标题： 在非对称奇异面上的最优感知 显示英文标题

标题： Optimal sensing on an asymmetric exceptional surface

摘要： 我们研究了例外点（EPs）与最优参数估计之间的联系，在一个由微环谐振器中两个反向传播的行波模式组成的简单系统中。 要估计的未知参数是这两个模式之间扰动交叉耦合的强度。 部分反射一个模式的输出到另一个模式中会创建一个非厄米哈密顿量，该哈密顿量表现出一组EPs，形成一个例外表面（ES）。 我们采用场输入和噪声源的完全量子处理方法，通过计算输出场中的量子费舍尔信息（QFI）来获得估计误差的定量界限，其逆给出了任何无偏估计器的均方误差的Cramér-Rao下限。 我们确定了两种输入状态的界限，即半经典相干态和高度非经典的NOON态。 我们发现，对于这两种输入状态，在EP存在的情况下QFI都会增强，并且这两种状态都可以达到Cramér-Rao界限。 然后，我们识别出理想化但实验上可行的测量方法，这些方法可以实现这两种输入状态的最小界限。 我们还研究了参数值不在ES上的QFI变化情况，发现这些情况可能具有更大的QFI，这表明了优化此问题参数估计的其他途径。 显示英文摘要

摘要： We study the connection between exceptional points (EPs) and optimal parameter estimation, in a simple system consisting of two counter-propagating traveling wave modes in a microring resonator. The unknown parameter to be estimated is the strength of a perturbing cross-coupling between the two modes. Partially reflecting the output of one mode into the other creates a non-Hermitian Hamiltonian which exhibits a family of EPs, creating an exceptional surface (ES). We use a fully quantum treatment of field inputs and noise sources to obtain a quantitative bound on the estimation error by calculating the quantum Fisher information (QFI) in the output fields, whose inverse gives the Cram\'er-Rao lower bound on the mean-squared-error of any unbiased estimator. We determine the bounds for two input states, namely, a semiclassical coherent state and a highly nonclassical NOON state. We find that the QFI is enhanced in the presence of an EP for both of these input states and that both states can saturate the Cram\'er-Rao bound. We then identify idealized yet experimentally feasible measurements that achieve the minimum bound for these two input states. We also investigate how the QFI changes for parameter values that do not lie on the ES, finding that these can have a larger QFI, suggesting alternative routes to optimize the parameter estimation for this problem.