Retrieval of the amplitude and phase of the dipole matrix element by attosecond electron-wave-packet interferometry

Abstract

We extend the ideas of wave-packet interferometry [Remetter et al., Nat. Phys. 2, 323 (2006)] to implement the algorithm of spectral phase interferometry for direct electric-field reconstruction (SPIDER) for characterizing the amplitude and phase of electron wave packets. Single-photon ionization by an attosecond pulse launches an electron wave packet in the continuum. Ionization by a train of two attosecond pulses in the presence of a moderate infrared pulse creates an interferogram in the final photoelectron momentum distribution. From the interferogram, the complex electron wave function can be reconstructed. If the pulses are well characterized, the amplitude and phase of the bound-free dipole matrix element can be reconstructed over a wide energy range. This is demonstrated by application of the retrieval method to momentum distributions obtained by numerical solution of the time-dependent Schrödinger equation. The case of Coulombic potentials requires appropriate treatment of the laser-Coulomb coupled dynamics.

Asymmetry of Wigner's time delay in a small molecule

“…These are constructed by numerically matching states in the grid to the asymptotic Coulomb wave (a) [5,25]. They can be efficiently computed for all values of the final momentum p. The momentum grid size is 10 a.u., and the momentum step is p = 0.01 a.u.…”

“…If the photon energies in the attosecond pulse are higher than the ionization potential, the electron is freed, and the electron momentum distribution maps the characteristics of the attosecond pulse and the parent system [3][4][5]. These electrons are not emitted instantaneously.…”

“…It is related to the so-called Wigner time [7,8], which measures the travel time difference between a free electron and an electron under the influence of a short-range potential. The response time of the atom or the molecule is encoded in the phase of the EWP and provides valuable information about the system [5,6]. But since the information is in the phase, traditional observables cannot access this quantity.…”

Interaction of attosecond and femtosecond pulses with atoms and molecules

“…Furthermore, when a SAP or an APT interacts with an atom or a molecule, a coherent ultra broadband EWP is created. If the photon energies of the attosecond pulse are higher than the ionization potential, the electron is then ionized and the momentum distribution of these electrons maps the characteristics of the attosecond pulse and the parent system [61,67].…”

“…As a first scheme, we introduce the Quantum Spectral Phase Interferometry for Direct Electron-wavepacket Reconstruction (QSPIDER) technique [67]. This method is a variant of the SPIDER [20,21] approach, but here it is applied to quantum wavefunctions.…”