New Method for Measuring Angle-Resolved Phases in Photoemission

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.

Popular Summary

Ultrafast lasers have enabled the science of physics at attosecond (${10}^{-18}$) timescales, so that it is at last possible to study matter on the natural timescale of the motion of electrons. An archetypal process in the quantum mechanics of electrons is photoemission, in which an atom absorbs a photon and emits an electron. The motion of the electron is described quantum mechanically by a wave packet, which has a group velocity and a certain phase. In our experiments, we measure the relative phases of these electron wave packets using high-energy, ultrafast pulses of short-wavelength light generated by a free-electron laser.

The electrons can be ejected by absorbing either a single photon or two photons with half the energy of the single photon, and we measure the phase difference between these two processes. For neon, we find phase differences corresponding to times between 0 and 230 attoseconds, depending on the direction of emission. These numbers are similar to values measured in other atoms and molecules, averaged over all angles, but here they are resolved in angle. This highlights the importance of considering the direction of emission when describing an electron wave packet.

This measurement complements existing methods for measuring the phases of such fast processes, which use an infrared pulse and extreme ultraviolet pulses. Having demonstrated the method on single atoms, we plan in the future to apply it to molecules, where the physics is complicated by lower symmetry, and the possible occurrence of processes not present in atoms.

Figure 1

Scheme of the experiment: Bichromatic, linearly polarized light (red and blue waves), with momentum ${\mathbf{k}}_{\gamma }$ and electric vector ${\mathbf{E}}_{\gamma }$, ionizes neon in the reaction volume. The electron wave packets (yellow and magenta waves) are emitted with electron momentum $\mathbf{k}$. The $m$-averaged phase difference $\mathrm{\Delta }\tilde{\eta }$ between wave packets created by one- and two-photon ionization depends on the emission angle. The photoelectron angular distribution depends on the relative (optical) $\omega \text{−}2\omega$ phase $\varphi$. Lower figures: Polar plots of photoelectron intensity at $E_k=16.6\mathrm{eV}$ for coherent harmonics (asymmetric, colored plot) and incoherent harmonics (symmetric, gray plot).

Figure 2

Upper: Typical photoelectron yields $I(\theta ;\varphi )$ as a function of optical phase $\varphi$ at intervals of polar angles $\theta$. The signal is integrated over the 5° intervals shown on the right. The curves are not shifted; thus, their vertical position reflects directly the value $A_0$ in Eq. (4). The photoelectron kinetic energy is 7.0 eV. Circles are experimental results; lines are sinusoidal fits of the experimental results. Lower: Extracted phase shift differences as a function of the polar angles, for four datasets and three photoelectron kinetic energies: left (c), 7.0 eV; middle (d), 10.2 eV; right (e), 16.6 eV. Circles are experimental results; shaded areas show their uncertainties. Dashed lines, perturbation theory; solid lines, real-time ab initio theory. Note that the curves in (a) and (b) oscillate in antiphase, because they correspond to emission directions on opposite sides of the photon propagation direction.

Figure 3

Phase shift differences $\mathrm{\Delta }\tilde{\eta }$ of two-photon ionization relative to single-photon ionization, calculated by perturbation theory, as a function of the polar angle $\theta$ and photoelectron kinetic energy. The large variation near 12.0 eV kinetic energy is due to the $2p\to 3s$ resonance.

Figure 4

Plot of $(5\cos 2\theta -1)/4$ as a function of $\theta$.