Periodically modulated interaction effect on transport of Bose–Einstein condensates in lattice with local defects
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摘要
We theoretically investigate the periodically modulated interaction effect on the propagation properties of a traveling plane wave in a Bose–Einstein condensate(BEC) trapped in a deep annular lattice with local defects both analytically and numerically. By using the two-mode ansatz and the tight-binding approximation, a critical condition for the system preserving the superfluidity is obtained analytically and confirmed numerically. We find that the coupled effects of periodic modulated atomic interactions, the quasi-momentum of the plane wave, and the defect can control the superfluidity of the system. Particularly, when we consider the periodic modulation in the system with single defect, the critical condition for the system entering the superfluid regime depends on both the defect and the momentum of the plane wave. This is different from the case for the system without the periodic modulation, where the critical condition is only determined by the defect. The modulation and quasi-momentum of the plane wave can enhance the system entering the superfluid regime. Interestingly, when the modulated amplitude/frequency, the defect strength, and the quasi-momentum of the plane wave satisfy a certain condition, the system will always be in the superfluid region. This engineering provides a possible means for studying the periodic modulation effect on propagation properties and the corresponding dynamics of BECs in disordered optical lattices.
We theoretically investigate the periodically modulated interaction effect on the propagation properties of a traveling plane wave in a Bose–Einstein condensate(BEC) trapped in a deep annular lattice with local defects both analytically and numerically. By using the two-mode ansatz and the tight-binding approximation, a critical condition for the system preserving the superfluidity is obtained analytically and confirmed numerically. We find that the coupled effects of periodic modulated atomic interactions, the quasi-momentum of the plane wave, and the defect can control the superfluidity of the system. Particularly, when we consider the periodic modulation in the system with single defect, the critical condition for the system entering the superfluid regime depends on both the defect and the momentum of the plane wave. This is different from the case for the system without the periodic modulation, where the critical condition is only determined by the defect. The modulation and quasi-momentum of the plane wave can enhance the system entering the superfluid regime. Interestingly, when the modulated amplitude/frequency, the defect strength, and the quasi-momentum of the plane wave satisfy a certain condition, the system will always be in the superfluid region. This engineering provides a possible means for studying the periodic modulation effect on propagation properties and the corresponding dynamics of BECs in disordered optical lattices.
We theoretically investigate the periodically modulated interaction effect on the propagation properties of a traveling plane wave in a Bose–Einstein condensate(BEC) trapped in a deep annular lattice with local defects both analytically and numerically. By using the two-mode ansatz and the tight-binding approximation, a critical condition for the system preserving the superfluidity is obtained analytically and confirmed numerically. We find that the coupled effects of periodic modulated atomic interactions, the quasi-momentum of the plane wave, and the defect can control the superfluidity of the system. Particularly, when we consider the periodic modulation in the system with single defect, the critical condition for the system entering the superfluid regime depends on both the defect and the momentum of the plane wave. This is different from the case for the system without the periodic modulation, where the critical condition is only determined by the defect. The modulation and quasi-momentum of the plane wave can enhance the system entering the superfluid regime. Interestingly, when the modulated amplitude/frequency, the defect strength, and the quasi-momentum of the plane wave satisfy a certain condition, the system will always be in the superfluid region. This engineering provides a possible means for studying the periodic modulation effect on propagation properties and the corresponding dynamics of BECs in disordered optical lattices.
引文
[1]Diver M,Robb G R M and Oppo G L 2015 Phys.Rev.A 91 033622
[2]Shadkhoo S and Bruinsma R 2015 Phys.Rev.Lett.115 135305
[3]Kengne E,Lakhssassi A,Liu W M and Vaillancourt R 2013 Phys.Rev.E 87 022914
[4]Jaksch D,Bruder C,Cirac J I,Gardiner C W and Zoller P 1998 Phys.Rev.Lett.81 3108
[5]Greiner M,Mandel O,Esslinger T,Hansch T W and Bloch I 2002 Nature 415 39
[6]Jiang J,Zhao L,Wang S T,Chen Z,Tang T,Duan L M and Liu Y 2016Phys.Rev.A 93 063607
[7]Li L,Li Z,Malomed B A,Mihalache D and Liu W M 2005 Phys.Rev.A 72 033611
[8]Wang D S,Hu X H,Hu J P and Liu W M 2010 Phys.Rev.A 81 025604
[9]Wang D S,Song S W,Xiong B and Liu W M 2011 Phys.Rev.A 84053607
[10]Yamazaki R,Taie S,Sugawa S and Takahashi Y 2010 Phys.Rev.Lett.105 050405
[11]Pollack S E,Dries D,Hulet R G,Magalh?aes K M F,Henn E A L,Ramos E R F,Caracanhas M A and Bagnato V S 2010 Phys.Rev.A 81053627
[12]Theis M,Thalhammer G,Winkler K,Hellwig M,Ruff G,Grimm Rand Denschlag J H 2004 Phys.Rev.Lett.93 123001
[13]Kevrekidis P G,Theocharis G,Frantzeskakis D J and Malomed B A2003 Phys.Rev.Lett.90 230401
[14]Abdullaev F K,Tsoy E N,Malomed B A and Kraenkel R A 2003 Phys.Rev.A 68 053606
[15]Parny L F,Rousseau V G and Roscilde T 2015 Phys.Rev.Lett.114195302
[16]Sabari S,Jisha C P,Porsezian K and Brazhnyi V A 2015 Phys.Rev.E92 032905
[17]Zhang S L,Zhou Z W and Wu B 2013 Phys.Rev.A 87 013633
[18]Ding C Y,Zhang X F,Zhao D,Luo H G and Liu W M 2011 Phys.Rev.A 84 053631
[19]Gong J B,Morales-Molina L and Hanggi P 2009 Phys.Rev.Lett.103133002
[20]RappA,Deng X L and Santos L 2012 Phys.Rev.Lett.109 203005
[21]Lewenstein M,Sanpera A,Ahufinger V,Damski B,Sen A and Sen U2007 Adv.Phys.56 243
[22]Bloch I,Dalibard J and Zwerger W 2008 Rev.Mod.Phys.80 885
[23]Hu Y,Liang Z X and Hu B B 2010 Phys.Rev.A 81 053621
[24]Yang S J and Nie S 2010 Phys.Rev.A 82 061607
[25]Wang B,Fu P,Liu J and Wu B 2006 Phys.Rev.A 74 063610
[26]Jian Y,Zhang A X,He C X,Qi X Y and Xue J K 2013 Phys.Rev.E 87053201
[27]Larson J,Martikainen J P,Collin A and Sjoqvist E 2010 Phys.Rev.A82 043620
[28]Yu Z F and Xue J K 2014 Phys.Rev.A 90 033618
[29]Liu S P,Li J H,Yu R and Wu Y 2013 Phys.Rev.A 87 062316
[30]Trombettoni A,Smerzi A and Bishop A R 2003 Phys.Rev.E 67 016607
[31]Trombettoni A,Smerzi A and Bishop A R 2002 Phys.Rev.Lett.88173902
[32]Deissler B,Zaccanti M,Roati G,D’Errico C,Fattori M,Modugno M,Modugno G and Inguscio M 2010 Nat.Phys.6 354
[33]Bai X D and Xue J K 2012 Phys.Rev.E 86 066605
[34]Brazhnyi V A and Malomed B A 2011 Phys.Rev.E 83 016604
[35]Zhang Y,Xu Y and Busch T 2015 Phys.Rev.A 91 043629
[36]Zhang Y,Mossman M E,Busch T,Engels P and Zhang C 2016 Front.Phys.11 118103
[37]Yulin A V,Bludov Y V,Konotop V V,Kuzmiak V and Salerno M 2011Phys.Rev.A 84 063638
[38]Skokos C and Flach S 2010 Phys.Rev.E 82 016208
[39]Stark C,Pollet L,Imamo?glu A and Renner R 2011 Phys.Rev.Lett.107030504
[40]Wang D S,Shi Y R,Feng W X and Wen L 2017 Physica D 351-35230
[41]Li Q,Wang D S,Wen X Y and Zhuang J H 2018 Nonlinear Dyn.91625
[42]Wang G F,Fu L B and Liu J 2006 Phys.Rev.A 73 013619
[43]Kayanuma Y and Mizumoto Y 2000 Phys.Rev.A 62 061401(R)
[2]Shadkhoo S and Bruinsma R 2015 Phys.Rev.Lett.115 135305
[3]Kengne E,Lakhssassi A,Liu W M and Vaillancourt R 2013 Phys.Rev.E 87 022914
[4]Jaksch D,Bruder C,Cirac J I,Gardiner C W and Zoller P 1998 Phys.Rev.Lett.81 3108
[5]Greiner M,Mandel O,Esslinger T,Hansch T W and Bloch I 2002 Nature 415 39
[6]Jiang J,Zhao L,Wang S T,Chen Z,Tang T,Duan L M and Liu Y 2016Phys.Rev.A 93 063607
[7]Li L,Li Z,Malomed B A,Mihalache D and Liu W M 2005 Phys.Rev.A 72 033611
[8]Wang D S,Hu X H,Hu J P and Liu W M 2010 Phys.Rev.A 81 025604
[9]Wang D S,Song S W,Xiong B and Liu W M 2011 Phys.Rev.A 84053607
[10]Yamazaki R,Taie S,Sugawa S and Takahashi Y 2010 Phys.Rev.Lett.105 050405
[11]Pollack S E,Dries D,Hulet R G,Magalh?aes K M F,Henn E A L,Ramos E R F,Caracanhas M A and Bagnato V S 2010 Phys.Rev.A 81053627
[12]Theis M,Thalhammer G,Winkler K,Hellwig M,Ruff G,Grimm Rand Denschlag J H 2004 Phys.Rev.Lett.93 123001
[13]Kevrekidis P G,Theocharis G,Frantzeskakis D J and Malomed B A2003 Phys.Rev.Lett.90 230401
[14]Abdullaev F K,Tsoy E N,Malomed B A and Kraenkel R A 2003 Phys.Rev.A 68 053606
[15]Parny L F,Rousseau V G and Roscilde T 2015 Phys.Rev.Lett.114195302
[16]Sabari S,Jisha C P,Porsezian K and Brazhnyi V A 2015 Phys.Rev.E92 032905
[17]Zhang S L,Zhou Z W and Wu B 2013 Phys.Rev.A 87 013633
[18]Ding C Y,Zhang X F,Zhao D,Luo H G and Liu W M 2011 Phys.Rev.A 84 053631
[19]Gong J B,Morales-Molina L and Hanggi P 2009 Phys.Rev.Lett.103133002
[20]RappA,Deng X L and Santos L 2012 Phys.Rev.Lett.109 203005
[21]Lewenstein M,Sanpera A,Ahufinger V,Damski B,Sen A and Sen U2007 Adv.Phys.56 243
[22]Bloch I,Dalibard J and Zwerger W 2008 Rev.Mod.Phys.80 885
[23]Hu Y,Liang Z X and Hu B B 2010 Phys.Rev.A 81 053621
[24]Yang S J and Nie S 2010 Phys.Rev.A 82 061607
[25]Wang B,Fu P,Liu J and Wu B 2006 Phys.Rev.A 74 063610
[26]Jian Y,Zhang A X,He C X,Qi X Y and Xue J K 2013 Phys.Rev.E 87053201
[27]Larson J,Martikainen J P,Collin A and Sjoqvist E 2010 Phys.Rev.A82 043620
[28]Yu Z F and Xue J K 2014 Phys.Rev.A 90 033618
[29]Liu S P,Li J H,Yu R and Wu Y 2013 Phys.Rev.A 87 062316
[30]Trombettoni A,Smerzi A and Bishop A R 2003 Phys.Rev.E 67 016607
[31]Trombettoni A,Smerzi A and Bishop A R 2002 Phys.Rev.Lett.88173902
[32]Deissler B,Zaccanti M,Roati G,D’Errico C,Fattori M,Modugno M,Modugno G and Inguscio M 2010 Nat.Phys.6 354
[33]Bai X D and Xue J K 2012 Phys.Rev.E 86 066605
[34]Brazhnyi V A and Malomed B A 2011 Phys.Rev.E 83 016604
[35]Zhang Y,Xu Y and Busch T 2015 Phys.Rev.A 91 043629
[36]Zhang Y,Mossman M E,Busch T,Engels P and Zhang C 2016 Front.Phys.11 118103
[37]Yulin A V,Bludov Y V,Konotop V V,Kuzmiak V and Salerno M 2011Phys.Rev.A 84 063638
[38]Skokos C and Flach S 2010 Phys.Rev.E 82 016208
[39]Stark C,Pollet L,Imamo?glu A and Renner R 2011 Phys.Rev.Lett.107030504
[40]Wang D S,Shi Y R,Feng W X and Wen L 2017 Physica D 351-35230
[41]Li Q,Wang D S,Wen X Y and Zhuang J H 2018 Nonlinear Dyn.91625
[42]Wang G F,Fu L B and Liu J 2006 Phys.Rev.A 73 013619
[43]Kayanuma Y and Mizumoto Y 2000 Phys.Rev.A 62 061401(R)