论文标题
线性玻感传感器和Schawlow-townes激光线宽极限的基本限制
Fundamental limit of linear bosonic sensors and the Schawlow-Townes laser linewidth limit
论文作者
论文摘要
近年来，已经提出了许多奇特的传感器，例如基于特殊点，平等时时间对称结构或非对流系统的传感器。评估这些传感方案的基本限制并判断是否有提高性能至关重要。几篇论文已经根据不同方面和标准调查了基本限制，其中一些导致了不同的结论。在本文中，我们建议，对于可以将其建模为耦合振荡器以下的线性玻璃体传感器，对模式频率$ w_0 $的测量不能超出$ \ frac {\ frac {\ sqrt {κ_0}}} {2 \ sqrt {n f rac {κ_0}} {$ sqrt {N是该模式下的平均粒子数，而$τ$是测量时间。对于单个模式被动传感器，已经可以达到这样的精确限制，并且我们已经证明，通过添加增益组件或将其耦合到其他模式以形成N模式线性传感器可以超过它。此外，我们认识到上述限制与频率不确定性（$ \ frac {\ frac {\ sqrt {κ_0}} {\ sqrt {2nτ}} $）对于上方的阈值振荡模式（例如，在threshold上方的threshold），与schaLOw-limess laseS laseS laseSlisthindine laseS laseSlistline laseS laseS laseLwids相关联（例如这一观察结果使我们猜想我们为线性传感器提出的极限可能是一个基本的一般限制，它限制了大多数（如果不是全部）传感器。
In recent years, many peculiar sensors have been proposed, such as the sensors based on exceptional points, Parity-Time symmetric structures or non-reciprocal systems. It is crucial to evaluate the fundamental limit of these sensing schemes and to judge whether there is an enhanced performance. Several papers have already investigated the fundamental limits based on different aspects and criteria, some led to different conclusions. In this paper, we suggest that for linear bosonic sensors that can be modeled as coupled oscillators below threshold, a measurement of the mode frequency $w_0$ can not has a precision beyond $\frac{\sqrt{κ_0}}{2\sqrt{nτ}}$, in which $κ_{0}$ is the intrinsic loss, $n$ is the average particle number at that mode and $τ$ is the measurement time. Such a precision limit can already be achieved for a single mode passive sensor, and we have proved that it can not be exceeded by adding gain components, or by coupling it to other modes to form a n-mode linear sensor. Further more, we recognize that the above limit is comparative to the frequency uncertainty ($\frac{\sqrt{κ_0}}{\sqrt{2 nτ}}$) for an above-threshold oscillation mode (e.g. a laser cavity above threshold), which is related to the Schawlow-Townes laser linewidth limit. This observation makes us conjecture that the limit we proposed for linear sensors may be a basic general limit which restricts most, if not all, sensors.
