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The realization of Bose-Einstein condensation in dilute atomic gases opens an exciting way to quantum mechanics and begins a new area of quantum simulation. As a macroscopic quantum object and a many-body bosonic system, the Bose-Einstein condensates can show numerous exotic quantum effects and have naturally attracted great attention. One of the simplest quantum many-body systems to be realized experimentally and studied theoretically is ultra-cold atoms in a double-well potential. This system can exhibit a great variety of quantum interference phenomena such as tunneling oscillation, self-trapping and the entanglement of macroscopic superpositions. Specifically, the double-well potentials built by optical or magnetic fields are easy to change and the many-body interaction between ultra-cold atoms can be changed by the method of Feshbach resonance, enabling the precise quantum control of the double-well dynamics of the condensates. In the present work, we study the dynamics of a condensate in a trapping potential consisting of an unalterable double-well trap and an additional moving optical lattice. If the lattice space is much smaller than the size of the double-well trap, the system can be simplified into a double-well trapped condensate with a tunable effective mass. Using the mean-field factorization assumption, together with a two-mode approximation, we obtain the analytic expressions for the dependence of the tunneling rate and the self-collision strength on the effective mass. The tunneling rate decays and the collision strength grows up with the increase of the effective mass. As a consequence of their different changes, we conclude that the adjustment of the effective mass of the ultra-cold atoms, rather than the changing of the trap barrier or adjusting of the atomic scattering length, is an alternative approach to controlling the double-well dynamics of the condensate. Via numerical simulations of the mean-field dynamical equations with some realistic parameters, we show that a transition between the quantum coherent tunneling and the self-trapping behaviors is experimentally realizable with the mass-control approach. Specifically, we show that the approach is still valid for the case of negative mass. Moreover, we find that the negative-mass case can be used even to stimulate the double-well dynamics of the condensate with a negative atomic scattering length.
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Keywords:
- Bose-Einstein condensation /
- double well /
- effective mass
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[21] He Z M, Wang D L, Ding J W, Yan X H 2012 Acta Phys. Sin. 61 230508 (in Chinese)[何章明, 王登龙, 丁建文, 颜晓红2012 61 230508]
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[23] Mosk A P 2005 Phys. Rev. Lett. 95 040403
[24] Zhang K Y, Meystre P, Zhang W P 2013 Phys. Rev. A 88 043632
[25] Ananikian D, Bergeman T 2006 Phys. Rev. A 73 013604
[26] Shin Y, Saba M, Pasquini T A, Ketterle W, Pritchard D E, Leanhardt A E 2004 Phys. Rev. Lett. 92 050405
[27] Dalfovo F, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys. 71 463
[28] Raghavan S, Smerzi A, Fantoni S, Shenoy S R 1999 Phys. Rev. A 59 620
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[31] Gati R, Oberthaler M K 2007 J. Phys. B:At. Mol. Opt. Phys. 40 R61
[32] Jack M W, Collett M J, Walls D F 1996 Phys. Rev. A 54 R4625
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[1] Hinds E A, Boshier M G, Hughes I G 1998 Phys. Rev. Lett. 80 645
[2] Thywissen J H, Olshanii M, Zabow G, Drndic M, Johnson K S, Westervelt R M, Prentiss M 1999 Eur. Phys. J. D 7 361
[3] Andersen M F, Ryu C, Cladé P, Natarajan V, Vaziri A, Helmeison K, Phillips W D 2006 Phys. Rev. Lett. 97 170406
[4] Dutton Z, Ruostekoski J 2004 Phys. Rev. Lett. 93 193602
[5] Giltner D M, McGowan R W, Lee S A 1995 Phys. Rev. Lett. 75 2638
[6] Gustavson T L, Bouyer P, Kasevich M A 1997 Phys. Rev. Lett. 78 2406
[7] Stringari S 2001 Phys. Rev. Lett. 86 4725
[8] Denschlag J H, Simsarian J E, Häffner H, McKenzie C, Browaeys A, Cho D, Helmerson K, Rolston S L, Phillips W D 2002 J. Phys. B:At. Mol. Opt. Phys. 35 3095
[9] Choi D, Niu Q 1999 Phys. Rev. Lett. 82 2022
[10] Milburn G J, Corney J, Wright E M, Walls D F 1997 Phys. Rev. A 55 4318
[11] Burger S, Cataliotti F S, Fort C, Minardi F, Inguscio M, Chiofalo M L, Tosi M P 2001 Phys. Rev. Lett. 86 4447
[12] Xu Z J, Cheng C, Yang H S, Wu Q, Xiong H W 2004 Acta Phys. Sin. 53 2835 (in Chinese)[徐志君, 程成, 杨欢耸, 武强, 熊宏伟2004 53 2835]
[13] Qi R, Yu X L, Li Z B, Liu W M 2009 Phys. Rev. Lett. 102 185301
[14] Jaksch D, Bruder C, Cirac J I, Gardiner C W, Zoller P 1998 Phys. Rev. Lett. 81 3108
[15] Greiner M, Mandel O, Esslinger T, Hänsch T W, Bloch I 2001 Nature 415 39
[16] Ji A C, Sun Q, Xie X C, Liu W M 2009 Phys. Rev. Lett. 102 023602
[17] Liu W M, Fan W B, Zheng W M, Liang J Q, Chui S T 2002 Phys. Rev. Lett. 88 170408
[18] Smerzi A, Fantoni S, Giovanazz S, Shenoy S R 1997 Phys. Rev. Lett. 79 4950
[19] Pu H, Baksmaty L O, Zhang W, Bigelow N P, Meystre P 2003 Phys. Rev. A 67 043605
[20] Strecker K E, Partridge G B, Truscott A G, Hulet R G 2002 Nature 417 150
[21] He Z M, Wang D L, Ding J W, Yan X H 2012 Acta Phys. Sin. 61 230508 (in Chinese)[何章明, 王登龙, 丁建文, 颜晓红2012 61 230508]
[22] He Z M, Wang D L 2007 Acta Phys. Sin. 56 3088 (in Chinese)[何章明, 王登龙2007 56 3088]
[23] Mosk A P 2005 Phys. Rev. Lett. 95 040403
[24] Zhang K Y, Meystre P, Zhang W P 2013 Phys. Rev. A 88 043632
[25] Ananikian D, Bergeman T 2006 Phys. Rev. A 73 013604
[26] Shin Y, Saba M, Pasquini T A, Ketterle W, Pritchard D E, Leanhardt A E 2004 Phys. Rev. Lett. 92 050405
[27] Dalfovo F, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys. 71 463
[28] Raghavan S, Smerzi A, Fantoni S, Shenoy S R 1999 Phys. Rev. A 59 620
[29] Michael A, Gati R, Fölling J, Hunsmann S, Cristiani M, Oberthaler M K 2005 Phys. Rev. Lett. 95 010402
[30] Spagnolli G, Semeghini G, Masi L, Ferioli G, Trenkwalder A, Coop S, Landini M, Pezzé L, Modugno G, Inguscio M, Smerzi A, Fattori M 2017 arxiv 1703. 02370[quant-ph]
[31] Gati R, Oberthaler M K 2007 J. Phys. B:At. Mol. Opt. Phys. 40 R61
[32] Jack M W, Collett M J, Walls D F 1996 Phys. Rev. A 54 R4625
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