Effects of nonlinearity on quantum resonance ratchet

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

doi:10.7498/aps.61.220503

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.

Keywords:

Authors and contacts

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
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).

References

[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

Cited By

[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]	Qiu Xu, Wang Lin-Xue, Chen Guang-Ping, Hu Ai-Yuan, Wen Lin. Dynamics of spin-tensor-momentum coupled Bose-Einstein condensates. Acta Physica Sinica, 2023, 72(18): 180304. doi: 10.7498/aps.72.20231076
[2]	Xing Jian-Chong, Zhang Wen-Jing, Yang Tao. Noncanonical vortex states and dynamics in Bose-Einstein condensates. Acta Physica Sinica, 2023, 72(10): 100306. doi: 10.7498/aps.72.20222289
[3]	Jia Rui-Yu, Fang Ping-Ping, Gao Chao, Lin Ji. Quenched solitons and shock waves in Bose-Einstein condensates. Acta Physica Sinica, 2021, 70(18): 180303. doi: 10.7498/aps.70.20210564
[4]	Guo Hui, Wang Ya-Jun, Wang Lin-Xue, Zhang Xiao-Fei. Dynamics of ring dark solitons in Bose-Einstein condensates. Acta Physica Sinica, 2020, 69(1): 010302. doi: 10.7498/aps.69.20191424
[5]	He Li, Yu Zeng-Qiang. Landau critical velocity of spin-orbit-coupled Bose-Einstein condensate across quantum phase transition. Acta Physica Sinica, 2017, 66(22): 220301. doi: 10.7498/aps.66.220301
[6]	Yuan Du-Qi. Boundary effects of Bose-Einstein condensation in a three-dimensional harmonic trap. Acta Physica Sinica, 2014, 63(17): 170501. doi: 10.7498/aps.63.170501
[7]	Li Zhi, Wang Jian-Zhong. Barrier scattering properties in spin-orbit coupled Bose-Einstein condensate. Acta Physica Sinica, 2013, 62(10): 100306. doi: 10.7498/aps.62.100306
[8]	Wang Jian-Zhong, Cao Hui, Dou Fu-Quan. Many-body quantum fluctuation effects of Rosen-Zener transition in Bose-Einstein condensates. Acta Physica Sinica, 2012, 61(22): 220305. doi: 10.7498/aps.61.220305
[9]	Song Li-Jun, Yan Dong, Liu Yie. Quantum Fisher information and chaos in the system of Bose-Einstein condensate. Acta Physica Sinica, 2011, 60(12): 120302. doi: 10.7498/aps.60.120302
[10]	Yan Dong, Song Li-Jun, Chen Dian-Wei. Spin squeezing of two-component Bose-Einstein condensate. Acta Physica Sinica, 2009, 58(6): 3679-3684. doi: 10.7498/aps.58.3679
[11]	Zong Feng-De, Yang Yang, Zhang Jie-Fang. Evolution and controlled manipulation of a Bose-Einstein condensate chirped soliton in external potentials. Acta Physica Sinica, 2009, 58(6): 3670-3678. doi: 10.7498/aps.58.3670
[12]	Qu Chun-Lei, Zhao Qing. Quantum-resonance ratchet in a kicked Bose-Einstein condensate. Acta Physica Sinica, 2009, 58(7): 4390-4395. doi: 10.7498/aps.58.4390
[13]	Wang Guan-Fang, Liu Hong. Irregular spin tunneling for Bose-Einstein condensates in a sweeping magnetic field. Acta Physica Sinica, 2008, 57(2): 667-673. doi: 10.7498/aps.57.667
[14]	Fang Yong-Cui, Yang Zhi-An. Chaos tunneling of Bose-Einstein condensates. Acta Physica Sinica, 2008, 57(12): 7438-7446. doi: 10.7498/aps.57.7438
[15]	Wang Hai-Lei, Yang Shi-Ping. Switch effect of Bose-Einstein condensates in a triple-well potential. Acta Physica Sinica, 2008, 57(8): 4700-4705. doi: 10.7498/aps.57.4700
[16]	Wang Zhi-Xia, Zhang Xi-He, Shen Ke. Anti-control of chaos in Bose-Einstein condensate. Acta Physica Sinica, 2008, 57(12): 7586-7590. doi: 10.7498/aps.57.7586
[17]	Fang Yong-Cui, Yang Zhi-An, Yang Li-Yun. Phase transition and entanglement entropy of Bose-Einstein condensates in double-well trap under periodic modulation. Acta Physica Sinica, 2008, 57(2): 661-666. doi: 10.7498/aps.57.661
[18]	Liu Ze-Zhuan, Yang Zhi-An. Influence of noise on self-trapping of Bose-Einstein condensates in double-well trap. Acta Physica Sinica, 2007, 56(3): 1245-1252. doi: 10.7498/aps.56.1245
[19]	Wang Guan-Fang, Fu Li-Bin, Zhao Hong, Liu Jie. Self-trapping and its periodic modulation of Bose-Einstein condensates in double-well trap. Acta Physica Sinica, 2005, 54(11): 5003-5013. doi: 10.7498/aps.54.5003
[20]	Cui Hai-Tao, Wang Lin-Cheng, Yi Xue-Xi. Low-dimensional Bose-Einstein condensation in finite-number trapped atoms. Acta Physica Sinica, 2004, 53(4): 991-995. doi: 10.7498/aps.53.991

Catalog

Vol. 61, Issue 22 - 2012-11-20

Metrics

Abstract views: 8488
PDF Downloads: 440
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板