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Effects of nonlinearity on quantum resonance ratchet

Zhao Wen-Lei Dou Fu-Quan Wang Jian-Zhong

Effects of nonlinearity on quantum resonance ratchet

Zhao Wen-Lei, Dou Fu-Quan, Wang Jian-Zhong
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  • We investigate the effect of the nonlinear interaction on the quantum resonance ratchet for the periodically kicked Bose-Einstein condensate that is realized on a ring. In the noninteracting case, the wave packet spreads asymmetrically in momentum space, leading to a directed current. We show that for the weak nonlinear interaction, the probability density distribution in momentum space has two peaks which linearly shift to ward positive and negative momentum, respectively. The force periodically acting on each peak is a constant with time evolution. The competition between the motions of the two parts of cold atoms leads to the reduce or the revival of the momentum current. For the strong nonlinearity, the momentum distribution has only one peak which does not shift with time. The force on this peak is almost zero with time evolution, thus the directed current varnishes.
    • Funds: Project supported by the National High Technology Research and Development Program of China (Grant No.2011AA120101), and the National Basic Research Program of China (Grant No. 2011CB921503).
    [1]

    Feynmann R P 1966 The Feynman Lectures on Physics (Addison-Wesley, Reading, MA)

    [2]

    Kohler S, Lehmann J, Hänggi P 2005 Phys. Rep. 406 379

    [3]

    Sun Y S 2009 Some Important Problems in Nonlinear Sciences (University of Science and Technology of China Press) p463 (in Chinese) [孙义燧, 2009 非线性科学若干前沿问题(合肥:中国科学技术大学出版社) 第463页]

    [4]

    Reimann P 2002 Phys. Rep. 361 57

    [5]

    Hänggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 1

    [6]

    Astumian R D 1997 Science 276 917

    [7]

    Reimann P, Hänggi P 2002 Appl. Phys. A 75 169

    [8]

    Dittrich T, Naranjo N 2010 Chem. Phys. 375 486

    [9]

    Jülicher F, Ajdari A, Prost J 1997 Rev. Mod. Phys. 69 1269

    [10]

    Astumian R D, Hänggi P 2002 Phys. Today. 55 33

    [11]

    Wambaugh J F 1999 Phys. Rev. Lett. 83 5106

    [12]

    Zhu B Y, Marchesoni F, Nori F 2004 Phys. Rev. Lett. 92 180602

    [13]

    Flach S, Yevtushenko O, Zolotaryuk Y 2000 Phys. Rev. Lett. 84 2358

    [14]

    Denisov S, Morales-Molina L, Flach S, Hänggi P 2007 Phys. Rev. A 75 063424

    [15]

    Schanz H, Otto M, Ketzmerick R, Dittrich T 2001 Phys. Rev. Lett. 87 070601

    [16]

    Schanz H, Dittrich T, Ketzmerick R 2005 Phys. Rev. E 71 026228

    [17]

    Izrailev F M 1990 Phys. Rep. 196 299

    [18]

    Hu B, Li B, Liu J, Gu Y 1999 Phys. Rev. Lett. 82 4224

    [19]

    Liu J, Cheng W T, Cheng C G 2000 Commun. Theor. Phys. 33 15

    [20]

    Moore F L, Robinson J C, Bharucha C F, Sundaram B, Raizen M G 1995 Phys. Rev. Lett. 75 4598

    [21]

    Duffy G J, Parkins S, Müller T, Sadgrove M, Leonhardt R, Wilson A C 2004 Phys. Rev. E 70 056206

    [22]

    Reimann P, Grifoni M, Hänggi P 1997 Phys. Rev. Lett. 79 10

    [23]

    Lehmann J, Kohler S, Hänggi P, Nitzan A 2002 Phys. Rev. Lett. 88 228305

    [24]

    Carlo G G, Benenti G, Casati G, Shepelyansky D L 2005 Phys. Rev. Lett. 94 164101

    [25]

    Carlo G G 2006 Phys. Rev. A 74 033617

    [26]

    Cavallasca L, Artuso R, Casati G 2007 Phys. Rev. E 75 066213

    [27]

    Gong J, Polleti D, Hänggi P 2007 Phys. Rev. A 75 033602

    [28]

    Gong J, Brumer P 2006 Phys. Rev. Lett. 97 240602

    [29]

    Gong J, Brumer P 2004 Phys. Rev. E 70 016202

    [30]

    Monteiro T S, Dando P A, Hutchings N A C, Isherwood M R 2002 Phys. Rev. E 89 194102

    [31]

    Jones P H, Goonasekera M, Meacher D R, Jonckheere T, Monteiro T S 2007 Phys. Rev. Lett. 98 073002

    [32]

    Lundh E, Wallin M 2005 Phys. Rev. Lett. 94 110603

    [33]

    Kenfack A, Gong J, Pattanayak A K 2008 Phys. Rev. Lett. 100 044104

    [34]

    Poletti D, Carlo G G, Li B 2007 Phys. Rev. E 75 01110

    [35]

    Sadgrove M, Horikoshi M, Sekimura T, Nakagawa K 2007 Phys. Rev. Lett. 99 043002

    [36]

    Dana I, Ramareddy V, Talukdar I, Summy G S 2008 Phys. Rev. Lett. 100 024103

    [37]

    Dana I, Roitberg V 2007 Phys. Rev. E 76 015201

    [38]

    Mennerat-Robilliard C 1999 Phys. Rev. Lett. 82 851

    [39]

    Schiavoni M, Sanchez-Palencia L, Renzoni F, Grynberg G 2003 Phys. Rev. Lett. 90 094101

    [40]

    Gommers R, Denisov S, Renzoni F 2006 Phys. Rev. Lett. 96 240604

    [41]

    Dalfovo F, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys. 71 463

    [42]

    Pitaevskii L P, Stringari S 2003 Bose-Einstein Condensation (Oxford University Press, New York)

    [43]

    Morales-Molina L, Flach S 2008 New J. Phys. 10 013008

    [44]

    Lundh E 2006 Phys. Rev. E 74 016212

    [45]

    Poletti D, Benenti G, Casati G, Li B 2007 Phys. Rev. A 76 023421

    [46]

    Poletti D, Benenti G, Casati G, Hänggi P, Li B 2009 Phys. Rev. Lett. 102 130604

    [47]

    Gupta S 2005 Phys. Rev. Lett. 95 143201

    [48]

    Ryu C 2007 Phys. Rev. Lett. 99 260401

    [49]

    Olson S E, Terraciano M L, Bashkansky M, Fatemi F K 2007 Phys. Rev. A 76 061404

    [50]

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

    [51]

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

    [52]

    Zhang C, Liu J, Raizen M G, Niu Q 2004 Phys. Rev. Lett. 92 054101

    [53]

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

    [54]

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

    [55]

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

    [56]

    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]

    [57]

    Ma Y, Fu L B, Yang Z A, Liu J 2006 Acta Phys. Sin. 55 5623 (in Chinese) [马云, 傅立斌, 杨志安, 刘杰 2006 物理学报 55 5623]

    [58]

    Bandrauk A D, Shen H 1994 J. Phys. A 27 7147

    [59]

    Wang G F, Fu L B, Liu J 2006 Phys. Rev. A 73 013619

    [60]

    Wang B, Fu P, Liu J, Wu B 2006 Phys. Rev. A 74 063610

    [61]

    Kottos T, Weiss M 2004 Phys. Rev. Lett. 93 190604

  • [1]

    Feynmann R P 1966 The Feynman Lectures on Physics (Addison-Wesley, Reading, MA)

    [2]

    Kohler S, Lehmann J, Hänggi P 2005 Phys. Rep. 406 379

    [3]

    Sun Y S 2009 Some Important Problems in Nonlinear Sciences (University of Science and Technology of China Press) p463 (in Chinese) [孙义燧, 2009 非线性科学若干前沿问题(合肥:中国科学技术大学出版社) 第463页]

    [4]

    Reimann P 2002 Phys. Rep. 361 57

    [5]

    Hänggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 1

    [6]

    Astumian R D 1997 Science 276 917

    [7]

    Reimann P, Hänggi P 2002 Appl. Phys. A 75 169

    [8]

    Dittrich T, Naranjo N 2010 Chem. Phys. 375 486

    [9]

    Jülicher F, Ajdari A, Prost J 1997 Rev. Mod. Phys. 69 1269

    [10]

    Astumian R D, Hänggi P 2002 Phys. Today. 55 33

    [11]

    Wambaugh J F 1999 Phys. Rev. Lett. 83 5106

    [12]

    Zhu B Y, Marchesoni F, Nori F 2004 Phys. Rev. Lett. 92 180602

    [13]

    Flach S, Yevtushenko O, Zolotaryuk Y 2000 Phys. Rev. Lett. 84 2358

    [14]

    Denisov S, Morales-Molina L, Flach S, Hänggi P 2007 Phys. Rev. A 75 063424

    [15]

    Schanz H, Otto M, Ketzmerick R, Dittrich T 2001 Phys. Rev. Lett. 87 070601

    [16]

    Schanz H, Dittrich T, Ketzmerick R 2005 Phys. Rev. E 71 026228

    [17]

    Izrailev F M 1990 Phys. Rep. 196 299

    [18]

    Hu B, Li B, Liu J, Gu Y 1999 Phys. Rev. Lett. 82 4224

    [19]

    Liu J, Cheng W T, Cheng C G 2000 Commun. Theor. Phys. 33 15

    [20]

    Moore F L, Robinson J C, Bharucha C F, Sundaram B, Raizen M G 1995 Phys. Rev. Lett. 75 4598

    [21]

    Duffy G J, Parkins S, Müller T, Sadgrove M, Leonhardt R, Wilson A C 2004 Phys. Rev. E 70 056206

    [22]

    Reimann P, Grifoni M, Hänggi P 1997 Phys. Rev. Lett. 79 10

    [23]

    Lehmann J, Kohler S, Hänggi P, Nitzan A 2002 Phys. Rev. Lett. 88 228305

    [24]

    Carlo G G, Benenti G, Casati G, Shepelyansky D L 2005 Phys. Rev. Lett. 94 164101

    [25]

    Carlo G G 2006 Phys. Rev. A 74 033617

    [26]

    Cavallasca L, Artuso R, Casati G 2007 Phys. Rev. E 75 066213

    [27]

    Gong J, Polleti D, Hänggi P 2007 Phys. Rev. A 75 033602

    [28]

    Gong J, Brumer P 2006 Phys. Rev. Lett. 97 240602

    [29]

    Gong J, Brumer P 2004 Phys. Rev. E 70 016202

    [30]

    Monteiro T S, Dando P A, Hutchings N A C, Isherwood M R 2002 Phys. Rev. E 89 194102

    [31]

    Jones P H, Goonasekera M, Meacher D R, Jonckheere T, Monteiro T S 2007 Phys. Rev. Lett. 98 073002

    [32]

    Lundh E, Wallin M 2005 Phys. Rev. Lett. 94 110603

    [33]

    Kenfack A, Gong J, Pattanayak A K 2008 Phys. Rev. Lett. 100 044104

    [34]

    Poletti D, Carlo G G, Li B 2007 Phys. Rev. E 75 01110

    [35]

    Sadgrove M, Horikoshi M, Sekimura T, Nakagawa K 2007 Phys. Rev. Lett. 99 043002

    [36]

    Dana I, Ramareddy V, Talukdar I, Summy G S 2008 Phys. Rev. Lett. 100 024103

    [37]

    Dana I, Roitberg V 2007 Phys. Rev. E 76 015201

    [38]

    Mennerat-Robilliard C 1999 Phys. Rev. Lett. 82 851

    [39]

    Schiavoni M, Sanchez-Palencia L, Renzoni F, Grynberg G 2003 Phys. Rev. Lett. 90 094101

    [40]

    Gommers R, Denisov S, Renzoni F 2006 Phys. Rev. Lett. 96 240604

    [41]

    Dalfovo F, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys. 71 463

    [42]

    Pitaevskii L P, Stringari S 2003 Bose-Einstein Condensation (Oxford University Press, New York)

    [43]

    Morales-Molina L, Flach S 2008 New J. Phys. 10 013008

    [44]

    Lundh E 2006 Phys. Rev. E 74 016212

    [45]

    Poletti D, Benenti G, Casati G, Li B 2007 Phys. Rev. A 76 023421

    [46]

    Poletti D, Benenti G, Casati G, Hänggi P, Li B 2009 Phys. Rev. Lett. 102 130604

    [47]

    Gupta S 2005 Phys. Rev. Lett. 95 143201

    [48]

    Ryu C 2007 Phys. Rev. Lett. 99 260401

    [49]

    Olson S E, Terraciano M L, Bashkansky M, Fatemi F K 2007 Phys. Rev. A 76 061404

    [50]

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

    [51]

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

    [52]

    Zhang C, Liu J, Raizen M G, Niu Q 2004 Phys. Rev. Lett. 92 054101

    [53]

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

    [54]

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

    [55]

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

    [56]

    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]

    [57]

    Ma Y, Fu L B, Yang Z A, Liu J 2006 Acta Phys. Sin. 55 5623 (in Chinese) [马云, 傅立斌, 杨志安, 刘杰 2006 物理学报 55 5623]

    [58]

    Bandrauk A D, Shen H 1994 J. Phys. A 27 7147

    [59]

    Wang G F, Fu L B, Liu J 2006 Phys. Rev. A 73 013619

    [60]

    Wang B, Fu P, Liu J, Wu B 2006 Phys. Rev. A 74 063610

    [61]

    Kottos T, Weiss M 2004 Phys. Rev. Lett. 93 190604

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  • Received Date:  13 May 2012
  • Accepted Date:  31 May 2012
  • Published Online:  20 November 2012

Effects of nonlinearity on quantum resonance ratchet

  • 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), and the National Basic Research Program of China (Grant No. 2011CB921503).

Abstract: We investigate the effect of the nonlinear interaction on the quantum resonance ratchet for the periodically kicked Bose-Einstein condensate that is realized on a ring. In the noninteracting case, the wave packet spreads asymmetrically in momentum space, leading to a directed current. We show that for the weak nonlinear interaction, the probability density distribution in momentum space has two peaks which linearly shift to ward positive and negative momentum, respectively. The force periodically acting on each peak is a constant with time evolution. The competition between the motions of the two parts of cold atoms leads to the reduce or the revival of the momentum current. For the strong nonlinearity, the momentum distribution has only one peak which does not shift with time. The force on this peak is almost zero with time evolution, thus the directed current varnishes.

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