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Many-body quantum fluctuation effects of Rosen-Zener transition in Bose-Einstein condensates

Wang Jian-Zhong Cao Hui Dou Fu-Quan

Many-body quantum fluctuation effects of Rosen-Zener transition in Bose-Einstein condensates

Wang Jian-Zhong, Cao Hui, Dou Fu-Quan
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  • We investigate many-body quantum fluctuation effects of Rosen-Zener transition of Bose-Einstein condensate (BEC) in a symmetric double-well potential through the relation between the average population imbalance of the final state (APIFS) and scanning period. In the linear case, we deduce the analytical expression of the APIFS which has the same behavior as in the mean-field level. We also employ numerical calculation to demonstrate it. In the nonlinear case, numerical results show that the APIFS in the sudden limit also accords with that in the mean-field level whereas in the adiabatic limit the many-body result is quite different from that of the mean-field case: the behavior of APIFS with respect to scanning period is similar to sinusoidal rather than rectangular oscillation, besides the oscillation period increases with both the total number N and the nonlinear parameter c increasing.
    • Funds: Project supported by the National High Technology Research and Development Program of China (Grant No. 2011AA120101).
    [1]

    Rosen N, Zener C 1932 Phys. Rev. 40 502

    [2]

    Rabi I I 1937 Phys. Rev. 51 652

    [3]

    Thomas G F 1983 Phys. Rev. A 27 2744

    [4]

    Osherov V I, Voronin A I 1994 Phys. Rev. A 49 265

    [5]

    Robiscoe R T 1978 Phys. Rev. A 17 247

    [6]

    Bambini A, Berman P R 1981 Phys. Rev. A 23 2496

    [7]

    Robiscoe R T 1983 Phys. Rev. A 27 1365

    [8]

    Vitanov N V 1993 J. Phys. B: At. Mol. Opt. Phys. 26 L53

    [9]

    Liu J, Hu B, Li B W 1998 Phys. Rev. Lett. 81 1749

    [10]

    Osherov V I, Nakamura H 1999 Phys. Rev. A 59 2486

    [11]

    Robinson E J, Berman P R 1983 Phys. Rev. A 27 1022

    [12]

    Bava E, Godone A, Novero C, Rocco H O D 1992 Phys. Rev. A 45 1967

    [13]

    Fu L B 2004 Phys. Rev. Lett. 92 130404

    [14]

    Olson R E 1972 Phys. Rev. A 6 1822

    [15]

    Suominen K A, Garraway B M, Stenholm S. 1992 Phys. Rev. A 45 3060

    [16]

    Fu L B, Xin G G, Ye D F, Liu J 2012 Phys. Rev. Lett. 108 103601

    [17]

    Robinson E J 1993 J. Phys.: Condens. Matter 5 13

    [18]

    Kirillov A S 2004 Advances in Space Research 33 993

    [19]

    Anderson M H, Ensher J R, Mattews M R, Wieman C E, Cornell E A 1995 Science 269 198

    [20]

    Davis K B, Mcwes M O, Andrews M R, Druten N J, Durfee D S, Kurn D M, Kerrerle W 1995 Phys. Rev. Lett. 75 3969

    [21]

    Bradley C C, Sackett C A, Tollett J J, Hulet R G 1995 Phys. Rev. Lett. 75 1687

    [22]

    Anderson M R, Townsend C G, Mienser H J, Durfee D S, Kurn D M, Ketterle W 1997 Science 275 637

    [23]

    Wang G F, Fu L B, Zhao H, Liu J 2005 Acta Phys.Sin. 54 5003 (in Chinese) [王冠芳, 傅立斌, 赵鸿, 刘杰 2005 物理学报 54 5003]

    [24]

    Wang G F, Fu L B, Liu J 2006 Phys. Rev. A 73 013609

    [25]

    Liu J, Wang W G, Zhang C W, Niu Q, Li B W 2005 Phys. Rev. A 72 063623

    [26]

    Liu J, Zhang C W, Raizen M G, Niu Q 2006 Phys. Rev. A 73 013601

    [27]

    Ye D F, Fu L B, Liu J 2008 Phys. Rev. A 77 013402

    [28]

    Jiang X, Duan W S, Li S C, Shi Y R 2009 J. Phys. B: At. Mol. Opt. Phys. 42 185001

    [29]

    Fu L B, Ye D F, Lee C H, Zhang W P, Liu J 2009 Phys. Rev. A 80 013619

    [30]

    Li S C, Fu L B, Duan W S, Liu J 2008 Phys. Rev. A 78 063621

    [31]

    Ishkhanyan A, Sokhoyan R, Joulakian B, Suominen K A 2009 Optics Communications 282 218

    [32]

    Xu X Q, Lu L H, Li Y Q 2008 Phys. Rev. A 78 043609

    [33]

    Torosov B T, Vitanov N V 2007 Phys. Rev. A 76 053404

    [34]

    Lu L H, Xu X Q, Li Y Q 2011 J. Phys. B: At. Opt. Phys. 44 145301

    [35]

    Klich I, Lannert C, Refael G 2007 Phys. Rev. Lett 99 205303

    [36]

    Franco D, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys 71 463

    [37]

    Anthony L 2001 Rev. Mod. Phys 73 307

    [38]

    Steel M J, Collett M J 1998 Phys. Rev. A 57 2920

    [39]

    Cirac J I, Lewenstein M, Momer K, Zoller P 1998 Phys. Rev. A 57 1208

  • [1]

    Rosen N, Zener C 1932 Phys. Rev. 40 502

    [2]

    Rabi I I 1937 Phys. Rev. 51 652

    [3]

    Thomas G F 1983 Phys. Rev. A 27 2744

    [4]

    Osherov V I, Voronin A I 1994 Phys. Rev. A 49 265

    [5]

    Robiscoe R T 1978 Phys. Rev. A 17 247

    [6]

    Bambini A, Berman P R 1981 Phys. Rev. A 23 2496

    [7]

    Robiscoe R T 1983 Phys. Rev. A 27 1365

    [8]

    Vitanov N V 1993 J. Phys. B: At. Mol. Opt. Phys. 26 L53

    [9]

    Liu J, Hu B, Li B W 1998 Phys. Rev. Lett. 81 1749

    [10]

    Osherov V I, Nakamura H 1999 Phys. Rev. A 59 2486

    [11]

    Robinson E J, Berman P R 1983 Phys. Rev. A 27 1022

    [12]

    Bava E, Godone A, Novero C, Rocco H O D 1992 Phys. Rev. A 45 1967

    [13]

    Fu L B 2004 Phys. Rev. Lett. 92 130404

    [14]

    Olson R E 1972 Phys. Rev. A 6 1822

    [15]

    Suominen K A, Garraway B M, Stenholm S. 1992 Phys. Rev. A 45 3060

    [16]

    Fu L B, Xin G G, Ye D F, Liu J 2012 Phys. Rev. Lett. 108 103601

    [17]

    Robinson E J 1993 J. Phys.: Condens. Matter 5 13

    [18]

    Kirillov A S 2004 Advances in Space Research 33 993

    [19]

    Anderson M H, Ensher J R, Mattews M R, Wieman C E, Cornell E A 1995 Science 269 198

    [20]

    Davis K B, Mcwes M O, Andrews M R, Druten N J, Durfee D S, Kurn D M, Kerrerle W 1995 Phys. Rev. Lett. 75 3969

    [21]

    Bradley C C, Sackett C A, Tollett J J, Hulet R G 1995 Phys. Rev. Lett. 75 1687

    [22]

    Anderson M R, Townsend C G, Mienser H J, Durfee D S, Kurn D M, Ketterle W 1997 Science 275 637

    [23]

    Wang G F, Fu L B, Zhao H, Liu J 2005 Acta Phys.Sin. 54 5003 (in Chinese) [王冠芳, 傅立斌, 赵鸿, 刘杰 2005 物理学报 54 5003]

    [24]

    Wang G F, Fu L B, Liu J 2006 Phys. Rev. A 73 013609

    [25]

    Liu J, Wang W G, Zhang C W, Niu Q, Li B W 2005 Phys. Rev. A 72 063623

    [26]

    Liu J, Zhang C W, Raizen M G, Niu Q 2006 Phys. Rev. A 73 013601

    [27]

    Ye D F, Fu L B, Liu J 2008 Phys. Rev. A 77 013402

    [28]

    Jiang X, Duan W S, Li S C, Shi Y R 2009 J. Phys. B: At. Mol. Opt. Phys. 42 185001

    [29]

    Fu L B, Ye D F, Lee C H, Zhang W P, Liu J 2009 Phys. Rev. A 80 013619

    [30]

    Li S C, Fu L B, Duan W S, Liu J 2008 Phys. Rev. A 78 063621

    [31]

    Ishkhanyan A, Sokhoyan R, Joulakian B, Suominen K A 2009 Optics Communications 282 218

    [32]

    Xu X Q, Lu L H, Li Y Q 2008 Phys. Rev. A 78 043609

    [33]

    Torosov B T, Vitanov N V 2007 Phys. Rev. A 76 053404

    [34]

    Lu L H, Xu X Q, Li Y Q 2011 J. Phys. B: At. Opt. Phys. 44 145301

    [35]

    Klich I, Lannert C, Refael G 2007 Phys. Rev. Lett 99 205303

    [36]

    Franco D, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys 71 463

    [37]

    Anthony L 2001 Rev. Mod. Phys 73 307

    [38]

    Steel M J, Collett M J 1998 Phys. Rev. A 57 2920

    [39]

    Cirac J I, Lewenstein M, Momer K, Zoller P 1998 Phys. Rev. A 57 1208

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  • Received Date:  29 March 2012
  • Accepted Date:  14 June 2012
  • Published Online:  20 November 2012

Many-body quantum fluctuation effects of Rosen-Zener transition in Bose-Einstein condensates

  • 1. School of Physics Beijing Institute of Technology, Beijing 100081, China;
  • 2. National Key Laboratory of Science and Technology on Computation Physics Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
  • 3. HEDPS Center for Applied Physics and Technology Peking University, Beijing 100084, China
Fund Project:  Project supported by the National High Technology Research and Development Program of China (Grant No. 2011AA120101).

Abstract: We investigate many-body quantum fluctuation effects of Rosen-Zener transition of Bose-Einstein condensate (BEC) in a symmetric double-well potential through the relation between the average population imbalance of the final state (APIFS) and scanning period. In the linear case, we deduce the analytical expression of the APIFS which has the same behavior as in the mean-field level. We also employ numerical calculation to demonstrate it. In the nonlinear case, numerical results show that the APIFS in the sudden limit also accords with that in the mean-field level whereas in the adiabatic limit the many-body result is quite different from that of the mean-field case: the behavior of APIFS with respect to scanning period is similar to sinusoidal rather than rectangular oscillation, besides the oscillation period increases with both the total number N and the nonlinear parameter c increasing.

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