双腔光力学系统中输出光场纠缠特性的研究
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摘要
腔光力学系统中的光辐射压力可以使系统中的各个子系统之间产生量子纠缠,最近在腔光力学系统中的量子纠缠引起了人们广泛的关注.本文研究了双腔光力系统中关于输出光场之间纠缠的性质,发现:此系统中力学振子的弛豫速率和滤波器带宽以及非相等耦合对输出光场之间纠缠的大小有着非常显著的影响,特别是在相等耦合条件下,输出光场中心频率与光腔本征频率近共振时,滤波器带宽对输出光场纠缠有着显著的抑制作用;但是如果采用非相等耦合,则可以有效抵制滤波器带宽对纠缠的抑制作用,使输出光场纠缠得到大幅提高.研究结果可应用在光力耦合系统中实现量子态转换、量子隐形传态等量子信息处理过程.
Radiation pressure in an optomechanical system can be used to generate various quantum entanglements between the subsystems. Recently, one paid more attention to the study of quantum entanglement in an optomechanical system.Here in this work, we study the properties of output entanglement between two filtered output optical fields by the logarithmic negativity method in a double-cavity optomechanical system. Our calculations show that the decay rate of the mechanical resonator, the bandwidth of filter function, and non-equal-coupling will evidently affect the value of the output entanglement. In particular, under the parameters of equal-coupling and zero filter bandwidth, the output entanglement in the vicinity of resonant frequency(ω = 0 in the rotating frame) will decease with mechanical decay rate increasing. But under the parameters of equal-coupling and non-zero filter bandwidth, the output entanglement will be suppressed if the center frequency of output field is in the vicinity of the resonant frequency. However, the output entanglement can be enhanced if we adopt a non-equal-coupling to counteract the suppression effect of the filter bandwidth. Furthermore, we find that there are three peaks in the whole center frequency domain of the output field if we adopt strong non-equal-coupling. This is because the normal mode of Hamiltonian Hint will split into three normal modes in this case. Our results can also be used in other parametrically coupled three-mode bosonic systems and may be applied to realizing the state transfer process and quantum teleportation in an optomechanical system.
Radiation pressure in an optomechanical system can be used to generate various quantum entanglements between the subsystems. Recently, one paid more attention to the study of quantum entanglement in an optomechanical system.Here in this work, we study the properties of output entanglement between two filtered output optical fields by the logarithmic negativity method in a double-cavity optomechanical system. Our calculations show that the decay rate of the mechanical resonator, the bandwidth of filter function, and non-equal-coupling will evidently affect the value of the output entanglement. In particular, under the parameters of equal-coupling and zero filter bandwidth, the output entanglement in the vicinity of resonant frequency(ω = 0 in the rotating frame) will decease with mechanical decay rate increasing. But under the parameters of equal-coupling and non-zero filter bandwidth, the output entanglement will be suppressed if the center frequency of output field is in the vicinity of the resonant frequency. However, the output entanglement can be enhanced if we adopt a non-equal-coupling to counteract the suppression effect of the filter bandwidth. Furthermore, we find that there are three peaks in the whole center frequency domain of the output field if we adopt strong non-equal-coupling. This is because the normal mode of Hamiltonian Hint will split into three normal modes in this case. Our results can also be used in other parametrically coupled three-mode bosonic systems and may be applied to realizing the state transfer process and quantum teleportation in an optomechanical system.
引文
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[2]Krauter H,Muschik C A,Jensen K,Wasilewski W,Petersen J M,Cirac J I,Polzik E S 2011 Phys.Rev.Lett.107 080503
[3]Berkley A J,Xu H,Ramos R G,Gubrud M A,Strauch F W,Johnson P R,Anderson J R,Dragt A J,Lobb C J,Wellstood F C 2003 Science 300 1548
[4]Neeley M,Bialczak R C,Lenander M,Lucero E,Mariantoni M,Sank D,Wang H,Weides M,Wenner J,Yin Y,Yamamoto T,Cleland A N,Martinis J M 2010Nature 467 570
[5]DiCarlo L,Reed M,Sun L,Johnson B L,Ghow J M,Gambetta J M,Frunzio L,Girvin S M,Devoret M H,Schoelkopf R J 2010 Nature 467 574
[6]Flurin E,Roch N,Mallet F,Devoret M H,Huard B 2012Phys.Rev.Lett.109 183901
[7]Aspelmeyer M,Kippenberg T J,Marquardt F 2014 Rev.Mod.Phys.86 1391
[8]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]
[9]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]
[10]Yan X B,Yang L,Tian X D,Liu Y M,Zhang Y 2014Acta Phys.Sin.63 204201(in Chinese)[严晓波,杨柳,田雪冬,刘一谋,张岩2014物理学报63 204201]
[11]Bhattacharya M,Giscard P L,Meystre P 2008 Phys.Rev.A 77 030303
[12]Chen R X,Shen L T,Yang Z B,Wu H Z,Zheng S B2014 Phys.Rev.A 89 023843
[13]Liao J Q,Wu Q Q,Nori F 2014 Phys.Rev.A 89 014302
[14]Yang C J,An J H,Yang W,Li Y 2015 Phys.Rev.A 92062311
[15]Paternostro M,Vitali D,Gigan S,Kim M S,Brukner C,Eisert J,Aspelmeyer M 2007 Phys.Rev.Lett.99 250401
[16]Wipf C,Corbitt T,Chen Y,Mavalvala N 2008 New J.Phys.10 095017
[17]Genes C,Mari A,Tombesi P,Vitali D 2008 Phys.Rev.A 78 032316
[18]Barzanjeh Sh,Vitali D,Tombesi P,Milburn G J 2011Phys.Rev.A 84 042342
[19]Barzanjeh Sh,Abdi M,Milburn G J,Tombesi P,Vitali D 2012 Phys.Rev.Lett.109 130503
[20]Barzanjeh Sh,Pirandola S,Weedbrook C 2013 Phys.Rev.A 88 042331
[21]Wang Y D,Clerk A A 2013 Phys.Rev.Lett.110 253601
[22]Tian L 2013 Phys.Rev.Lett.110 233602
[23]Kuzyk M C,van Enk S J,Wang H 2013 Phys.Rev.A88 062341
[24]Wang Y D,Chesi S Clerk A A 2015 Phys.Rev.A 91013807
[25]Deng Z J,Habraken S J M,Marquardt F 2016 New J.Phys.18 063022
[26]Deng Z J,Yan X B,Wang Y D,Wu C W 2016 Phys.Rev.A 93 033842
[27]Vitali D,Gigan S,Ferreira A,Bohm H R,Tombesi P,Guerreiro A,Vedral V,Zeilinger A,Aspelmeyer M 2007Phys.Rev.Lett.98 030405
[28]Hofer S G,Wieczorek W,Aspelmeyer M,Hammerer K2011 Phys.Rev.A 84 052327
[29]Akram U,Munro W,Nemoto K,Milburn G J 2012 Phys.Rev.A 86 042306
[30]Sinha K,Lin S Y,Hu B L 2015 Phys.Rev.A 92 023852
[31]He Q Y,Ficek Z 2014 Phys.Rev.A 89 022332
[32]Kiesewetter S,He Q Y,Drummond P D,Reid M D 2014Phys.Rev.A 90 043805
[33]He Q Y,Reid M D 2013 Phys.Rev.A 88 052121
[34]Wang M,Gong Q H,Ficek Z,He Q Y 2015 Sci.Rep.512346
[35]Wang M,Gong Q H,Ficek Z,He Q Y 2014 Phys.Rev.A 90 023801
[36]Palomaki T A,Teufel J D,Simmonds R W,Lehnert K W 2013 Science 342 710
[37]DeJesus E X,Kaufman C 1987 Phys.Rev.A 35 5288
[38]Vidal G,Werner R F 2002 Phys.Rev.A 65 032314
[39]Plenio M B 2005 Phys.Rev.Lett.95 090503