多模光力系统中的非传统声子阻塞
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摘要
本文提出在多模光力系统中实现声子阻塞.多模光力系统由一个机械模和两个光学模组成.研究发现,当光学模与机械模同时受到外加驱动场作用时,即使在弱光力耦合条件下也可以实现声子阻塞效应,即非传统声子阻塞效应;给出了非传统声子阻塞效应出现的最佳条件.另外,发现通过调节外加驱动场间强度的比值和相位差可以控制声子的统计性质,这为实现可控的单声子源提供了一个有效方法.最后,讨论了热声子对非传统声子阻塞的不利影响,发现适当提高驱动场强度有利于观测非传统声子阻塞效应.
In this paper, we proposed to observe a phonon blockade in multimode optomechanical system. The multimode optomechanical system is consisting of one mechanical mode driven by a weakly mechanical field and two optical modes driven by two optical fields(a weak one and a strong one). Under the interaction of the strong optical driving field, the multimode optomechanical system can be reduced to a much simple model for a mechanical mode linearly coupled to an optical mode with Kerr nonlinearity. Our calculations show that strong phonon antibunching effects can be observed even with weak optomechanical coupling. This counter-intuitive phenomenon, i.e., unconventional phonon blockade,results from the destructive interference between different paths for two-phonon excitation and the optimal conditions for unconventional phonon blockade are obtained analytically. Moreover, the statistical properties of the phonons can be controlled by regulating the strength ratio and the relative phase between the weakly driving fields, and this provides us an effective way to realize tunable single-phonon sources. Finally, we show that the thermal phonons have a detrimental impact on the unconventional phonon blockade and a proper increase of the strengths of the weakly driving fields can be helpful to overcome the detrimental impact induced by the thermal phonons.
In this paper, we proposed to observe a phonon blockade in multimode optomechanical system. The multimode optomechanical system is consisting of one mechanical mode driven by a weakly mechanical field and two optical modes driven by two optical fields(a weak one and a strong one). Under the interaction of the strong optical driving field, the multimode optomechanical system can be reduced to a much simple model for a mechanical mode linearly coupled to an optical mode with Kerr nonlinearity. Our calculations show that strong phonon antibunching effects can be observed even with weak optomechanical coupling. This counter-intuitive phenomenon, i.e., unconventional phonon blockade,results from the destructive interference between different paths for two-phonon excitation and the optimal conditions for unconventional phonon blockade are obtained analytically. Moreover, the statistical properties of the phonons can be controlled by regulating the strength ratio and the relative phase between the weakly driving fields, and this provides us an effective way to realize tunable single-phonon sources. Finally, we show that the thermal phonons have a detrimental impact on the unconventional phonon blockade and a proper increase of the strengths of the weakly driving fields can be helpful to overcome the detrimental impact induced by the thermal phonons.
引文
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[55]Anetsberger G,Arcizet O,Unterreithmeier Q P,Riviere R,Schliesser A,Weig E M,Kotthaus J P,Kippenberg T J 2009 Nature Phys.5 909
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[57]Fang K,Matheny M M,Luan X,Painter O 2016 Nature Photon.10 489
[58]Han X,Zou C,Tang H 2016 Phys.Rev.Lett.117 123603
[2]Birnbaum K M,Boca A,Miller R,Boozer A D,Northup T E,Kimble H J 2005 Nature 436 87
[3]Dayan B,Parkins A S,Aoki T,Ostby E P,Vahala K J,Kimble H J 2008 Science 319 1062
[4]Dubin F,Russo C,Barros H G,Stute A,Becher C,Schmidt P O,Blatt R 2010 Nature Phys.6 350
[5]Faraon A,Fushman I,Englund D,Stoltz N,Petroff P,Vu?kovi?J 2008 Nature Phys.4 859
[6]Lang C,Bozyigit D,Eichler C,Steffen L,Fink J M,Abdumalikov Jr A A,Baur M,Filipp S,da Silva M P,Blais A,Wallraff A 2011 Phys.Rev.Lett.106 243601
[7]Hoffman A J,Srinivasan S J,Schmidt S,Spietz L,Aumentado J,Türeci H E,Houck A A 2011 Phys.Rev.Lett.107 053602
[8]Aspelmeyer M,Kippenberg T J,Marquardt F 2014 Rev.Mod.Phys.86 1391
[9]Liu Y C,Hu Y W,Wong C W,Xiao Y F 2013 Chin.Phys.B 22 114213
[10]Chen X,Liu X W,Zhang K Y,Yuan C H,Zhang W P2015 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]
[11]Chen H J,Mi X W 2011 Acta Phys.Sin.60 124206(in Chinese)[陈华俊,米贤武2011物理学报60 124206]
[12]Zhang D,Zheng Q 2013 Chin.Phys.Lett.30 024213
[13]Jiang C,Cui Y,Li X 2016 Chin.Phys.B 25 54204
[14]Rabl P 2011 Phys.Rev.Lett.107 063601
[15]Qiu L,Gan L,Ding W,Li Z Y 2013 J.Opt.Soc.Am.B 30 1683
[16]Xu X W,Li Y J,Liu Y X 2013 Phys.Rev.A 87 025803
[17]Liao J Q,Law C K 2013 Phys.Rev.A 87 043809
[18]Liao J Q,Nori F 2013 Phys.Rev.A 88 023853
[19]Hu D,Huang S Y,Liao J Q,Tian L,Goan H S 2015Phys.Rev.A 91 013812
[20]LüX Y,Wu Y,Johansson J R,Jing H,Zhang J,Nori F 2015 Phys.Rev.Lett.114 093602
[21]Xie H,Lin G W,Chen X,Chen Z H,Lin X M 2016Phys.Rev.A 93 063860
[22]Liu Y X,Miranowicz A,Gao Y B,Bajer J,Sun C P,Nori F 2010 Phys.Rev.A 82 032101
[23]Didier N,Pugnetti S,Blanter Y M,Fazio R 2011 Phys.Rev.B 84 054503
[24]Miranowicz A,Bajer J,Lambert N,Liu Y X,Nori F2016 Phys.Rev.A 93 013808
[25]Wang X,Miranowicz A,Li H R,Nori F 2016 Phys.Rev.A 93 063861
[26]Ramos T,Sudhir V,Stannigel K,Zoller P,Kippenberg T J 2013 Phys.Rev.Lett.110 193602
[27]Xu X W,Chen A X,Liu Y X 2016 Phys.Rev.A 94063853
[28]Nunnenkamp A,B?rkje K,Girvin S M 2011 Phys.Rev.Lett.107 063602
[29]L?rch N,Hammerer K 2015 Phys.Rev.A 91 061803
[30]Seok H,Wright E M 2017 Phys.Rev.A 95 053844
[31]Ludwig M,Safavi-Naeini A H,Painter O,Marquardt F2012 Phys.Rev.Lett.109 063601
[32]Stannigel K,Komar P,Habraken S J M,Bennett S D,Lukin M D,Zoller P,Rabl P 2012 Phys.Rev.Lett.109013603
[33]Wang Y D,Clerk A A 2012 Phys.Rev.Lett.108 153603
[34]Tian L 2012 Phys.Rev.Lett.108 153604
[35]Li H K,Ren X X,Liu Y C,Xiao Y F 2013 Phys.Rev.A 88 053850
[36]Grudinin I S,Lee H,Painter O,Vahala K J 2010 Phys.Rev.Lett.104 083901
[37]Wang H,Wang Z X,Zhang J,?zdemir S K,Yang L,Liu Y X 2014 Phys.Rev.A 90 053814
[38]Gu W J,Li G X 2013 Phys.Rev.A 87 025804
[39]Ojanen T,B?rkje K 2014 Phys.Rev.A 90 013824
[40]Guo Y J,Li K,Nie W J,Li Y 2014 Phys.Rev.A 90053841
[41]Liu Y C,Xiao Y F,Luan X S,Gong Q H,Wong C W2015 Phys.Rev.A 91 033818
[42]Xu X W,Li Y J 2013 J.Opt.B:At.Mol.Opt.Phys.46 035502
[43]Chen H J,Fang X W,Chen C Z,Li Y 2016 Acta Phys.Sin.65 194205(in Chinese)[陈华俊,方贤文,陈昌兆,李洋2016物理学报65 194205]
[44]Liew T C H,Savona V 2010 Phys.Rev.Lett.104 183601
[45]Bamba M,Imamoglu A,Carusotto I,Ciuti C 2011 Phys.Rev.A 83 021802
[46]Lemonde M A,Didier N,Clerk A A 2014 Phys.Rev.A90 063824
[47]Gerace D,Savona V 2014 Phys.Rev.A 89 031803
[48]Kyriienko O,Shelykh I A,Liew T C H 2014 Phys.Rev.A 90 033807
[49]Xu X W,Li Y 2014 Phys.Rev.A 90 033809
[50]Xu X W,Li Y 2014 Phys.Rev.A 90 043822
[51]Kyriienko O,Liew T C H 2014 Phys.Rev.A 90 063805
[52]Shen H Z,Zhou Y H,Yi X X 2015 Phys.Rev.A 91063808
[53]Zhou Y H,Shen H Z,Yi X X 2015 Phys.Rev.A 92023838
[54]Tang J,Geng W,Xu X 2015 Sci.Rep.5 9252
[55]Anetsberger G,Arcizet O,Unterreithmeier Q P,Riviere R,Schliesser A,Weig E M,Kotthaus J P,Kippenberg T J 2009 Nature Phys.5 909
[56]Carmichael H J 1993 An Open Systems Approach to Quantum Optics(Lecture Notes in Physics vol.18)(Berlin:Springer)pp9-13
[57]Fang K,Matheny M M,Luan X,Painter O 2016 Nature Photon.10 489
[58]Han X,Zou C,Tang H 2016 Phys.Rev.Lett.117 123603
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