-
The traditional opto-mechanical coupling in an opto-mechanical system is a linear coupling which is proportional to the field intensity I and oscillator displacement x. The nonlinear spatial coupling effect becomes obvious and important in a strong cavity field with large oscillating amplitude, and then the nonlinear effect with quadratic coupling in opt-mechanical device is also significant. In this article, we find that a general opto-mechanical system with quadratic coupling will produce a stable self-sustained oscillation when the energy injected by external driving equals that of dissipations in certain parametric regions. We numerically solve the semi-classical equation of motion of the system and find high-dimensional limit circles in its phase space under the control of driving and damping. We verify the high-dimensional limit circles by the closed orbits in all the projective three-dimensional phase space and show a highly controllable topological structure of the phase orbit which is very similar to Lissajous figures formed in a two-dimensional case. The self-sustained oscillations of the driving resonator with controllable amplitudes and frequencies demonstrate a reliable physical application of opto-mechanical system under quadratic coupling.
[1] Stannigel K, Komar P, Habraken S J M, Bennett S D, Lukin M D, Zoller P, Rabl P 2012 Phys. Rev. Lett. 109 013603
[2] Bocko M F, Onofrio R 1996 Rev. Mod. Phys. 68 755
[3] Pirkkalainen J M, Cho S U, Jian Li, Paraoanu G S, Hakonen P J, SillanpääM A 2013 Nature 494 211
[4] Mi X W, Bai J X, Li D J 2012 Chin. Phys. B 21 030303
[5] Zhang D, Zhang X P, Zheng Q 2013 Chin. Phys. B 22 064206
[6] Zhang D, Zheng Q 2013 Chin. Phys. Lett. 30 024213
[7] Karuza M, Molinelli C, Galassi M, Biancofiore C, Natali R, Tombesi P, Giuseppe G Di, Vitali D 2012 New J. Phys. 14 095015
[8] Chen H J, Mi X W 2011 Acta Phys. Sin. 60 124206 (in Chinese) [陈华俊, 米贤武 2011 60 124206]
[9] Bonin K D, Kourmanov B, Walker T G 2002 Opt. Express 10 984
[10] Kippenberg T J, Rokhsari H, Carmon T, Scherer A, Vahala K J 2005 Phys. Rev. Lett. 95 033901
[11] Arcizet O, Cohadon P F, Briant T, Pinard M, Heidmann A 2006 Nature 444 71
[12] Gröblache S, Hammerer K, Vanner M R, Aspelmeyer M 2009 Nature 460 724
[13] Sankey J C, Yang C, Zwickl B M, Jayich A M, Harris J G E 2010 Nature Phys. 6 707
[14] Thompson J D, Zwickl B M, Jayich A M, Marquardt F, Girvin S M, Harris J G E 2008 Nature 452 72
[15] Nunnenkamp A, Borkje K, Harris J G E, Girvin S M 2010 Phys. Rev. A 82 021806
[16] Teng J H, Wu S L, Cui B, Yi X X 2012 J. Phys. B: At. Mol. Opt. Phys. 45 185506
[17] Jenkins A 2013 Phys. Reports 525 167
[18] Holmes C A, Milburn G J 2009 Fortschr. Phys. 57 1052
[19] Domokos P, Ritsch H 2003 J. Opt. Soc. Am. B 20 1098
[20] Zippilli S, Morigi G 2005 Phys. Rev. A 72 053408
[21] Wilson-Rae I, Nooshi N, Dobrindt J, Kippenberg T J, Zwerger W 2008 New J. Phys. 10 095007
[22] Gigan S, Bohm H R, Paternostro M, Blaser F, Langer G, Hertzberg J B, Schwab K C, Bäuerle D, Aspelmeyer M, Zeilinger A 2006 Nature 444 67
[23] Bhattacharya M, Shi H, Preble S 2013 Am. J. Phys. 81 267
[24] Feng G L, Dong W J, Jia X J, Cao H X 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林, 董文杰, 贾晓静, 曹鸿兴 2002 51 1181]
[25] Liu S H, Tang J S 2007 Acta Phys. Sin. 56 3145 (in Chinese) [刘素华, 唐驾时 2007 56 3145]
[26] Zhao Q, Liu S K, Liu S D 2012 Acta Phys. Sin. 61 220201 (in Chinese) [赵强, 刘式适, 刘式达 2012 61 220201]
[27] Giacomini H, Llibre J, Viano M 1996 Nonlinearity 9 501
[28] Blows T R, Lloyd N G 1984 Proc. Roy. Soc. Edinb. 98A 215
[29] Suh J, Shaw M D, LeDuc H G, Weinstein A J, Schwab K C 2012 Nano Lett. 12 6260
-
[1] Stannigel K, Komar P, Habraken S J M, Bennett S D, Lukin M D, Zoller P, Rabl P 2012 Phys. Rev. Lett. 109 013603
[2] Bocko M F, Onofrio R 1996 Rev. Mod. Phys. 68 755
[3] Pirkkalainen J M, Cho S U, Jian Li, Paraoanu G S, Hakonen P J, SillanpääM A 2013 Nature 494 211
[4] Mi X W, Bai J X, Li D J 2012 Chin. Phys. B 21 030303
[5] Zhang D, Zhang X P, Zheng Q 2013 Chin. Phys. B 22 064206
[6] Zhang D, Zheng Q 2013 Chin. Phys. Lett. 30 024213
[7] Karuza M, Molinelli C, Galassi M, Biancofiore C, Natali R, Tombesi P, Giuseppe G Di, Vitali D 2012 New J. Phys. 14 095015
[8] Chen H J, Mi X W 2011 Acta Phys. Sin. 60 124206 (in Chinese) [陈华俊, 米贤武 2011 60 124206]
[9] Bonin K D, Kourmanov B, Walker T G 2002 Opt. Express 10 984
[10] Kippenberg T J, Rokhsari H, Carmon T, Scherer A, Vahala K J 2005 Phys. Rev. Lett. 95 033901
[11] Arcizet O, Cohadon P F, Briant T, Pinard M, Heidmann A 2006 Nature 444 71
[12] Gröblache S, Hammerer K, Vanner M R, Aspelmeyer M 2009 Nature 460 724
[13] Sankey J C, Yang C, Zwickl B M, Jayich A M, Harris J G E 2010 Nature Phys. 6 707
[14] Thompson J D, Zwickl B M, Jayich A M, Marquardt F, Girvin S M, Harris J G E 2008 Nature 452 72
[15] Nunnenkamp A, Borkje K, Harris J G E, Girvin S M 2010 Phys. Rev. A 82 021806
[16] Teng J H, Wu S L, Cui B, Yi X X 2012 J. Phys. B: At. Mol. Opt. Phys. 45 185506
[17] Jenkins A 2013 Phys. Reports 525 167
[18] Holmes C A, Milburn G J 2009 Fortschr. Phys. 57 1052
[19] Domokos P, Ritsch H 2003 J. Opt. Soc. Am. B 20 1098
[20] Zippilli S, Morigi G 2005 Phys. Rev. A 72 053408
[21] Wilson-Rae I, Nooshi N, Dobrindt J, Kippenberg T J, Zwerger W 2008 New J. Phys. 10 095007
[22] Gigan S, Bohm H R, Paternostro M, Blaser F, Langer G, Hertzberg J B, Schwab K C, Bäuerle D, Aspelmeyer M, Zeilinger A 2006 Nature 444 67
[23] Bhattacharya M, Shi H, Preble S 2013 Am. J. Phys. 81 267
[24] Feng G L, Dong W J, Jia X J, Cao H X 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林, 董文杰, 贾晓静, 曹鸿兴 2002 51 1181]
[25] Liu S H, Tang J S 2007 Acta Phys. Sin. 56 3145 (in Chinese) [刘素华, 唐驾时 2007 56 3145]
[26] Zhao Q, Liu S K, Liu S D 2012 Acta Phys. Sin. 61 220201 (in Chinese) [赵强, 刘式适, 刘式达 2012 61 220201]
[27] Giacomini H, Llibre J, Viano M 1996 Nonlinearity 9 501
[28] Blows T R, Lloyd N G 1984 Proc. Roy. Soc. Edinb. 98A 215
[29] Suh J, Shaw M D, LeDuc H G, Weinstein A J, Schwab K C 2012 Nano Lett. 12 6260
Catalog
Metrics
- Abstract views: 5881
- PDF Downloads: 485
- Cited By: 0
下载:
