Dynamics of Bose-Einstein condensation in an asymmetric double-well potential

Ying Yao-Jun; Li Hai-Bin

doi:10.7498/aps.72.20230419

Abstract

Josephson effect of Bose-Einstein condensate in double-well potential is an obvious manifestation of macroscopic quantum coherence. Most of researches focus on the symmetric double-well potential. In this work, we investigate the dynamic of Bose-Einstein condensates in an asymmetric double-well potential by using two-mode theory and computer simulation. In the absence of the interaction between atoms, the dynamic equation of condensate can be solved analytically. The amplitude as a function of energy difference of two wells is obtained. We can find that the change of energy difference will lead to the different dynamic behaviors of condensate. If the energy difference is relatively large, the condensate will primarily occupy the well that is occupied more than the other well at the beginning time. It is interesting that such a trap phenomenon is not dependent on the position of the high energy potential well nor the position of low energy potential well. If the energy difference becomes small, the tunneling and oscillation of condensate will be enhanced. When the interaction between atoms is present, our numerical calculations show that as the nonlinear interaction increases, the dynamic behavior of condensate exhibits different characteristics, such as trapping in a well, enhancing the tunneling and oscillation between two wells, and enhancing the trapping in a well at large nonlinear interaction, which is similar to the dynamic change caused by the energy difference in the case of ideal condensate. That is to say, on the one hand, the nonlinear interaction can lead to the trap of condensate as well as the dynamic trap to happen in symmetric double-well potential. On the other hand, the nonlinearity can promote the tunneling of condensate, counteracting the effect of the asymmetry of potential. And, this counteracting effect is related to the difference in energy between asymmetric potential wells. To understand the underlying mechanism, the full dynamic behavior of two-mode model is illustrated and the dynamic transition can be seen clearly. Combining the results obtained with and without interaction, regarding nonlinear interaction as effective potential provides a clear way to explain dynamic transition of condensate in an asymmetric double-well potential. In addition, we also perform the numerical simulations of the Gross-Pitaevskii equation, and the results are consistent with the conclusions obtained by using the two-mode theory.

Keywords:

Authors and contacts

College of Science, Zhejiang University of Technology, Hangzhou 310023, China

Corresponding author: Li Hai-Bin, hbli@zjut.edu.cn

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References

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Cited By

图 1 $ z\left(0\right)=0.6 $时, 无相互作用下当$ \gamma $变化时占据数差随时间的演化

Figure 1. Population imbalance versus time at different $ \gamma $ without interactions at $ z\left(0\right)=0.6$.

DownLoad: Full-Size Img PowerPoint

图 2 $ z\left(0\right)=0.6 $时, 当非线性相互作用取不同值时, 振幅对能量差的依赖关系

Figure 2. Amplitude versus energy difference when the nonlinear interaction parameter is different at $ z\left(0\right)=0.6 $.

DownLoad: Full-Size Img PowerPoint

图 3 $ z\left(0\right)=0.6 $, $ \gamma =-5 $, 当$ \lambda $变化时, 占据数差随时间的演化

Figure 3. Population imbalance versus time at different $ \lambda $ at $ z\left(0\right)=0.6 $, $ \gamma =-5 $.

DownLoad: Full-Size Img PowerPoint

图 4 $ z\left(0\right)=0.6 $, 势阱能量差取不同值时, 振幅随$ \lambda $的变化

Figure 4. Amplitude versus $ \lambda $when energy difference is different at $ z\left(0\right)=0.6 $.

DownLoad: Full-Size Img PowerPoint

图 5 $ z\left(0\right)=0.6 $, 相空间中的等能量线

Figure 5. Constant energy line in phase-space at $ z\left(0\right)=0.6 $.

DownLoad: Full-Size Img PowerPoint

图 6 $ \beta =20 $, $ z\left(0\right)=0.6 $, 不同$ g $条件下粒子占据数差随时间的变化

Figure 6. Population imbalance versus time at different $ g $, $\beta =20 \;{\rm{and}} \;z\left(0\right)=0.6$.

DownLoad: Full-Size Img PowerPoint

[1]	Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198 Google Scholar
[2]	Davis K B, Mewes M O, Andrews M R, Vandruten N J, Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 75 3969 Google Scholar
[3]	Bradley C C, Sackett C A, Tollett J J, Hulet R G 1995 Phys. Rev. Lett. 75 1687 Google Scholar
[4]	Andrews M R, Townsend C G, Miesner H J, Durfee D S, Kurn D M, Ketterle W 1997 Science 275 637 Google Scholar
[5]	Gross E P 1961 Il Nuovo Cimento 20 454 Google Scholar
[6]	Pitaevskii L P 1961 Sov. Phys. JETP 13 451
[7]	Dalfovo F, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys. 71 463 Google Scholar
[8]	Bloch I, Dalibard J, Zwerger W 2008 Rev. Mod. Phys. 80 885 Google Scholar
[9]	Josephson B D 1962 Phys. Lett. 1 251 Google Scholar
[10]	Milburn G J, Corney J, Wright E M, Walls D F 1997 Phys. Rev. A 55 4318 Google Scholar
[11]	Smerzi A, Fantoni S, Giovanazzi S, Shenoy S R 1997 Phys. Rev. Lett. 79 4950 Google Scholar
[12]	Raghavan S, Smerzi A, Fantoni S, Shenoy S R 1999 Phys. Rev. A 59 620 Google Scholar
[13]	Cataliotti F S, Burger S, Fort C, Maddaloni P, Minardi F, Trombettoni A, Smerzi A, Inguscio M 2001 Science 293 843 Google Scholar
[14]	Albiez M, Gati R, Folling J, Hunsmann S, Cristiani M, Oberthaler M K 2005 Phys. Rev. Lett. 95 010402 Google Scholar
[15]	Giovanazzi S, Smerzi A, Fantoni S 2000 Phys. Rev. Lett. 84 4521 Google Scholar
[16]	Zhang Y B, Muller-Kirsten H J W 2001 Phys. Rev. A 64 023608 Google Scholar
[17]	Ananikian D, Bergeman T 2006 Phys. Rev. A 73 013604 Google Scholar
[18]	Giovanazzi S, Esteve J, Oberthaler M K 2008 New J. Phys. 10 045009 Google Scholar
[19]	Julia-Diaz B, Martorell J, Mele-Messeguer M, Polls A 2010 Phys. Rev. A 82 063626 Google Scholar
[20]	Jezek D M, Capuzzi P, Cataldo H M 2013 Phys. Rev. A 87 053625 Google Scholar
[21]	Burchianti A, Fort C, Modugno M 2017 Phys. Rev. A 95 023627 Google Scholar
[22]	Fu L, Liu J 2006 Phys. Rev. A 74 063614 Google Scholar
[23]	Spagnolli G, Semeghini G, Masi L, Ferioli G, Trenkwalder A, Coop S, Landini M, Pezze L, Modugno G, Inguscio M, Smerzi A, Fattori M 2017 Phys. Rev. Lett. 118 230403 Google Scholar
[24]	Zhang D W, Fu L B, Wang Z D, Zhu S L 2012 Phys. Rev. A 85 043609 Google Scholar
[25]	Wang W Y, Dou F Q, Duan W S 2018 J. Phys. B: At. Mol. Opt. Phys. 51 035002 Google Scholar
[26]	Hou J, Luo X W, Sun K, Bersano T, Gokhroo V, Mossman S, Engels P, Zhang C 2018 Phys. Rev. Lett. 120 120401 Google Scholar
[27]	王冠芳, 傅立斌, 赵鸿, 刘杰 2005 物理学报 54 5003 Google Scholar Wang G F, Fu L B, Zhao H, Liu J 2005 Acta Phys. Sin. 54 5003 Google Scholar
[28]	刘泽专, 杨志安 2007 物理学报 56 1245 Google Scholar Liu Z Z, Yang Z A 2007 Acta Phys. Sin. 56 1245 Google Scholar
[29]	房永翠, 杨志安, 杨丽云 2008 物理学报 57 661 Google Scholar Fang Y C, Yang Z A, Yang L Y 2008 Acta Phys. Sin. 57 661 Google Scholar
[30]	黄芳, 李海彬 2011 物理学报 60 020303 Google Scholar Huang F, Li H B 2011 Acta Phys. Sin. 60 020303 Google Scholar
[31]	马云, 傅立斌, 杨志安, 刘杰 2006 物理学报 55 5623 Google Scholar Ma Y, Fu L B, Yang Z A, Liu J 2006 Acta Phys. Sin. 55 5623 Google Scholar
[32]	臧小飞, 李菊萍, 谭磊 2007 物理学报 56 4348 Google Scholar Zang X F, Li J P, Tan L 2007 Acta Phys. Sin. 56 4348 Google Scholar
[33]	李菊萍, 谭磊, 臧小飞, 杨科 2008 物理学报 57 7467 Google Scholar Li J P, Tan L, Zang X F, Yang K 2008 Acta Phys. Sin. 57 7467 Google Scholar
[34]	张恒, 段文山 2013 物理学报 62 160303 Google Scholar Zhang H, Duan W S 2013 Acta Phys. Sin. 62 160303 Google Scholar
[35]	Levy S, Lahoud E, Shomroni I, Steinhauer J 2007 Nature 449 579 Google Scholar
[36]	LeBlanc L J, Bardon A B, McKeever J, Extavour M H T, Jervis D, Thywissen J H, Piazza F, Smerzi A 2011 Phys. Rev. Lett. 106 025302 Google Scholar
[37]	Trenkwalder A, Spagnolli G, Semeghini G, Coop S, Landini M, Castilho P, Pezze L, Modugno G, Inguscio M, Smerzi A, Fattori M 2016 Nat. Phys. 12 826 Google Scholar
[38]	肖宇飞, 王登龙, 王凤姣, 颜晓红 2006 物理学报 55 547 Google Scholar Xiao Y F, Wang D L, Wang F J, Yan X H 2006 Acta Phys. Sin. 55 547 Google Scholar
[39]	Julia-Diaz B, Martorell J, Polls A 2010 Phys. Rev. A 81 063625 Google Scholar
[40]	Hunn S, Zimmermann K, Hiller M, Buchleitner A 2013 Phys. Rev. A 87 043626 Google Scholar
[41]	Cataldo H M, Jezek D M 2014 Phys. Rev. A 90 043610 Google Scholar
[42]	Cosme J G, Andersen M F, Brand J 2017 Phys. Rev. A 96 013616 Google Scholar
[43]	Haldar S K, Alon O E 2019 New J. Phys. 21 103037 Google Scholar

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