Abstract
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 $\Delta \tilde \eta$ between one- and two-photon ionization channels, averaged over multiple wave packets, are extracted for neon $2p$ electrons as a function of emission angle at photoelectron energies 7.9, 10.2, and 16.6 eV. $\Delta \tilde \eta$ 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 \textit{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.
Highlights
The age of attosecond physics was ushered in by the invention of methods for probing phenomena on a timescale less than femtoseconds [1]
The velocity map imaging (VMI) measures the projection of the photoelectron angular distribution (PAD) onto the planar detector; the PAD is obtained as an inverse Abel transform of this projection, using the BASEX method [39]
We elucidate the relationship of our data, i.e., photoelectron angular distributions created by collinearly polarized biharmonics, to time-delay studies described in the introduction
Summary
The age of attosecond physics was ushered in by the invention of methods for probing phenomena on a timescale less than femtoseconds [1]. The photoemission delay can be expressed as the energy derivative of the phase of the photoionization amplitude, and, measuring the photoemission delay and the energy-dependent phase of the photoionization amplitude are practically equivalent. Their measurement is one of the central interests in attosecond science [3,4,5,6,7,8,9,10,11,12,13,14], because they are a fundamental probe of the photoionization process and can reveal important information about, for example, electron-electron correlations Their measurement is one of the central interests in attosecond science [3,4,5,6,7,8,9,10,11,12,13,14], because they are a fundamental probe of the photoionization process and can reveal important information about, for example, electron-electron correlations (see, e.g., Ref. [15])
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