通过Floquet工程条件手性激发制备多模NOON态

中文摘要 AI 辅助

NOON态具有海森堡极限相位灵敏度，对量子增强计量学至关重要。在我们的工作中，我们开发了一个Floquet工程条件路由框架，其中$d$能级量子控制器介导$d$个玻色子模式的动力学。对于任意奇数维度$d=2s+1$，$d$能级系统可通过调节其初始态充当“量子旋钮”，以相干控制手性激发流的方向，使得不同的控制器本征态产生玻色子激发的不同循环路由分支。通过选择$s$个谐波，我们构造了一个精确的qudit控制的循环置换，并利用它制定了制备奇数$d$模NOON态的一般协议。同一框架还通过适当制备控制器态实现可编程复振幅。作为具体实现，我们展示了三模情况仅需单个谐波，并表现出两个方向相反的手性分支以及一个静态分支，而五模情况需要两个谐波，并涉及最近邻和次近邻手性跳跃。同时，以三模实现为代表示例，我们评估了系统缺陷和耗散对条件路由动力学的影响，并确定了路由操作保持准确的参数区域。我们的结果建立了在任意奇数维网络中可控手性路由和多模NOON态生成的系统性Floquet构造，在量子信息处理和量子计量学中具有潜在应用。

英文摘要

The NOON states possess Heisenberg-limited phase sensitivity and are crucial for quantum-enhanced metrology. In our work, we develop a Floquet-engineered conditional-routing framework in which a $d$-level quantum controller mediates the dynamics of $d$ bosonic modes. For an arbitrary odd dimension $d=2s+1$, the $d$-level system can act as a ``quantum knob" by tuning its initial states to coherently control the direction of chiral excitation flow, such that different controller eigenstates generate distinct cyclic-routing branches of the bosonic excitations. By choosing $s$ harmonics, we construct an exact qudit-controlled cyclic permutation and use it to formulate a general protocol for preparing odd-$d$-mode NOON states. The same framework also enables programmable complex amplitudes through appropriate preparation of the controller state. As concrete realizations, we show that the three-mode case requires only a single harmonic and exhibits two oppositely directed chiral branches together with a stationary branch, whereas the five-mode case requires two harmonics and both nearest- and next-nearest-neighbor chiral hoppings. Meanwhile, taking the three-mode realization as a representative example, we assess the influence of systematic imperfections and dissipation on the conditional-routing dynamics and identify parameter regimes in which the routing operation remains accurate. Our results establish a systematic Floquet construction for controllable chiral routing and multimode NOON-state generation in arbitrary odd-dimensional networks, with potential applications in quantum information processing and quantum metrology.

发表机构

• Northeast Normal University（东北师范大学）

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