Holographic angular streaking of electrons and the Wigner time delay

Abstract

For a circularly polarized single-color field at a central frequency of 2ω, the final electron momentum distribution upon strong field ionization does not carry any information about the phase of the initial momentum distribution. Adding a weak, corotating, circularly polarized field at a central frequency of ω gives rise to a subcycle interference pattern [holographic angular streaking of electrons (HASE)]. This interference pattern allows for the retrieval of the derivative of the phase of the initial momentum distribution after tunneling φ off (p i). A trajectory-based semiclassical model (HASE model) is introduced which links the experimentally accessible quantities to φ off (p i). It is shown that a change in φ off is equivalent to a displacement in position space x of the initial wave packet after tunneling. This offset in position space allows for an intuitive interpretation of the Wigner time delay τ W in strong-field ionization for circularly polarized single-color fields. The influence of Coulomb interaction after tunneling is investigated quantitatively.

Angular dependence of the Wigner time delay upon tunnel ionization of H2

“…In this classical perspective, Δ τ occurs solely due to a displacement of the mean birth location of the electron. The resulting delay is, however, consistent 13 with the definition of the β - and energy-dependent contribution to the Wigner time delay Δ τ W,M (Eqs. 1 and 2 ).…”

“…First, the electron leaves its initial bound state by tunneling and afterward, the electron follows a classical trajectory that is determined by the classical dynamics in the time-dependent potential formed by the laser field. If this classical trajectory is shifted in position space in the direction that is parallel (antiparallel) to the electron’s emission direction, then the electron arrives earlier (later) at a hypothetical detector 13 . Building on this trivial idea, Fig.…”

“…1 . Hence, the final electron momentum is parallel or antiparallel to s ⊥ 13 , 18 , 19 and one can relate the position-space offsets Δ s ⊥ directly to changes of the arrival time at a hypothetical detector (that is far away from the electron’s birth position) 13 by . Figure 1d displays the corresponding emission angle-dependent delays, that can be expected from this simple modeling, which vary from −20 attoseconds (as) to +20 as.…”

“…A missing piece, which has not been studied, so far, is the Wigner time delay for the strong-field ionization of aligned molecules. Historically, the Wigner time delay, τ Wigner , was introduced to describe scattering processes 9 and it is defined as the derivative of the phase of the electron’s wave function ψ with respect to the electron’s energy E 5 , 10 – 13 : …”

“…According to this definition, τ Wigner characterizes the spectral phase of the photoelectron wave packet and is closely related to its group delay 11 – 13 . In the original context of a scattering process, the origin of a phase shift is the potential (by which the electron is scattered) as it modulates the electron’s wavelength upon passage.…”