Active SU(1,1) interferometers are designed to enhance phase sensitivity beyond the standard quantum limit. An atomic version of such an interferometer can be constructed by means of a spinor Bose-Einstein condensate with an $F=1$ groundstate manifold in which spin-changing collisions create entangled pairs of $m=\pm1$ atoms. We use Bethe Ansatz techniques to find exact eigenstates and eigenvalues of the Hamiltonian that models such spin-changing collisions. Using these results, we express the interferometer's phase sensitivity, Fisher information, and Hellinger distance in terms of the Bethe rapidities. By evaluating these expressions we study scaling properties and the interferometer's performance in the presence of depletion, i.e., without the idealising assumption necessary for ideal SU(1,1) interferometry.

中文翻译：

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可积分活性原子干涉测量

有源 SU(1,1) 干涉仪旨在增强超出标准量子限制的相位灵敏度。这种干涉仪的原子版本可以通过自旋玻色-爱因斯坦凝聚体和 $F=1$ 基态流形来构建，其中自旋变化的碰撞产生纠缠的 $m=\pm1$ 原子对。我们使用 Bethe Ansatz 技术来找到模拟这种自旋变化碰撞的哈密顿量的准确本征态和本征值。使用这些结果，我们用 Bethe 快速度表示干涉仪的相位灵敏度、Fisher 信息和 Hellinger 距离。通过评估这些表达式，我们研究了存在耗尽时的缩放特性和干涉仪的性能，即没有理想 SU(1,1) 干涉测量所需的理想化假设。