从弱测量得出的动态结构因子

E. Altuntas, R. G. Lena, S. Flannigan, A. J. Daley, I. B. Spielman
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引用次数: 0

摘要

我们对量子系统的大部分了解都包含在赫米特算子的期望值中,这些期望值是通过投影测量的平均值在实验中获得的。然而,动力学特性通常是由不同时间的算子评估乘积来描述的;这些观测值无法通过单个投影测量来测量,因为投影测量是在单个时间进行的。例如,动态结构因子描述了声子等密度激波的传播,由在不同时间评估的空间密度操作导出。传统的测量方法是首先以特定的波矢和频率激发系统,然后测量其响应。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。我们通过相位对比成像对一维玻色-哈伯德模型进行弱测量的矩阵乘积静态模拟,对这一技术进行了数值确认。我们探讨了该方法的局限性,并展示了它在成像分辨率有限的实际实验中的适用性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Dynamical Structure Factor from Weak Measurements
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.
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