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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 excitations in a Bose-Einstein condensate lead to quantum entanglement between real bosonic atoms in the system. By employing spectral expansion method, the eigenvalues and eigenstates of Bogoliubov-de Gennes equation are numerically calculated in a quasi-one-dimension 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 onedimension 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 to investigate many-particle entanglement in a quasi-one-dimension trapped BEC where the quantum entanglement closely relates with the interaction strength between particles. -
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