We theoretically study a scheme for generating entanglement between two Bose–Einstein condensates (BECs). The scheme involves placing two BECs in the path of a Mach–Zehnder interferometer, where the coherent light interacts with the atoms due to a quantum nondemolition Hamiltonian. In contrast to standard approaches where a Holstein–Primakoff approximation is used, we use an exact wavefunction approach where the atoms can be initialized in an arbitrary state and the light–atom interaction times can be arbitrary. In the short time regime, it is possible to construct a very simple approximate theory for the overall effect of the scheme: amplitudes in the superposition between the two BECs with unequal spin eigenvalues are damped. We analyze the types of correlations, entanglement, Einstein–Podolsky–Rosen (EPR) steering, and Bell correlations that are produced and show that the state is similar to a spin-EPR state. Using a two-pulse sequence the correlations can be dramatically improved, where the state further approaches a spin-EPR state.

我们从理论上研究了在两个玻色-爱因斯坦凝聚体 (BEC) 之间产生纠缠的方案。该方案包括将两个 BEC 放置在 Mach-Zehnder 干涉仪的路径中，由于量子非爆破哈密顿量，相干光与原子相互作用。与使用 Holstein-Primakoff 近似的标准方法相比，我们使用精确波函数方法，其中原子可以在任意状态下初始化，并且光原子相互作用时间可以是任意的。在短时间范围内，可以为该方案的整体效果构建一个非常简单的近似理论：具有不等自旋特征值的两个 BEC 之间叠加中的振幅被阻尼。我们分析了相关性、纠缠、爱因斯坦-波多尔斯基-罗森 (EPR) 转向的类型，和 Bell 相关性产生并表明该状态类似于自旋 EPR 状态。使用双脉冲序列可以显着改善相关性，其中状态进一步接近自旋 EPR 状态。