Quantum mechanically, photoionization can be fully described by the complex photoionization amplitudes that describe the transition between the ground state and the continuum state. Knowledge of the value of the phase of these amplitudes has been a central interest in photoionization studies and newly developing attosecond science, since the phase can reveal important information about phenomena such as electron correlation. We present a new attosecond-precision interferometric method of angle-resolved measurement for the phase of the photoionization amplitudes, using two phase-locked extreme ultraviolet pulses of frequency $\omega$ and $2\omega$, from a free-electron laser. Phase differences $\mathrm{\Delta }\tilde{\eta }$ between one- and two-photon ionization channels, averaged over multiple wave packets, are extracted for neon $2p$ electrons as a function of the emission angle at photoelectron energies 7.9, 10.2, and 16.6 eV. $\mathrm{\Delta }\tilde{\eta }$ is nearly constant for emission parallel to the electric vector but increases at 10.2 eV for emission perpendicular to the electric vector. We model our observations with both perturbation and ab initio theory and find excellent agreement. In the existing method for attosecond measurement, reconstruction of attosecond beating by interference of two-photon transitions (RABBITT), a phase difference between two-photon pathways involving absorption and emission of an infrared photon is extracted. Our method can be used for extraction of a phase difference between single-photon and two-photon pathways and provides a new tool for attosecond science, which is complementary to RABBITT.

中文翻译：

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测量光发射角分辨相位的新方法

从机械角度讲，光电离可以通过描述基态和连续态之间过渡的复杂光电离幅度来充分描述。这些相位的相位值的知识一直是光电离研究和新兴的阿秒科学领域的主要兴趣，因为相位可以揭示有关电子相关现象的重要信息。我们使用两个锁相的极紫外脉冲频率，提出了一种新的精确到角度的测量方法，用于光电离振幅的相位角分辨测量$\omega$ 和 $2\omega$，来自自由电子激光器。相位差$\mathrm{\Delta }\stackrel{〜}{\eta }$ 在一个和两个光子电离通道之间提取多个波包的平均值，以获取氖 $2p$ 电子在光电子能量7.9、10.2和16.6 eV时随发射角的变化而变化。 $\mathrm{\Delta }\stackrel{〜}{\eta }$对于平行于电矢量的发射几乎为常数，但是对于垂直于电矢量的发射则为10.2 eV。我们用摄动和从头算理论对我们的观察进行建模，并找到极好的一致性。在现有的阿秒测量方法中，通过双光子跃迁的干扰（RABBITT）重建了阿秒跳动，提取了涉及红外光子吸收和发射的两个光子路径之间的相位差。我们的方法可用于提取单光子和双光子路径之间的相位差，并为阿秒科学提供了新的工具，它是对RABBITT的补充。