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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, 我们研究了玻色-爱因斯坦凝聚体的量子纠缠熵随散射长度的变化. 我们的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.
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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. -
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. 散射长度分别为$ 0.1 \;{\mathrm{nm}} $(上图)与$ 5 \;{\mathrm{nm}} $(下图)
Fig. 1. XXXXXXXXXXXXXXXXXXX
表 1 拟合参数, 其中SSE(Sum of square error)表示误差平方和
Table 1. XXXXXXXXXXXX
数据 $ c_1 $ $ c_2 $ $ c_3 $ SSE $ S_0 $ 4.669 e+05 0.7803 0 2.3327 e-04 $ S_1 $ 1.9058 e+05 0.7158 0.0482 7.482 e-04 
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