半无限深势阱中自旋相关玻色-爱因斯坦凝聚体的量子反射与干涉

赵文静; 文灵华

doi:10.7498/aps.66.230301

摘要

玻色-爱因斯坦凝聚体与势垒或势阱的量子反射及干涉是考察宏观物质波奇特物性的最有效途径之一.利用传播子方法和基于冷原子实验广泛采用的飞行时间吸收成像方案，研究自旋相关玻色-爱因斯坦凝聚体在半无限深势阱中的反射和干涉演化动力学，得到了自旋相关的凝聚体波函数的严格解析解.结果表明，当自旋相关光晶格关闭后，非局域于不同格点中相同自旋态的物质波在自由膨胀过程中发生量子干涉，形成了对比度明显的干涉条纹.与此同时，扩张的自旋相关物质波包与半无限深势阱壁相遇发生量子反射，反射波与入射波产生二重干涉，在密度分布两边对称的局部位置出现剧烈的振荡，干涉条纹表现出显著的调制效应.分析讨论了自旋态、相干输运距离和相对相位等因素对干涉条纹的影响.该研究有助于促进对自旋相关凝聚体宏观量子特性的认识，为深入检验自旋相关光晶格中凝聚体干涉的理论模型和物理机理提供依据和新方案.

关键词:

Abstract

The quantum reflection and interference of Bose-Einstein condensates (BECs) encountering a potential barrier or well is one of the most efficient ways of studying the exotic properties of macroscopic matter waves. As a matter of fact, one can reveal the quantum nature, coherence properties, and many-body effects as well as the potential applications of ultracold atomic gases by virtue of the quantum reflection and interference of BECs. Although there have been extensive investigations regarding the quantum reflection and interference of single-component BECs, so far there have been very few studies regarding those of multi-component BECs. In this work, we investigate the quantum reflections and interferences of spin-dependent BECs in semi-infinite potential wells by using the propagation method and the time-of-flight imaging scheme which is widely used in cold atom experiments. We obtain the exact analytical solutions of the spin-dependent condensate wave functions in the semi-infinite potential wells. It is shown that once the spin-dependent optical lattice is switched off the spin-dependent matter wave packets delocalized in different lattice sites interfere with each other during the free expansion. Consequently, the interference fringes with high contrast are formed. At the same time, the expanded spin-dependent matter waves encounter the hard wall of the semi-infinite potential well, which leads to a quantum reflection. There is a double interference between the reflected wave and the freely expanded incident wave, which is characterized by the significant modulation effect in the interference patterns. Concretely, there exist intense density oscillations in several symmetric and local regions of the interference fringes. Essentially, the double interference is a self-interference of BECs, and it results from the interference between the spin-dependent BEC and the BEC image, where the hard wall severs as a mirror plane. Therefore it is similar to Young's double-slit interference in wave optics, and a standing wave node is formed at the trap wall. In particular, the positions and the intervals of the local density oscillations in the interference patterns are determined by evolution time, laser wavelength and laser intensity, which is verified in the numerical simulations and calculations. In addition, the effects of spin state, transport distance, and relative phase on the interference fringes are analyzed and discussed. The present investigation is helpful in understanding the macroscopic quantum properties of the spin-dependent BECs, and provides a new scheme to test the theoretical model and physical mechanism of the condensate interference in a spin-dependent optical lattice.

Keywords:

spin-dependent Bose-Einstein condensates /
semi-infinite potential well /
quantum reflection /
quantum interference

作者及机构信息

1.
燕山大学理学院, 河北省微结构材料物理重点实验室, 秦皇岛 066004

通信作者: 文灵华, linghuawen@ysu.edu.cn

基金项目: 国家自然科学基金（批准号：11475144）、河北省自然科学基金（批准号：A2015203037）和燕山大学人才引进科研启动基金（批准号：B846）资助的课题.

Authors and contacts

1.
Key Laboratory for Microstructural Material Physics of Hebei Province, College of Science, Yanshan University, Qinhuangdao 066004, China

Corresponding author: Wen Ling-Hua, linghuawen@ysu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11475144), the Natural Science Foundation of Hebei Province of China (Grant No. A2015203037), and the Research Foundation for Advanced Talents of Yanshan University, China (Grant No. B846).

参考文献

[1]	Andrews M R, Townsend C G, Miesner H J, Durfee D S, Kurn D M, Ketterle W 1997 Science 275 637
[2]	Pasquini T A, Shin Y, Sanner C, Saba M, Schirotzek A, Pritchard D E, Ketterle W 2004 Phys. Rev. Lett. 93 223201
[3]	Pasquini T A, Saba M, Jo G, Shin Y, Ketterle W, Pritchard D E, Savas T A, Mulders N 2006 Phys. Rev. Lett. 97 093201
[4]	Greiner M, Mandel O, Esslinger T, Hänsch T W, Bloch I 2002 Nature 415 39
[5]	Hofferberth S, Lesanovsky I, Schumm T, Imambekov A, Gritsev V, Demler E, Schmiedmayer J 2008 Nat. Phys. 4 489
[6]	Fang B, Johnson A, Roscilde T, Bouchoule I 2016 Phys. Rev. Lett. 116 050402
[7]	Chang R, Bouton Q, Cayla H, Qu C, Aspect A, Westbrook C I, Clement D 2016 Phys. Rev. Lett. 117 235303
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[11]	Marchant A L, Billam T P, Yu M M H, Rakonjac A, Helm J L, Polo J, Weiss C, Gardiner S A, Cornish S L 2016 Phys. Rev. A 93 021604
[12]	Berrada T, van Frank S, Bucker R, Schumm T, Schaff J F, Schmiedmayer J, Julia-Diaz B, Polls A 2016 Phys. Rev. A 93 063620
[13]	Fouda M F, Fang R, Ketterson J B, Shahriar M S 2016 Phys. Rev. A 94 063644
[14]	Mandel O, Greiner M, Widera A, Rom T, Hänsch T W, Bloch I 2003 Phys. Rev. Lett. 91 010407
[15]	Castin Y, Dalibard J 1997 Phys. Rev. A 55 4330
[16]	Yang X X, Wu Y 1999 Phys. Lett. A 253 219
[17]	Liu W M, Wu B, Niu Q 2000 Phys. Rev. Lett. 84 2294
[18]	Xiong H, Liu S, Huang G, Xu Z 2002 J. Phys. B 35 4863
[19]	Liu S, Xiong H, Xu Z, Huang G 2003 J. Phys. B 36 2083
[20]	Xiong H, Liu S, Zhan M 2006 New J. Phys. 8 245
[21]	Bach R, Rzazewski K 2004 Phys. Rev. Lett. 92 200401
[22]	Liu S, Xiong H 2007 New J. Phys. 9 412
[23]	Hadzibabic Z, Stock S, Battelier B, Bretin V, Dalibard J 2004 Phys. Rev. Lett. 93 180403
[24]	Ashhab S 2005 Phys. Rev. A 71 063602
[25]	Wen L H, Liu M, Xiong H W, Zhan M S 2005 Eur. Phys. J. D 36 89
[26]	Wen L H, Liu M, Kong L B, Chen A X, Zhan M S 2005 Chin. Phys. 14 690
[27]	Wen L H, Liu M, Kong L B, Zhan M S 2005 Chin. Phys. Lett. 22 812
[28]	Yue X, Liu S, Wu B, Xiong H 2017 Chin. Phys. B 26 050501
[29]	Wen L H, Xiong H W, Wu B 2010 Phys. Rev. A 82 053627
[30]	Wen L H, Li J H 2014 Phys. Rev. A 90 053621
[31]	Feynman R P, Hibbs A R 1965 Quantum Mechanics and Path Integrals (New York:McGraw-Hill Inc.) pp26-74
[32]	Akhundova E A, Dodonov V V, Man'ko V I 1985 J. Phys. A 18 467
[33]	Pedri P, Pitaevskii L, Stringari S, Fort C, Burger S, Cataliotti F S, Maddaloni P, Minardi F, Inguscio M 2001 Phys. Rev. Lett. 87 220401
[34]	Robinett W 2006 Phys. Scr. 73 681

施引文献

[1]	Andrews M R, Townsend C G, Miesner H J, Durfee D S, Kurn D M, Ketterle W 1997 Science 275 637
[2]	Pasquini T A, Shin Y, Sanner C, Saba M, Schirotzek A, Pritchard D E, Ketterle W 2004 Phys. Rev. Lett. 93 223201
[3]	Pasquini T A, Saba M, Jo G, Shin Y, Ketterle W, Pritchard D E, Savas T A, Mulders N 2006 Phys. Rev. Lett. 97 093201
[4]	Greiner M, Mandel O, Esslinger T, Hänsch T W, Bloch I 2002 Nature 415 39
[5]	Hofferberth S, Lesanovsky I, Schumm T, Imambekov A, Gritsev V, Demler E, Schmiedmayer J 2008 Nat. Phys. 4 489
[6]	Fang B, Johnson A, Roscilde T, Bouchoule I 2016 Phys. Rev. Lett. 116 050402
[7]	Chang R, Bouton Q, Cayla H, Qu C, Aspect A, Westbrook C I, Clement D 2016 Phys. Rev. Lett. 117 235303
[8]	Castellanos E, Rivas J I 2015 Phys. Rev. D 91 084019
[9]	Wen L H, Wang J S, Feng J, Hu H Q 2008 J. Phys. B 41 135301
[10]	Scott R G, Martin A M, Fromhold T M, Sheard F W 2005 Phys. Rev. Lett. 95 073201
[11]	Marchant A L, Billam T P, Yu M M H, Rakonjac A, Helm J L, Polo J, Weiss C, Gardiner S A, Cornish S L 2016 Phys. Rev. A 93 021604
[12]	Berrada T, van Frank S, Bucker R, Schumm T, Schaff J F, Schmiedmayer J, Julia-Diaz B, Polls A 2016 Phys. Rev. A 93 063620
[13]	Fouda M F, Fang R, Ketterson J B, Shahriar M S 2016 Phys. Rev. A 94 063644
[14]	Mandel O, Greiner M, Widera A, Rom T, Hänsch T W, Bloch I 2003 Phys. Rev. Lett. 91 010407
[15]	Castin Y, Dalibard J 1997 Phys. Rev. A 55 4330
[16]	Yang X X, Wu Y 1999 Phys. Lett. A 253 219
[17]	Liu W M, Wu B, Niu Q 2000 Phys. Rev. Lett. 84 2294
[18]	Xiong H, Liu S, Huang G, Xu Z 2002 J. Phys. B 35 4863
[19]	Liu S, Xiong H, Xu Z, Huang G 2003 J. Phys. B 36 2083
[20]	Xiong H, Liu S, Zhan M 2006 New J. Phys. 8 245
[21]	Bach R, Rzazewski K 2004 Phys. Rev. Lett. 92 200401
[22]	Liu S, Xiong H 2007 New J. Phys. 9 412
[23]	Hadzibabic Z, Stock S, Battelier B, Bretin V, Dalibard J 2004 Phys. Rev. Lett. 93 180403
[24]	Ashhab S 2005 Phys. Rev. A 71 063602
[25]	Wen L H, Liu M, Xiong H W, Zhan M S 2005 Eur. Phys. J. D 36 89
[26]	Wen L H, Liu M, Kong L B, Chen A X, Zhan M S 2005 Chin. Phys. 14 690
[27]	Wen L H, Liu M, Kong L B, Zhan M S 2005 Chin. Phys. Lett. 22 812
[28]	Yue X, Liu S, Wu B, Xiong H 2017 Chin. Phys. B 26 050501
[29]	Wen L H, Xiong H W, Wu B 2010 Phys. Rev. A 82 053627
[30]	Wen L H, Li J H 2014 Phys. Rev. A 90 053621
[31]	Feynman R P, Hibbs A R 1965 Quantum Mechanics and Path Integrals (New York:McGraw-Hill Inc.) pp26-74
[32]	Akhundova E A, Dodonov V V, Man'ko V I 1985 J. Phys. A 18 467
[33]	Pedri P, Pitaevskii L, Stringari S, Fort C, Burger S, Cataliotti F S, Maddaloni P, Minardi F, Inguscio M 2001 Phys. Rev. Lett. 87 220401
[34]	Robinett W 2006 Phys. Scr. 73 681

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