量子光学中单光子的逆散射问题

中文摘要 AI 辅助

我们研究描述单光子与静止两能级原子介质相互作用的时谐单光子模型的逆问题。经时谐约化后，未知的紧支原子密度表现为半拉普拉斯散射方程中与频率相关的势。我们针对三类强度数据证明了高频唯一性结果：源驱动测量、重归一化远场强度测量，以及由入射平面波相干叠加得到的无相位远场测量。在所有足够大的频率下，对应的数据均可唯一确定原子密度；源驱动结果要求源与观测集满足几何可视性条件。

英文摘要

We study inverse problems for a time-harmonic one-photon model describing the interaction of a single photon with a medium of stationary two-level atoms. After time-harmonic reduction, the unknown compactly supported atomic density appears as a frequency-dependent potential in a scattering equation for the half Laplacian. We prove high-frequency uniqueness results for three types of intensity data: source-driven measurements, renormalized far-field intensity measurements, and phaseless far-field measurements obtained from coherent superpositions of incident plane waves. In each case, the corresponding data, given at all sufficiently large frequencies, determine the atomic density uniquely; the source-driven result requires a geometric visibility condition on the source and observation sets.

发表机构

• University of Jyväskylä（于韦斯屈莱大学）
• University of Helsinki（赫尔辛基大学）
• Qazaq AI Research University（哈萨克斯坦AI研究大学）
• Yale University（耶鲁大学）

机构由 AI 辅助整理，请以论文原文为准。