AI 中文总结
本文探究SU(1,1)干涉仪在估计时空涨落强度或关联长度上是否优于SU(2)干涉仪，通过计算两类干涉仪的量子与经典费舍尔信息并对比不同参数区间完成评估。
AI 中文摘要
高精度激光干涉仪通常用于搜寻随机时空涨落的信号，以探究引力的基本本质，这类实验研究传统上采用SU(2)干涉仪。受[K. Zheng等人，Photon. Res. 8, 1653 (2020)]的启发，本文评估使用SU(1,1)干涉仪替代SU(2)干涉仪是否存在优势。为此，本文计算了两种干涉仪中用于估计时空涨落强度和关联长度的量子费舍尔信息，以及考虑不同实验相关测量方案的对应经典费舍尔信息；并对比了与当前及未来可能的实验装置相关的不同参数区间对应的信息度量，以此评估SU(1,1)干涉仪在何种情况下、是否能在估计时空涨落强度或关联长度方面优于SU(2)干涉仪。
英文摘要
High-precision laser interferometers are commonly used to search for signatures of random spacetime fluctuations, in an attempt to understand the fundamental nature of gravity. Conventionally, $SU(2)$ interferometers have been used in such experimental investigations. Motivated by [K. Zheng \textit{et al.}, Photon. Res. \textbf{8}, 1653 (2020)], I assess if there is any advantage to be gained by using an $SU(1,1)$ interferometer instead of the $SU(2)$ interferometer. To this end, I compute the quantum Fisher information for estimating the strength and the correlation length of the spacetime fluctuations, and the corresponding classical Fisher information considering different experimentally relevant measurement schemes, in both types of interferometers. I compare the information metrics corresponding to different parameter regimes that are relevant to both current and possible future experimental setups. This helps me assess if and when the $SU(1,1)$ interferometer offers any advantage over the $SU(2)$ interferometer for estimating either the fluctuation strength or correlation length of the spacetime fluctuations.
Comments9 pages, 5 figures
