标题： 弱测量的动态结构因子 显示英文标题

标题： Dynamical Structure Factor from Weak Measurements

摘要： 我们对量子系统的大部分知识都包含在厄米算符的期望值中，这些期望值通过平均投影测量实验获得。 然而，动态特性通常由不同时间点算符的乘积来描述；这种可观测量不能通过单个时间点的投影测量来测量。 例如，动态结构因子描述了密度激发（如声子）的传播，并且是从不同时间点的时空密度算符导出的。 传统上，这是通过在特定波矢和频率下激发系统，然后测量响应来实现的。 在这里，我们描述了一种使用一对时间分离的弱测量的替代方法，并分析表明它们的交叉相关函数可以直接恢复动态结构因子。 我们通过一维玻色-哈伯德模型的矩阵乘积态模拟，以及相位对比成像的弱测量，对该技术进行了数值验证。 我们探讨了该方法的极限，并展示了其在成像分辨率有限的实际实验中的适用性。 显示英文摘要

摘要： Much of our knowledge of quantum systems is encapsulated in the expectation value of Hermitian operators, experimentally obtained by averaging projective measurements. However, dynamical properties are often described by products of operators evaluated at different times; such observables cannot be measured by individual projective measurements, which occur at a single time. For example, the dynamical structure factor describes the propagation of density excitations, such as phonons, and is derived from the spatial density operator evaluated at different times. Conventionally, this is measured by first exciting the system at a specific wavevector and frequency, then measuring the response. Here, we describe an alternative approach using a pair of time-separated weak measurements, and analytically show that their cross-correlation function directly recovers the dynamical structure factor. We provide numerical confirmation of this technique with a matrix product states simulation of the one-dimensional Bose-Hubbard model, weakly measured by phase contrast imaging. We explore the limits of the method and demonstrate its applicability to real experiments with limited imaging resolution.