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玻色-爱因斯坦凝聚体内的准粒子激发导致系统里真实的玻色原子间产生量子纠缠. 采用谱展开的方法, 本文在准一维无限深方势阱下数值求解了Bogoliubov-de Gennes方程的本征值和本征态. 针对准粒子低能激发态, 研究了玻色-爱因斯坦凝聚体的量子纠缠熵随散射长度的变化. 本文结果表明纠缠熵随散射长度增加缓慢增大, 并且这种增大趋势可以近似用幂函数模型描述. 这种幂函数的趋势类似于一维均匀玻色-爱因斯坦凝聚体的Bogoliubov基态的纠缠熵近似与散射长度的1/2次幂成正比的情形.
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关键词:
- 玻色-爱因斯坦凝聚 /
- Bogoliubov理论 /
- 量子纠缠熵
Quasi-particle excitation in a Bose-Einstein condensate leads to quantum entanglement between real bosonic atoms in the system. By using spectral expansion method, the eigenvalues and eigenstates of Bogoliubov-de Gennes equation are numerically calculated in a quasi-one-dimensional infinite square well potential. For the low-energy collective excitations of the quasi-particles, we explore the dependence of quantum entanglement entropy of the Bose-Einstein condensate on scattering length. Our results show that the entanglement entropy increases slowly with the increase of the scattering length, and such an increasing trend can be well described by a power function. These results are analogous to those in a one-dimensional uniform BEC, where the entanglement entropy of the Bogoliubov ground state is approximately proportional to the square root of the scattering length. This work provides a viable way for investigating many-particle entanglement in a quasi-one-dimensional trapped Bose-Einstein condensate where the quantum entanglement is closely related to the interaction strength between particles.[1] Pethick C J, Smith H 2008 Bose–Einstein Condensation in Dilute Gases (Cambridge: Cambridge University Press) pp26, 194, 236
[2] Leggett A J 2009 Compendium of Quantum Physics (Berlin: Springer Berlin Heidelberg Press) p77
[3] Carr L D, Clark C W, Reinhardt W P 2000 Phys. Rev. A 62 063610
Google Scholar
[4] Teo J C Y, Kane C L 2010 Phys. Rev. B 82 115120
Google Scholar
[5] Li B, Duan L, Wang S, Yang Z Y 2025 Phys. Lett. A 548 130534
Google Scholar
[6] Hayashi N, Isoshima T, Ichioka M, Machida K 1998 Phys. Rev. Lett. 80 2921
Google Scholar
[7] Cichy A, Ptok A 2020 J. Phys. Commun. 4 055006
Google Scholar
[8] You L, Hoston W, Lewenstein M 1997 Phys. Rev. A 55 R1581
Google Scholar
[9] Walczak P B, Anglin J R 2011 Phys. Rev. A 84 013611
Google Scholar
[10] Hu B, Huang G X, Ma Y L 2004 Phys. Rev. A 69 063608
Google Scholar
[11] 焦宸, 简粤, 张爱霞, 薛具奎 2023 72 060302
Google Scholar
Jiao C, Jian Y, Zhang A X, Xue J K 2023 Acta Phys. Sin. 72 060302
Google Scholar
[12] Nielsen M A, Chuang I L 2010 Quantum Computation and Quantum Information (10th Anniversary Ed.) (Cambridge: Cambridge University Press) pp571−580
[13] Lambert N, Emary C, Brandes T 2004 Phys. Rev. Lett. 92 073602
Google Scholar
[14] Brukner C, Vedral V, Zeilinger A 2006 Phys. Rev. A 73 012110
Google Scholar
[15] Osborne T J, Nielsen M A 2002 Phys. Rev. A 66 032110
Google Scholar
[16] Vidal J, Dusuel S, Barthel T 2007 J. Stat. Mech. 2007 P01015
Google Scholar
[17] Yoshino T, Furukawa S, Ueda M 2021 Phys. Rev. A 103 043321
Google Scholar
[18] Ueda M 2010 Fundamentals and New Frontiers of Bose-Einstein Condensation (World Scientific) pp33−72
[19] Chin C, Grimm R, Julienne P, Tiesinga E 2010 Rev. Mod. Phys. 82 1225
Google Scholar
[20] Landau L 1949 Phys. Rev. 75 884
Google Scholar
[21] Blaizot J P, Ripka G 1986 Quantum Theory of Finite Systems (Cambridge: MIT Press
[22] Brauner T 2010 Symmetry 2 609
Google Scholar
[23] Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865
Google Scholar
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图 1 弱相互作用与强相互作用下准一维无限深方势阱里BdG方程的最低3个能量本征态, 其中散射长度分别为$ 0.1 \;{\mathrm{nm}} $(上图)与$ 5 \;{\mathrm{nm}} $(下图)
Fig. 1. Three lowest-energy eigenstates of BdG equation in a quasi-one-dimensional box potential. The weak and strong interaction are denoted by the scattering length being 0.1 nm (upper panels) and 5 nm (lower panels).
表 1 拟合参数, 其中SSE (sum of square error)表示误差平方和
Table 1. Fitting parameters (SSE, sum of square error).
数据 $ c_1 $ $ c_2 $ $ c_3 $ SSE $ S_0 $ 4.669×105 0.7803 0 2.3327×10–4 $ S_1 $ 1.9058×105 0.7158 0.0482 7.482×10–4 
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[1] Pethick C J, Smith H 2008 Bose–Einstein Condensation in Dilute Gases (Cambridge: Cambridge University Press) pp26, 194, 236
[2] Leggett A J 2009 Compendium of Quantum Physics (Berlin: Springer Berlin Heidelberg Press) p77
[3] Carr L D, Clark C W, Reinhardt W P 2000 Phys. Rev. A 62 063610
Google Scholar
[4] Teo J C Y, Kane C L 2010 Phys. Rev. B 82 115120
Google Scholar
[5] Li B, Duan L, Wang S, Yang Z Y 2025 Phys. Lett. A 548 130534
Google Scholar
[6] Hayashi N, Isoshima T, Ichioka M, Machida K 1998 Phys. Rev. Lett. 80 2921
Google Scholar
[7] Cichy A, Ptok A 2020 J. Phys. Commun. 4 055006
Google Scholar
[8] You L, Hoston W, Lewenstein M 1997 Phys. Rev. A 55 R1581
Google Scholar
[9] Walczak P B, Anglin J R 2011 Phys. Rev. A 84 013611
Google Scholar
[10] Hu B, Huang G X, Ma Y L 2004 Phys. Rev. A 69 063608
Google Scholar
[11] 焦宸, 简粤, 张爱霞, 薛具奎 2023 72 060302
Google Scholar
Jiao C, Jian Y, Zhang A X, Xue J K 2023 Acta Phys. Sin. 72 060302
Google Scholar
[12] Nielsen M A, Chuang I L 2010 Quantum Computation and Quantum Information (10th Anniversary Ed.) (Cambridge: Cambridge University Press) pp571−580
[13] Lambert N, Emary C, Brandes T 2004 Phys. Rev. Lett. 92 073602
Google Scholar
[14] Brukner C, Vedral V, Zeilinger A 2006 Phys. Rev. A 73 012110
Google Scholar
[15] Osborne T J, Nielsen M A 2002 Phys. Rev. A 66 032110
Google Scholar
[16] Vidal J, Dusuel S, Barthel T 2007 J. Stat. Mech. 2007 P01015
Google Scholar
[17] Yoshino T, Furukawa S, Ueda M 2021 Phys. Rev. A 103 043321
Google Scholar
[18] Ueda M 2010 Fundamentals and New Frontiers of Bose-Einstein Condensation (World Scientific) pp33−72
[19] Chin C, Grimm R, Julienne P, Tiesinga E 2010 Rev. Mod. Phys. 82 1225
Google Scholar
[20] Landau L 1949 Phys. Rev. 75 884
Google Scholar
[21] Blaizot J P, Ripka G 1986 Quantum Theory of Finite Systems (Cambridge: MIT Press
[22] Brauner T 2010 Symmetry 2 609
Google Scholar
[23] Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865
Google Scholar
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