用于表征非线性介质的量子探针
Quantum probes for the characterization of nonlinear media
AI总结：
本文研究用压缩量子探针表征非线性介质，证明其可在固定能量下提升非线性耦合与非线性阶数的单独及联合估计精度。
摘要：
导致形式为 $H=\tilde\lambda\\,(a+a^{\dagger})^\zeta$ 的相互作用哈密顿量的有源光学介质，是量子光学技术的一种关键资源。在本文中，我们讨论利用量子探针而非半经典探针对这些非线性介质进行表征。特别地，我们研究压缩探针如何改进对非线性耦合 $\tilde\lambda$ 和非线性阶数 $\zeta$ 的单独估计与联合估计。运用量子估计工具，我们表明：i）这两个参数是相容的，即可以在不引入额外量子噪声的情况下对其进行联合估计；ii）在探针总能量固定时，使用压缩探针可提高精度；iii）对于低能量探针，压缩真空是最便利的选择，而随着能量增加，可以确定一个最优压缩比例；iv）与半经典相干探针相比，使用优化的量子探针时，无论对两个参数进行单独估计还是联合估计，相应精度随能量的标度都会改善。我们得出结论：量子探针是提高非线性介质表征精度的一种资源，并预见其在当前技术条件下具有潜在应用。
英文摘要：
Active optical media leading to interaction Hamiltonians of the form $ H = \tildeλ\, (a + a^{\dagger})^ζ$ represent a crucial resource for quantum optical technology. In this paper, we address the characterization of those nonlinear media using quantum probes, as opposed to semiclassical ones. In particular, we investigate how squeezed probes may improve individual and joint estimation of the nonlinear coupling $\tildeλ$ and of the nonlinearity order $ζ$. Upon using tools from quantum estimation, we show that: i) the two parameters are compatible, i.e. the may be jointly estimated without additional quantum noise; ii) the use of squeezed probes improves precision at fixed overall energy of the probe; iii) for low energy probes, squeezed vacuum represent the most convenient choice, whereas for increasing energy an optimal squeezing fraction may be determined; iv) using optimized quantum probes, the scaling of the corresponding precision with energy improves, both for individual and joint estimation of the two parameters, compared to semiclassical coherent probes. We conclude that quantum probes represent a resource to enhance precision in the characterization of nonlinear media, and foresee potential applications with current technology.
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