Phys. Rev. Lett. 68 1132
[74] Fleischhauer M, Imamoglu A, Marangos J P 2005 Rev. Mod. Phys. 77 633
[75] [76] [77] Corbitt T, Wipf C, Bodiya T, Ottaway D, Sigg D, Smith N, Whitcomb S, Mavalvala N 2007 Phys. Rev. Lett. 99 160801
[78] Verlot P, Tavernarakis A, Briant T, Cohadon P F, Heidmann A 2010 Phys. Rev. Lett. 104 133602
[79] -
[1] Aspelmeyer M, Groblacher S, Hammerer K, Kiesel N 2010 J. Opt. Soc. Am. B 27 A189
[2] La Haye M D, Buu O, Camarota B, Schwab K C 2004 Science 304 74
[3] [4] Ekinci K L, Yang Y T, Roukes M L 2004 J. Appl. Phys. 95 2682
[5] [6] [7] Caves C M 1980 Phys. Rev. Lett. 45 75
[8] Schwab K C, Roukes M L 2005 Phys. Today 58 36
[9] [10] Leggett A J 2002 J. Phys: Condens. Matter 14 R415
[11] [12] [13] Marshall W, Simon C, Penrose R, Bouwmeester D 2003 Phys. Rev. Lett. 91 130401
[14] Kippenberg T J, Vahala K J 2008 Science 321 1172
[15] [16] [17] Gigan S, Bhm H R, Paternostro M, Blaser F, Langer G, Hertzberg J B, Schwab K C, Bauerle D, Aspelmeyer M, Zeilinger A 2006 Nature 444 67
[18] Kleckner D, Bouwmeester D 2006 Nature 444 75
[19] [20] [21] Poggio M, Degen C L, Mamin H J, Rugar D 2007 Phys. Rev. Lett. 99 017201
[22] Arcizet O, Cohadon P F, Briant T, Pinard M, Heidmann A 2006 Nature 444 71
[23] [24] Bhattacharya M, Meystre P 2007 Phys. Rev. Lett. 99 073601
[25] [26] [27] Schliesser A, Del'Haye P, Nooshi N, Vahala K L, Kippenberg T J 2006 Phys. Rev. Lett. 97 243905
[28] [29] Wilson-Rae I, Nooshi N, Zwerger W, Kippenberg T J 2007 Phys. Rev. Lett. 99 093901
[30] Marquardt F, Chen J P, Clerk A, Girvin S M 2007 Phys. Rev. Lett. 99 093902
[31] [32] [33] Ma R, Schliesser A, Del'Haye P, Dabirian A, Anetsberger G, Kippenberg T J 2007 Opt. Lett. 32 2200
[34] [35] Thompson J D, Zwickl B M, Jayich A M, Marquardt F, Girvin S M, Harris J G E 2008 Nature 452 72
[36] [37] Wilson-Rae I, Nooshi N, Dobrindt J, Kippenberg T J, Zwerger W 2008 New J. Phys. 10 095007
[38] Metzger C H, Karrai K 2004 Nature 432 1002
[39] [40] Corbitt T, Chen Y, Innerhofer E, Muller-Ebhardt H, Ottaway D, Rehbein H, Sigg D, Whitcomb S, Wipf C, Mavalvala N 2007 Phys. Rev. Lett. 98 150802
[41] [42] [43] Schliesser A, Riviere R, Anetsberger G, Arcizet O, Kippenberg T J 2008 Nat. Phys. 4 415
[44] [45] Park Y S, Wang H L 2009 Nat. Phys. 5 489
[46] [47] Li Y, Wang Y D, Xue F, Bruder C 2008 Phys. Rev. B 78 134301
[48] Tian L 2009 Phys. Rev. B 79 193407
[49] [50] [51] Grlacher S, Hammerer K, Vanner M R, Aspelmeyer M 2009 Nature 460 724
[52] Dobrindt J M, Wilson-Rae I, Kippenberg T J 2008 Phys. Rev. Lett. 101 263602
[53] [54] Huang S M, Agarwal G S 2009 Phys. Rev. A 80 033807
[55] [56] Paternostro M, Gigan S, Kim M S, Blaser F, Bohm H R, Aspelmeyer M 2006 New J. Phys. 8 107
[57] [58] Gardiner C W, Zoller P 1991 Quantum Noise (Berlin: Springer-Verlag) p50
[59] [60] [61] Giovannetti V, Vitali D 2001 Phys. Rev. A 63 023812
[62] [63] Walls D F, Milburn G J 1994 Quantum Optics (Berlin: Springer) p296
[64] [65] DeJesus E X, Kaufman C 1987 Phys. Rev. A 35 5288
[66] Teufel J D, Regal C A, Lehnert K W 2008 New J. Phys. 10 095002
[67] [68] [69] Genes C, Vitali D, Tombesi P, Gigan S, Aspelmeyer M 2008 Phys. Rev. A 77 033804
[70] Wallraff A, Schuster D I, Blais A, Frunzio L, Huang R S, Majer J, Kumar S, Girvin S M, Schoelkopf R J 2004 Nature 431 162
[71] [72] [73] Thompson R J, Rempe G, Kimble H J 1992 Phys. Rev. Lett. 68 1132
[74] Fleischhauer M, Imamoglu A, Marangos J P 2005 Rev. Mod. Phys. 77 633
[75] [76] [77] Corbitt T, Wipf C, Bodiya T, Ottaway D, Sigg D, Smith N, Whitcomb S, Mavalvala N 2007 Phys. Rev. Lett. 99 160801
[78] Verlot P, Tavernarakis A, Briant T, Cohadon P F, Heidmann A 2010 Phys. Rev. Lett. 104 133602
[79]
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