利用立方非线性动力学研究纠缠自旋
Entangling spins using cubic nonlinear dynamics
摘要：
具有大量$N$原子自旋的纠缠态是量子信息处理和量子精密测量的关键成分。目前，这种状态的制备主要依赖于二次非线性动力学。本文利用立方非线性动力学理论，研究了量子费舍尔信息见证下自旋-自旋多体纠缠的制备。我们发现，在弱耦合的制度，立方计划可以大大加快纠缠产生的速度相比，二次计划（约$N$倍快）。在强耦合区，立方非线性动力学使得在时间上周期性地产生各种各样的新型宏观叠加态，这使我们能够实现近海森堡极限的相位灵敏度。此外，我们还发现了一个有趣的特性，即三次方案产生的纠缠量对$N$的宇称具有宏观的敏感性，这在二次非线性动力学中是没有的，可以用来在单自旋水平上检测$N$的宇称.我们还提出了一种新的方法，快速和高保真度的最大纠缠Greenberger-Horne-Zeilinger（GHZ）态的产生。通过使用一种替代的二次混合型非线性相互作用，我们表明，可以加速GHZ态产生的过程。还考虑了立方非线性动力学的实现，表明立方非线性动力学可以通过重复使用线性和二次非线性动力学或利用光介导的相互作用在一个步骤中实现。最后，通过考虑实际的缺陷，我们发现立方格式对强耦合区的单自旋衰变是敏感的，而对集体退相是鲁棒的。
英文摘要：
Entangled states with a large number of $N$ atomic spins are a key ingredient for quantum information processing and quantum metrology. Nowadays, the preparation of such states has mainly relied on the quadratic nonlinear dynamics. Here, we investigate the preparation of spin-spin multipartite entanglement, witnessed by quantum Fisher information, by using the cubic nonlinear dynamics. We find that, in the regime of weak coupling, the cubic scheme can greatly speed up the rate of entanglement generation as compared to the quadratic scheme (about $N$ times faster). In the strong coupling regime, the cubic nonlinear dynamics enables the periodic in time generation of a broad variety of new-type macroscopic superposition states, which allow us to realize near-Heisenberg-limit phase sensitivity. In addition, we also reveal an interesting feature that the amount of entanglement generated by the cubic scheme has a macroscopic sensitivity to the parity of $N$, which has no counterpart in quadratic nonlinear dynamics and can be exploited for sensing the parity of $N$ at the single-spin level. We also propose a new approach for a fast and high-fidelity generation of maximally entangled Greenberger-Horne-Zeilinger (GHZ) states. By using an alternative cubic-quadratic-admixture type of nonlinear interaction, we show that one may accelerate the procedure of GHZ-state generation. The realization of the cubic nonlinear dynamics is also considered, showing that the cubic nonlinear dynamics can be realized by either repeatedly using linear- and quadratic-nonlinear dynamics or utilizing light-mediated interactions in just one step. Finally, by taking realistic imperfections into account, we find that the cubic scheme is sensitivity to the single-spin decay in the strong coupling regime, while is robust against the collective dephasing.
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