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Photon squeezing of the Rabi model

Yu Li-Xian Liang Qi-Feng Wang Li-Rong Zhu Shi-Qun

Photon squeezing of the Rabi model

Yu Li-Xian, Liang Qi-Feng, Wang Li-Rong, Zhu Shi-Qun
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  • Recent experiments about the circuit cavity quantum electrodynamics have realized the ultrastrong couplings between the artificial atom and the photon, in which the coupling strengths have the same order of the photon frequency. In such a regime, the well-known rotating wave approximation is invalid, and the system dynamics is thus governed by the Rabi model. In this paper, we investigate the photon squeezing of the Rabi model. We find numerically that with the increase of the atom-photon coupling strength, the photon squeezing does not increase linearly, but displays a maximum in the ultrastrong coupling regime. In addition, we also reveal that the photonsqueezing can be enhanced by the counter-rotating terms of the Rabi model. Our results are of benefit to preparing the required squeezing state of the photon in experiment.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11074184, 11275129, 61275211) and the Natural Science Foundation of Zhejiang Province, China (Grant No. LY13A040001).
    [1]

    Jaynes E T, Cummings F W 1963 Proc. IEEE 51 89

    [2]

    Scully M O, Zubairy M S 1997 Quantum Optics (Cambridge: Cambridge University Press)

    [3]

    Holstein T 1959 Ann. Phys. (Amsterdam, Neth.) 8 325

    [4]

    Raimond J M, Brune M, Haroche S 2001 Rev. Mod. Phys. 73 565

    [5]

    Blais A, Huang R S, Wallraff A, Girvin S M, Schoelkopf R J 2004 Phys. Rev. B 69 62320

    [6]

    Wallraff A, Schuster D, Blais A, Frunzio L, Huang R S, Majer J, Kumar S, Girvin S, Schoelkopf R 2004 Nature 431 162

    [7]

    Niemczyk T, Deppe F, Huebl H, Menzel E P, Hocke F, Schwarz M J, Garcia-Ripoll J J, Zueco D, Hummer T, Solanoet E 2010 Nat. Phys. 6 772

    [8]

    Fedorov A, Feofanov A K, Macha P, Forn-Díaz P, Harmans C J P M, Mooij J E 2010 Phys. Rev. Lett. 105 060503

    [9]

    Crespi A, Longhi S, Osellame R 2012 Phys. Rev. Lett. 108 163601

    [10]

    Ballester D, Romero G, García-Ripoll J, Deppe F, Solano E 2012 Phys. Rev. X 2 021007

    [11]

    Arne G L 2013 Phys. Rev. A 87 033814

    [12]

    Forn-Díaz P, Lisenfeld J, Marcos D, García-Ripoll J J, Solano E, Harmans C J P M, Mooij J E 2010 Phys. Rev. Lett. 105 237001

    [13]

    Rabi I I 1936 Phys. Rev. 49 324

    [14]

    Irish E K 2007 Phys. Rev. Lett. 99 173601

    [15]

    Zhang Y W, Chen G, Yu L X, Liang Q F, Liang J Q, Jia S T 2011 Phys. Rev. A 83 065802

    [16]

    Yu L X, Zhu S Q, Liang Q F, Chen G, Jia S T 2012 Phys. Rev. A 86 015803

    [17]

    Braak D 2011 Phys. Rev. Lett. 107 100401

    [18]

    Zhang Y Y, Chen Q H, Wang K L 2010 Phys. Rev. B 81 121105

    [19]

    Chen Q H, Wang C, He S, Liu T, Wang K L 2012 Phys. Rev. A 86 023822

    [20]

    Chen Q H, Liu T, Zhang Y Y, Wang K L 2011 Europhys. Lett. 96 14003

    [21]

    Li X Q, Wang J, Wang F, Hu X M 2008 Acta Phys. Sin. 57 2236 (in Chinese) [李晓奇, 王剑, 王飞, 胡响明2008 物理学报 57 2236]

    [22]

    Jia F, Xie S Y, Yang Y P 2006 Acta Phys. Sin. 56 5835 (in Chinese) [贾飞, 谢双媛, 羊亚平 2006 物理学报 56 5835]

    [23]

    Liao X, Cong H L, Jiang D L, Ren X Z 2010 Acta Phys. Sin. 59 5508 (in Chinese) [廖旭, 丛红璐, 姜道来, 任学藻 2010 物理学报 59 5508]

    [24]

    Bonci L, Roncaglia R, West B J, Grigolini P 1991 Phys. Rev. Lett. 67 2593

    [25]

    Ashhab S 2013 Phys. Rev. A 87 013826

    [26]

    Ridolfo A, Leib M, Savasta S, Hartmann M J 2012 Phys. Rev. Lett. 109 193602

    [27]

    Romero G, Ballester D, Wang Y M, Scarani V, Solano E 2012 Phys. Rev. Lett. 108 120501

    [28]

    Zheng H, Zhu S Y, Zubairy M S 2008 Phys. Rev. Lett. 101 200404

    [29]

    Liang Q F, Yu L X, Chen G, Jia S T 2013 Eur. Phys. J. D 67 21

    [30]

    Stoler D 1970 Phys. Rev. D 1 3217

    [31]

    Hollenhorst J N 1979 Phys. Rev. D 19 1669

    [32]

    Peng K C 2001 Physics 30 300 (in Chinese) [彭堃墀 2001 物理 30 300]

    [33]

    Zhang Y, Wang H, Li X Y, Jing J T, Xie C D, Peng K C 2000 Phys. Rev. A 62 023813

    [34]

    Zhang J, Ye C G, Gao F, Xiao M 2008 Phys. Rev. Lett. 101 233602

    [35]

    Song J, Fan H Y, Zhou J 2011 Acta Phys. Sin. 60 110302 (in Chinese) [宋军, 范洪义, 周军 2011 物理学报 60 110302]

    [36]

    Fan H Y, Pan X Y 1998 Chin. Phys. Lett. 15 625

    [37]

    Zhao J G, Sun C Y, Liang B L, Su J 2009 Acta Phys. Sin. 58 4635 (in Chinese) [赵建刚, 孙长勇, 梁宝龙, 苏杰 2009 物理学报 58 4635]

    [38]

    Li Z H, Yu M Z, Yang Y P 2008 Acta Phys. Sin. 57 1693 (in Chinese) [李征鸿, 于明章, 杨亚平 2008 物理学报 57 1693]

    [39]

    Meystre P, Zubairy M S 1982 Phys. Lett. A 89 390

    [40]

    Knight P L 1986 Phys. Scr. 86 51

    [41]

    Kukliński J, Madajczyk J 1988 Phys. Rev. A 37 3175

    [42]

    Ma J, Wang X G, Sun C P, Nori F 2011 Phys. Rep. 509 89

    [43]

    Hillery M 1987 Phys. Rev. A 36 3796

    [44]

    Casanova J, Romero G, Lizuain I, García-Ripoll J J, Solano E 2010 Phys. Rev. Lett. 105 263603

    [45]

    Hillery M 1989 Phys. Rev. A 39 1556

  • [1]

    Jaynes E T, Cummings F W 1963 Proc. IEEE 51 89

    [2]

    Scully M O, Zubairy M S 1997 Quantum Optics (Cambridge: Cambridge University Press)

    [3]

    Holstein T 1959 Ann. Phys. (Amsterdam, Neth.) 8 325

    [4]

    Raimond J M, Brune M, Haroche S 2001 Rev. Mod. Phys. 73 565

    [5]

    Blais A, Huang R S, Wallraff A, Girvin S M, Schoelkopf R J 2004 Phys. Rev. B 69 62320

    [6]

    Wallraff A, Schuster D, Blais A, Frunzio L, Huang R S, Majer J, Kumar S, Girvin S, Schoelkopf R 2004 Nature 431 162

    [7]

    Niemczyk T, Deppe F, Huebl H, Menzel E P, Hocke F, Schwarz M J, Garcia-Ripoll J J, Zueco D, Hummer T, Solanoet E 2010 Nat. Phys. 6 772

    [8]

    Fedorov A, Feofanov A K, Macha P, Forn-Díaz P, Harmans C J P M, Mooij J E 2010 Phys. Rev. Lett. 105 060503

    [9]

    Crespi A, Longhi S, Osellame R 2012 Phys. Rev. Lett. 108 163601

    [10]

    Ballester D, Romero G, García-Ripoll J, Deppe F, Solano E 2012 Phys. Rev. X 2 021007

    [11]

    Arne G L 2013 Phys. Rev. A 87 033814

    [12]

    Forn-Díaz P, Lisenfeld J, Marcos D, García-Ripoll J J, Solano E, Harmans C J P M, Mooij J E 2010 Phys. Rev. Lett. 105 237001

    [13]

    Rabi I I 1936 Phys. Rev. 49 324

    [14]

    Irish E K 2007 Phys. Rev. Lett. 99 173601

    [15]

    Zhang Y W, Chen G, Yu L X, Liang Q F, Liang J Q, Jia S T 2011 Phys. Rev. A 83 065802

    [16]

    Yu L X, Zhu S Q, Liang Q F, Chen G, Jia S T 2012 Phys. Rev. A 86 015803

    [17]

    Braak D 2011 Phys. Rev. Lett. 107 100401

    [18]

    Zhang Y Y, Chen Q H, Wang K L 2010 Phys. Rev. B 81 121105

    [19]

    Chen Q H, Wang C, He S, Liu T, Wang K L 2012 Phys. Rev. A 86 023822

    [20]

    Chen Q H, Liu T, Zhang Y Y, Wang K L 2011 Europhys. Lett. 96 14003

    [21]

    Li X Q, Wang J, Wang F, Hu X M 2008 Acta Phys. Sin. 57 2236 (in Chinese) [李晓奇, 王剑, 王飞, 胡响明2008 物理学报 57 2236]

    [22]

    Jia F, Xie S Y, Yang Y P 2006 Acta Phys. Sin. 56 5835 (in Chinese) [贾飞, 谢双媛, 羊亚平 2006 物理学报 56 5835]

    [23]

    Liao X, Cong H L, Jiang D L, Ren X Z 2010 Acta Phys. Sin. 59 5508 (in Chinese) [廖旭, 丛红璐, 姜道来, 任学藻 2010 物理学报 59 5508]

    [24]

    Bonci L, Roncaglia R, West B J, Grigolini P 1991 Phys. Rev. Lett. 67 2593

    [25]

    Ashhab S 2013 Phys. Rev. A 87 013826

    [26]

    Ridolfo A, Leib M, Savasta S, Hartmann M J 2012 Phys. Rev. Lett. 109 193602

    [27]

    Romero G, Ballester D, Wang Y M, Scarani V, Solano E 2012 Phys. Rev. Lett. 108 120501

    [28]

    Zheng H, Zhu S Y, Zubairy M S 2008 Phys. Rev. Lett. 101 200404

    [29]

    Liang Q F, Yu L X, Chen G, Jia S T 2013 Eur. Phys. J. D 67 21

    [30]

    Stoler D 1970 Phys. Rev. D 1 3217

    [31]

    Hollenhorst J N 1979 Phys. Rev. D 19 1669

    [32]

    Peng K C 2001 Physics 30 300 (in Chinese) [彭堃墀 2001 物理 30 300]

    [33]

    Zhang Y, Wang H, Li X Y, Jing J T, Xie C D, Peng K C 2000 Phys. Rev. A 62 023813

    [34]

    Zhang J, Ye C G, Gao F, Xiao M 2008 Phys. Rev. Lett. 101 233602

    [35]

    Song J, Fan H Y, Zhou J 2011 Acta Phys. Sin. 60 110302 (in Chinese) [宋军, 范洪义, 周军 2011 物理学报 60 110302]

    [36]

    Fan H Y, Pan X Y 1998 Chin. Phys. Lett. 15 625

    [37]

    Zhao J G, Sun C Y, Liang B L, Su J 2009 Acta Phys. Sin. 58 4635 (in Chinese) [赵建刚, 孙长勇, 梁宝龙, 苏杰 2009 物理学报 58 4635]

    [38]

    Li Z H, Yu M Z, Yang Y P 2008 Acta Phys. Sin. 57 1693 (in Chinese) [李征鸿, 于明章, 杨亚平 2008 物理学报 57 1693]

    [39]

    Meystre P, Zubairy M S 1982 Phys. Lett. A 89 390

    [40]

    Knight P L 1986 Phys. Scr. 86 51

    [41]

    Kukliński J, Madajczyk J 1988 Phys. Rev. A 37 3175

    [42]

    Ma J, Wang X G, Sun C P, Nori F 2011 Phys. Rep. 509 89

    [43]

    Hillery M 1987 Phys. Rev. A 36 3796

    [44]

    Casanova J, Romero G, Lizuain I, García-Ripoll J J, Solano E 2010 Phys. Rev. Lett. 105 263603

    [45]

    Hillery M 1989 Phys. Rev. A 39 1556

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  • Received Date:  07 April 2013
  • Accepted Date:  25 April 2013
  • Published Online:  20 August 2013

Photon squeezing of the Rabi model

  • 1. School of Physical Science and Technology, Soochow University, Suzhou 215006, China;
  • 2. Department of Physics, Shaoxing University, Shaoxing 312000, China;
  • 3. Laser Spectroscopy Laboratory, Shanxi University, Taiyuan 030006, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 11074184, 11275129, 61275211) and the Natural Science Foundation of Zhejiang Province, China (Grant No. LY13A040001).

Abstract: Recent experiments about the circuit cavity quantum electrodynamics have realized the ultrastrong couplings between the artificial atom and the photon, in which the coupling strengths have the same order of the photon frequency. In such a regime, the well-known rotating wave approximation is invalid, and the system dynamics is thus governed by the Rabi model. In this paper, we investigate the photon squeezing of the Rabi model. We find numerically that with the increase of the atom-photon coupling strength, the photon squeezing does not increase linearly, but displays a maximum in the ultrastrong coupling regime. In addition, we also reveal that the photonsqueezing can be enhanced by the counter-rotating terms of the Rabi model. Our results are of benefit to preparing the required squeezing state of the photon in experiment.

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