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Ultracold atoms trapped in an optical lattice of double-well potential, the so-called optical superlattice, have received much attention in the field of cold atoms. A protocol generalized to three-well optical superlattice is suggested in this paper. The ground-state diagrams of ultracold spin-1 atoms trapped in a symmetric three-well optical superlattice in a weak magnetic field are studied based on the exact diagonalization. It is shown that the ground-state diagrams are remarkably different for the ferromagnetic and antiferromagnetic atoms. There does not exist the type of ground state for the antiferromagnetic interaction atoms, where the magnetic quantum number of the total spin of the system along the external magnetic field are ±2. But for the ferromagnetic interaction atoms, there do exist. In addition, there exist only the fully polarized ground-states for the ferromagnetic atoms in the negative quadratic-Zeeman-energy region. The physicsal origin of the dependence of the ground states on the controllable parameters are analyzed. These quantum spin-states can be controlled easily and exactly by modulating the external magnetic field and the height of the optical barrier, which may be a tool for the study of spin-entanglement.
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Keywords:
- three-well optical superlattice /
- spin-1 atom /
- weak magnetic field
[1] Greiner M, Mandel O, Esslinger T, Hänsch T W, Bloch I 2002 Nature 419 51
[2] Lewenstein M, Sanpera A, Ahufinger V, Damski B, Sen A, Sen U 2007 Advances in Physics 56 243
[3] Sebby-Strabley J, Anderlini M, Jessen P S, Porto J V 2006 Phys. Rev. A 73 033605
[4] Anderlini M, Lee P J, Brown B L, Sebby-Strabley J, Phillips W D, Porto J V 2007 Nature 448 452
[5] Fölling S, Trotzky S, Cheinet P, Feld M, Saers R, Widera A, Mller T, Bloch I 2007 Nature 448 1029
[6] Cheinet P, Trotzky S, Feld M, Schnorrberger U, Moreno-Cardoner M, Fölling S, Bloch I 2008 Phys. Rev. Lett. 101 090404
[7] Trotzky S, Chen Y A, Schnorrberger U, Cheinet P, Bloch I 2010 Phys. Rev. Lett. 105 265303
[8] Wagner A, Bruder C, Demler E 2011 Phys. Rev. A 84 063636
[9] Zhang Y B, Harri M, Kalle-Antti S 2005 Chin. Phys. Lett. 22 536
[10] Pang W, Li Z B, Bao C G 2007 Chin. Phys. Lett. 24 2745
[11] Chen B L, Kou S P, Zhang Y B, Chen S 2010 Phys. Rev. A 81 053608
[12] Liang J Q, Liu J L, Li W D, Li Z J 2009 Phys. Rev. A 79 033617
[13] Pethick C J, Smith H 2002 Bose-Einstein Condensation in Dilute Gases (Cambridge: Cambridge University Press) p331
[14] Zheng G P, Tong Y G, Wang F L 2010 Phys. Rev. A 81 063633
[15] Gerbier F, Widera A, Fölling S, Mandel O, Bloch I 2006 Phys. Rev. A 73 041602
[16] Ueda M 2012 Annu. Rev. Condens. Matter Phys. 3 263
[17] Ho T L 1998 Phys. Rev. Lett. 81 742
[18] Demler E, Zhou F 2002 Phys. Rev. Lett. 88 163001
[19] Hao Y J, Liang J Q 2006 Chin. Phys. 15 1161
[20] Yan D, Song L J, Chen D W 2009 Acta Phys. Sin. 58 3679 (in Chinese) [严冬, 宋立军, 陈殿伟 2009 物理学报 58 3679]
[21] Xu Y, Fan W, Chen B, Li Z X 2011 Acta Phys. Sin. 60 060305 (in Chinese) [徐岩, 樊炜, 陈兵, 李照鑫 2011 物理学报 60 060305]
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[1] Greiner M, Mandel O, Esslinger T, Hänsch T W, Bloch I 2002 Nature 419 51
[2] Lewenstein M, Sanpera A, Ahufinger V, Damski B, Sen A, Sen U 2007 Advances in Physics 56 243
[3] Sebby-Strabley J, Anderlini M, Jessen P S, Porto J V 2006 Phys. Rev. A 73 033605
[4] Anderlini M, Lee P J, Brown B L, Sebby-Strabley J, Phillips W D, Porto J V 2007 Nature 448 452
[5] Fölling S, Trotzky S, Cheinet P, Feld M, Saers R, Widera A, Mller T, Bloch I 2007 Nature 448 1029
[6] Cheinet P, Trotzky S, Feld M, Schnorrberger U, Moreno-Cardoner M, Fölling S, Bloch I 2008 Phys. Rev. Lett. 101 090404
[7] Trotzky S, Chen Y A, Schnorrberger U, Cheinet P, Bloch I 2010 Phys. Rev. Lett. 105 265303
[8] Wagner A, Bruder C, Demler E 2011 Phys. Rev. A 84 063636
[9] Zhang Y B, Harri M, Kalle-Antti S 2005 Chin. Phys. Lett. 22 536
[10] Pang W, Li Z B, Bao C G 2007 Chin. Phys. Lett. 24 2745
[11] Chen B L, Kou S P, Zhang Y B, Chen S 2010 Phys. Rev. A 81 053608
[12] Liang J Q, Liu J L, Li W D, Li Z J 2009 Phys. Rev. A 79 033617
[13] Pethick C J, Smith H 2002 Bose-Einstein Condensation in Dilute Gases (Cambridge: Cambridge University Press) p331
[14] Zheng G P, Tong Y G, Wang F L 2010 Phys. Rev. A 81 063633
[15] Gerbier F, Widera A, Fölling S, Mandel O, Bloch I 2006 Phys. Rev. A 73 041602
[16] Ueda M 2012 Annu. Rev. Condens. Matter Phys. 3 263
[17] Ho T L 1998 Phys. Rev. Lett. 81 742
[18] Demler E, Zhou F 2002 Phys. Rev. Lett. 88 163001
[19] Hao Y J, Liang J Q 2006 Chin. Phys. 15 1161
[20] Yan D, Song L J, Chen D W 2009 Acta Phys. Sin. 58 3679 (in Chinese) [严冬, 宋立军, 陈殿伟 2009 物理学报 58 3679]
[21] Xu Y, Fan W, Chen B, Li Z X 2011 Acta Phys. Sin. 60 060305 (in Chinese) [徐岩, 樊炜, 陈兵, 李照鑫 2011 物理学报 60 060305]
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