Quantum reflection of a Bose-Einstein condensate with a dark soliton from a step potential

doi:10.1088/1674-1056/ac051e

中国物理B ›› 2021, Vol. 30 ›› Issue (12): 120303-120303.doi: 10.1088/1674-1056/ac051e

Quantum reflection of a Bose-Einstein condensate with a dark soliton from a step potential

Dong-Mei Wang(王冬梅)¹, Jian-Chong Xing(邢健崇)¹, Rong Du(杜荣)¹, Bo Xiong(熊波)^2,†, and Tao Yang(杨涛)^1,3,4,‡

1 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics, Northwest University, Xi'an 710127, China;
2 School of Science, Wuhan University of Technology, Wuhan 430070, China;
3 School of Physics, Northwest University, Xi'an 710127, China;
4 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China

收稿日期:2021-03-28 修回日期:2021-04-19 接受日期:2021-05-26 出版日期:2021-11-15 发布日期:2021-11-15
通讯作者: Bo Xiong, Tao Yang E-mail:boxiongpd@gmail.com;yangt@nwu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11775178, 12075175, 11934015, and 12047502), the Major Basic Research Program of Natural Science of Shaanxi Province, China (Grant Nos. 2017KCT-12 and 2017ZDJC-32), and the Open Research Fund of Shaanxi Key Laboratory for Theoretical Physics Frontiers (Grant No. SXKLTPF-K20190602).

Quantum reflection of a Bose-Einstein condensate with a dark soliton from a step potential

Dong-Mei Wang(王冬梅)¹, Jian-Chong Xing(邢健崇)¹, Rong Du(杜荣)¹, Bo Xiong(熊波)^2,†, and Tao Yang(杨涛)^1,3,4,‡

1 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics, Northwest University, Xi'an 710127, China;
2 School of Science, Wuhan University of Technology, Wuhan 430070, China;
3 School of Physics, Northwest University, Xi'an 710127, China;
4 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China

Received:2021-03-28 Revised:2021-04-19 Accepted:2021-05-26 Online:2021-11-15 Published:2021-11-15
Contact: Bo Xiong, Tao Yang E-mail:boxiongpd@gmail.com;yangt@nwu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11775178, 12075175, 11934015, and 12047502), the Major Basic Research Program of Natural Science of Shaanxi Province, China (Grant Nos. 2017KCT-12 and 2017ZDJC-32), and the Open Research Fund of Shaanxi Key Laboratory for Theoretical Physics Frontiers (Grant No. SXKLTPF-K20190602).

摘要/Abstract

摘要： We study dynamical behaviors of a Bose-Einstein condensate (BEC) containing a dark soliton reflected from potential wells and potential barriers, respectively. The orientation angle of the dark soliton and the width of the potential change play key roles on the reflection probability R_s. Variation of the reflection probability with respect to the orientation angle θ of the dark soliton can be well described by a cosine function R_s~cos[λ(θ-π/2)], where λ is a parameter determined by the width of the potential change. There are two characteristic lengths which determine the reflection properties. The dependence of the reflection probability on the width of the potential change shows distinct characters for potential wells and potential barriers. The length of the dark soliton determines the sensitive width of potential wells, whereas for potential barriers, the decay length of the matter wave in the region of the barrier qualifies the sensitive width of the barrier. The time evolution of the density profiles of the system during the reflection process is studied to disclose the different behaviors of matter waves in the region of the potential variation.

关键词: Bose-Einstein condensate, dark soliton, quantum reflection

Abstract: We study dynamical behaviors of a Bose-Einstein condensate (BEC) containing a dark soliton reflected from potential wells and potential barriers, respectively. The orientation angle of the dark soliton and the width of the potential change play key roles on the reflection probability R_s. Variation of the reflection probability with respect to the orientation angle θ of the dark soliton can be well described by a cosine function R_s~cos[λ(θ-π/2)], where λ is a parameter determined by the width of the potential change. There are two characteristic lengths which determine the reflection properties. The dependence of the reflection probability on the width of the potential change shows distinct characters for potential wells and potential barriers. The length of the dark soliton determines the sensitive width of potential wells, whereas for potential barriers, the decay length of the matter wave in the region of the barrier qualifies the sensitive width of the barrier. The time evolution of the density profiles of the system during the reflection process is studied to disclose the different behaviors of matter waves in the region of the potential variation.

Key words: Bose-Einstein condensate, dark soliton, quantum reflection

中图分类号: (Other Bose-Einstein condensation phenomena)

03.75.Nt

05.45.Yv (Solitons) 34.50.-s (Scattering of atoms and molecules)

Dong-Mei Wang(王冬梅), Jian-Chong Xing(邢健崇), Rong Du(杜荣), Bo Xiong(熊波), and Tao Yang(杨涛). Quantum reflection of a Bose-Einstein condensate with a dark soliton from a step potential[J]. 中国物理B, 2021, 30(12): 120303-120303.

参考文献

[1] Friedrich H and Trost J 2004 Phys. Rep. 397 359
[2] Landau L D, Landau L D and Landau L D 1992 Lehrbuch der Theoretischen Physik I!I!I. Quantenmechanik (Europa Lehrmittel Verlag)
[3] Landragin A, Courtois J Y, Labeyrie G, Vansteenkiste N, Westbrook C I and Aspect A 1996 Phys. Rev. Lett 77 1464
[4] Segev B, Côté R and Raizen M G 1997 Phys. Rev. A 56 R3350
[5] Côté R, Segev B and Raizen M G 1998 Phys. Rev. A 58 3999
[6] Pasquini T A, Saba M, Jo G B, Shin Y, Ketterle W, Pritchard D E, Savas T A and Mulders N 2006 Phys. Rev. Lett 97 093201
[7] Dufour G, Guérout R, Lambrecht A, Nesvizhevsky V V, Reynaud S and Voronin A Yu 2013 Phys. Rev. A 87 022506
[8] Zhao B S, Schewe H C, Meijer G and Schöllkopf W 2010 Phys. Rev. A 105 133203
[9] Shimizu F 2001 Phys. Rev. Lett. 86 987
[10] Scott R G, Martin A M, Fromhold T M and Sheard F W 2005 Phys. Rev. Lett. 95 073201
[11] Pasquini T A, Shin Y, Sanner C, Saba M, Schirotzek A, Pritchard D E and Ketterle W 2004 Phys. Rev. Lett. 93 223201
[12] Silvestre M, Cysne Tarik P, Szilard D, Pinheiro F A and Farina C 2019 Phys. Rev. A 100 033605
[13] Judd T E, Scott R G, Martin A M, Kaczmarek B and Fromhold T M 2011 New J. Phys. 13 083020
[14] Cornish S L, Parker N G, Martin A M, Judd T E, Scott R G, Fromhold T M and Adams C S 2009 Physica D 238 1299
[15] Dodd, Roger K, Eilbeck, Chris J, John D, Morris and Hedley C 1982 Solitons and Nonlinear Wave Equations (New York:Academic Press)
[16] Hirota and Ryogo 1973 J. Math. Phys. 14 810
[17] Kuznetsov E A, Rubenchik A M and Zakharov V E 1987 Physics Reports 142 103
[18] Lonngren K E 2000 Plasma Phys. 25 943
[19] Tang D Y, Zhang H, Zhao L M and Wu X 2008 Phys. Rev. Lett. 101 153904
[20] Gibbon J D, Caudrey P J, Bullough R K and Eilbeck J C 1973 Lettere Al Nuovo Cimento 8 775
[21] Zabusky N J 1968 Phys. Rev. 168 124
[22] Newell A C 1980 The Inverse Scattering Transform (Berlin:Springer)
[23] Proukakis N P, Parker N G, Frantzeskakis D J and Adams C S 2004 J. Opt. B 6 S380
[24] Wu M Z, Kalinikos B A and Patton C E 2004 Phys. Rev. Lett. 93 157207
[25] Sakaguchi H and Malomed B A 2016 New J. Phys. 18 025020
[26] Burger S, Bongs K, Dettmer S, Ertmer W, Sengstock K, Sanpera A, Shlyapnikov G V and Lewenstein M 1999 Phys. Rev. Lett. 83 5198
[27] Denschlag J, Simsarian J E, Feder D L, Clark Charles W, Collins L A, Cubizolles J, Deng L, Hagley E W, Helmerson K and Reinhardt W P 2000 Science 287 97
[28] Denschlag J, Simsarian J E, Feder D L, Clark C W, Collins L A, Cubizolles J, Deng L, Hagley E W, Helmerson K and Reinhardt W P 1999 Generating Solitons by Phase Engineering of a Bose-Einstein Condensate (Laser Cooling:Bose-Einstein Condensation and Atom Laser-Proceedings of CCAST (World Laboratory Workshop)
[29] Stellmer S, Becker C, Soltan-Panahi P, Richter E-M, Dörscher S, Baumert M, Kronjäger J, Bongs K and Sengstock K 2008 Phys. Rev. Lett. 101 120406
[30] Anderson B P, Haljan P C, Regal C A, Feder D L, Collins L A, Clark C W, Cornell E A 2001 Phys. Rev. Lett. 86 2926
[31] Engels P and Atherton C 2007 Phys. Rev. Lett. 99 160405
[32] Chang J J, Engels P and Hoefer M A 2008 Phys. Rev. Lett. 101 170404
[33] Jo G B, Choi J H, Christensen C A, Pasquini T A, Lee Y R, Ketterle W and Pritchard D E 2007 Phys. Rev. Lett. 98 180401
[34] Weller A, Ronzheimer J P, Gross C, Esteve J, Oberthaler M K, Frantzeskakis D J, Theocharis G and Kevrekidis P G 2008 Phys. Rev. Lett. 101 130401
[35] Jurisch A and Rost J M 2010 Phys. Rev. A 81 043610
[36] Scott R G, Hutchinson D A W and Gardiner C W 2006 Phys. Rev. A 74 053605
[37] Martin A D, Adams C S and Gardiner S A 2007 Phys. Rev. Lett. 98 020402
[38] Martin A D, Adams C S and Gardiner S A 2008 Phys. Rev. A 77 013620
[39] Lee C and Brand J 2005 Europhys. Lett. 73 321
[40] Xu T F, Zhang Y F, Xu L C and Li Z D 2017 Chin. Phys. B 26 100304
[41] Xu Y, Zhang Y and Wu B 2013 Phys. Rev. A 87 013614
[42] M Liu, L She, H W Xiong and M S Zhan 2006 Phys. Rev. A 74 043619
[43] Martin A M, Scott R G and Fromhold T M 2007 Phys. Rev. A 75 065602
[44] Cheng Q L, Bai W K, Zhang Y Z, Xiong B and Yang T 2019 Laser Phys. 29 015501
[45] Sciacca M, Barenghi C F and Parker N G 2017 Phys. Rev. A 95 013628
[46] Gaunt A L, Schmidutz T F, Gotlibovych I, Smith R P and Hadzibabic Z 2013 Phys. Rev. Lett. 110 200406
[47] Meyrath T P, Schreck F, Hanssen J L, Chuu C S and Raizen M G 2005 Phys. Rev. A 71 041604(R)
[48] Xiong B, Yang T and Benedict K A 2013 Phys. Rev. A 88 043602
[49] Yang T, Xiong B and Benedict K A 2013 Phys. Rev. A 87 023603
[50] Liu Z, Jia W G, Wang H Y, Wang Y, Neimule M K and Zhang J P 2020 Chin. Phys. B 29 064212
[51] Xu T F, Li W L, Li Z D and Zhang C 2018 Chaos, Solitons & Fractals 111 62

Quantum reflection of a Bose-Einstein condensate with a dark soliton from a step potential

Quantum reflection of a Bose-Einstein condensate with a dark soliton from a step potential

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