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研究了玻色-爱因斯坦凝聚体中非线性相互作用对量子共振棘流的影响. 满足量子共振条件的周期驱动使得波包在动量空间出现弹道扩散, 当波包扩散具有特定方向时, 系统就出现定向的动量流.弱非线性相互作用下的冷原子分成两簇, 它们分别受到方向相反的稳定周期驱动力, 以各自恒定的加速度沿相反方向运动.波包在动量空间的扩散表现为两个稳定的沿相反方向运动的峰.非线性相互作用的增强使得正方向运动的冷原子减少, 负方向运动的冷原子增加, 从而系统的动量流减弱甚至反转.当非线性相互作用足够强时, 动量空间中的波包只有一个稳定的峰, 且峰值对应的动量不随时间变化.此时冷原子受的周期驱动力为零, 定向的动量流消失.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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Keywords:
- Bose-Einstein condensate /
- quantum resonance /
- ratchet
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[55] Liu J, Hu B, Li B 1998 Phys. Rev. Lett. 81 1749
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[58] Bandrauk A D, Shen H 1994 J. Phys. A 27 7147
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[60] Wang B, Fu P, Liu J, Wu B 2006 Phys. Rev. A 74 063610
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-
[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 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 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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