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Physical Review A

Time-resolved ultrafast electron ( e , 2 e ) momentum spectroscopy

Hua‐Chieh Shao, Anthony F. Starace

Published May 10, 2013• 13 citations
Publisher

Abstract

The ($e,2e$) process is analyzed for the case of an ultrafast electron pulse incident upon a target prepared in a time-varying, coherent superposition of states. Conditions under which time-resolved target momentum densities can be obtained from experimental measurements are discussed. Results for coherent electronic motions in both the H atom and the H${}_{2}{}^{+}$ molecule are used to illustrate the capability of an ultrafast electron pulse to image time-dependent target electron dynamics.

DOI
10.1103/physreva.87.050701

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The (e,2ee,2ee,2e) process is analyzed for the case of an ultrafast electron pulse incident upon a target prepared in a time-varying, coherent superposition of states. Conditions under which time-resolved target momentum densities can be obtained from experimental measurements are discussed. Results for coherent electronic motions in both the H atom and the H2+{}_{2}{}^{+}2​+ molecule are used to illustrate the capability of an ultrafast electron pulse to image time-dependent target electron dynamics.
Improving our understanding of electron dynamics is essential for advancing energy transfer, optoelectronics, light harvesting systems and quantum computing. Recent developments in attosecond x-ray sources provide the fundamental possibility of observing these dynamics with atomic-scale resolution. However, connecting a time-resolved signal to dynamics is challenging due to the broad bandwidth of an attosecond probe pulse. This makes exploring the capabilities of different attosecond imaging techniques crucial. Here, we propose attosecond momentum-resolved resonant inelastic x-ray scattering as a prominent technique for tracking ultrafast dynamics. We demonstrate that the scattering signal contains an information about the instantaneous distribution of charge density across the scattering atoms. To illustrate this, we consider scattering from an ααα-sexithiophene molecule, in which coupled electron-hole dynamics are excited.
Revealing possible long-living coherence in ultrafast processes allows detecting genuine quantum mechanical effects in molecules. To investigate such effects from a quantum chemistry perspective, we have developed a method for simulating the time evolution of molecular systems based on ab initio calculations, which includes relaxation and environment-induced dephasing of the molecular wave function whose rates are external parameters. The proposed approach combines a quantum chemistry description of the molecular target with a real-time propagation scheme within the time-dependent stochastic Schrödinger equation. Moreover, it allows a quantitative characterization of the state and dynamics coherence through the l1-norm of coherence and the linear entropy, respectively. To test the approach, we have simulated femtosecond pulse-shaping ultrafast spectroscopy of terrylenediimide, a well-studied fluorophore in single-molecule spectroscopy. Our approach is able to reproduce the experimental findings [R. Hildner et al., Nat. Phys. 7, 172 (2011)], confirming the usefulness of the approach and the correctness of the implementation.
By solving the three-dimensional, time-dependent Schr\"odinger equation, we have demonstrated that the ultrafast charge-transfer process in ion-atom collisions can be mapped out with attosecond extreme uv (xuv) pulses. During the dynamic-charge transfer from the target atom to the projectile ion, the electron coherently populates the two sites of both nuclei, which can be viewed as a ``short-lived'' molecular state. A probing attosecond xuv pulse can instantly unleash the delocalized electron from such a ``transient molecule,'' so that the resulting photoelectron may exhibit a ``double-slit'' interference. On the contrary, either reduced or no photoelectron interference will occur if the attosecond xuv pulse strikes well before or after the collision. Therefore, by monitoring the photoelectron interference visibility, one can precisely time the ultrafast charge-transfer process in atomic collisions with time-delayed attosecond xuv pulses.
An experimental continuous-wave (cw) pump-probe scheme is demonstrated by investigating the population and photoionization dynamics of an atomic system. Specifically, 6^66Li atoms are initially prepared in optically pumped 22S1/22^{2}S_{1/2}22S1/2​ and 22P3/22^{2}P_{3/2}22P3/2​ states before being excited via multi-photon absorption from a tunable femtosecond laser. The subsequent cascade back to the ground state is analyzed by ionizing the atoms in the field of a cw optical dipole trap laser. Conventional spectroscopic methods such as standard cold-target recoil-ion momentum spectroscopy (COLTRIMS) or velocity map imaging (VMI) cannot provide simultaneous momentum and time-resolved information on an event-by-event basis for the system investigated here. The new approach overcomes this limitation by leveraging electron-recoil ion coincidences, momentum conservation, and the cyclotron motion of the photoelectron in the magnetic spectrometer field. This enables the reconstruction of ionization times and time-of-flight of the charged target fragments with nanosecond resolution. As a result, not only can three-dimensional photoelectron momentum vectors be determined, but the (incoherent) population dynamics of the atomic system also become accessible. Future applications exploring coherent atomic dynamics on the nanosecond timescale would not only expand the scope of time-resolved spectroscopy but can also aid in developing coherent control schemes for precise atomic manipulation.
Excited-state dynamics in condensed matter systems plays a crucial role in determining their properties. Understanding and controlling ultrafast dynamics across multiple dimensions—such as time, space, energy, momentum, and spin—has become a key emerging direction in modern condensed matter physics. In recent decades, time-resolved ultrafast laser technology based on pump-probe techniques has advanced significantly. This technology has been integrated with various experimental methods, leading to developments in ultrafast spectroscopy, time- and angle-resolved photoemission spectroscopy (TR-ARPES), ultrafast scanning tunneling microscopy (STM), ultrafast electron diffraction (UED), and ultrafast X-ray techniques, enabling the study of lattice, electron, and spin dynamics. Meanwhile, to provide a clearer physical picture of ultrafast dynamics, real-time first-principles methods have been developed by combining electronic structure methods with dynamic approaches, allowing the study of multidimensional lattice, electron, and spin behaviors. This article reviews recent progress in the field and discusses its future challenges and opportunities.
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