Extended virtual detector theory for strong-field atomic ionization

Reconciling Conflicting Approaches for the Tunneling Time Delay in Strong Field Ionization

Several recent attoclock experiments have investigated the fundamental question of a quantum mechanically induced time delay in tunneling ionization via extremely precise photoelectron momentum spectroscopy. The interpretations of those attoclock experimental results were controversially discussed, because the entanglement of the laser and Coulomb field did not allow for theoretical treatments without undisputed approximations. The method of semiclassical propagation matched with the tunneled wave function, the quasistatic Wigner theory, the analytical R-matrix theory, the backpropagation method, and the under-the-barrier recollision theory are the leading conceptual approaches put forward to treat this problem, however, with seemingly conflicting conclusions on the existence of a tunneling time delay. To resolve the contradicting conclusions of the different approaches, we consider a very simple tunneling scenario which is not plagued with complications stemming from the Coulomb potential of the atomic core, avoids consequent controversial approximations and, therefore, allows us to unequivocally identify the origin of the tunneling time delay.

Quantum battles in attoscience: tunnelling

ABSTRACT

What is the nature of tunnelling? This yet unanswered question is as pertinent today as it was at the dawn of quantum mechanics. This article presents a cross section of current perspectives on the interpretation, computational modelling, and numerical investigation of tunnelling processes in attosecond physics as debated in the Quantum Battles in Attoscience virtual workshop 2020.

GRAPHIC ABSTRACT

Theory of Subcycle Linear Momentum Transfer in Strong-Field Tunneling Ionization

Interaction of a strong laser pulse with matter transfers not only energy but also linear momentum of the photons. Recent experimental advances have made it possible to detect the small amount of linear momentum delivered to the photoelectrons in strong-field ionization of atoms. We present numerical simulations as well as an analytical description of the subcycle phase (or time) resolved momentum transfer to an atom accessible by an attoclock protocol. We show that the light-field-induced momentum transfer is remarkably sensitive to properties of the ultrashort laser pulse such as its carrier-envelope phase and ellipticity. Moreover, we show that the subcycle-resolved linear momentum transfer can provide novel insights into the interplay between nonadiabatic and nondipole effects in strong-field ionization. This work paves the way towards the investigation of the so-far unexplored time-resolved nondipole nonadiabatic tunneling dynamics.

Identification of tunneling and multiphoton ionization in intermediate Keldysh parameter regime

Quantitative identification of tunneling ionization (TI) and multiphoton ionization (MPI) with Keldysh parameter γ in intermediate regime is of great importance to better understand various ionization-triggered strong-field phenomena. We theoretically demonstrate that the numerical observable ionization delay time is a more reliable indicator for characterizing the transition from TI to MPI under different laser parameters. Using non-linear iterative curve fitting algorithm (NICFA), the detected time-dependent probability current of ionized electrons can be decoupled into weighted TI and MPI portions. This enables us to confirm that the observed plateau-like structure in ionization delay time picture at the intermediate γ originates from the competition between TI and MPI processes. A hybrid quantum and classical approach (HQCA) is developed to evaluate the weights of TI and MPI electrons in good agreement with NICFA result. Moreover, the well separated TI and MPI electrons using HQCA are further propagated classically for mapping their final momentum, which well reproduces the experimental or ab-initio numerical calculated signatures of ionized electron momentum distribution in a rather broad γ regime.

Attosecond Time Delay of Retrapped Resonant Ionization

A recent ultrafast pump-probe technique has allowed measurement of time delays during photoemission in a variety of systems ranging from atoms and molecules to solids with unprecedented temporal resolution. However, identifying the underlying physics is still a challenge especially in complicated multichannel above-threshold ionization (ATI) experiments. Here we demonstrate that the time delays of different ionization pathways in ATI can be clearly resolved and extracted with a semiclassical statistical method. The remarkable phase shift of near threshold photoelectrons can be attributed to a temporary retrapping of a photoelectron by the atomic potential in a quasibound state after emerging in the continuum state. This continuum-bound-continuum scattering manifests as a new resonant effect in strong-field photoemission. Our results unify the seemingly opposing quantum Eisenbud-Wigner-Smith time delay and classical Coulomb-induced time delay by highlighting the same physical picture, which holds promise for an intuitive interpretation of time-resolved fundamental electronic processes in strong-field experiments and epistemological reexamination of the quantum-classical correspondence.

Numerical Detector Theory for the Longitudinal Momentum Distribution of the Electron in Strong Field Ionization

The lack of analytical solutions for the exit momentum in the laser-driven tunneling theory is a well-recognized problem in strong field physics. Theoretical studies of electron momentum distributions in the neighborhood of the tunneling exit depend heavily on ad hoc assumptions. In this Letter, we apply a new numerical method to study the exiting electron's longitudinal momentum distribution under intense short-pulse laser excitation. We present the first realizations of the dynamic behavior of an electron near the so-called tunneling exit region without adopting a tunneling approximation.

Energy-Resolved Ultrashort Delays of Photoelectron Emission Clocked by Orthogonal Two-Color Laser Fields

A phase-controlled orthogonal two-color (OTC) femtosecond laser pulse is employed to probe the time delay of photoelectron emission in the strong-field ionization of atoms. The OTC field spatiotemporally steers the emission dynamics of the photoelectrons and meanwhile allows us to unambiguously distinguish the main and sideband peaks of the above-threshold ionization spectrum. The relative phase shift between the main and sideband peaks, retrieved from the phase-of-phase of the photoelectron spectrum as a function of the laser phase, gradually decreases with increasing electron energy, and becomes zero for the fast electron which is mainly produced by the rescattering process. Furthermore, a Freeman resonance delay of 140±40 attoseconds between photoelectrons emitted via the 4f and 5p Rydberg states of argon is observed.

Tunneling Ionization Time Resolved by Backpropagation

We determine the ionization time in tunneling ionization by an elliptically polarized light pulse relative to its maximum. This is achieved by a full quantum propagation of the electron wave function forward in time, followed by a classical backpropagation to identify tunneling parameters, in particular, the fraction of electrons that has tunneled out. We find that the ionization time is close to zero for single active electrons in helium and in hydrogen if the fraction of tunneled electrons is large. We expect our analysis to be essential to quantify ionization times for correlated electron motion.

Ionization Time and Exit Momentum in Strong-Field Tunnel Ionization

Tunnel ionization belongs to the fundamental processes of atomic physics. The so-called two-step model, which describes the ionization as instantaneous tunneling at the electric field maximum and classical motion afterwards with zero exit momentum, is commonly employed to describe tunnel ionization in adiabatic regimes. In this contribution, we show by solving numerically the time-dependent Schrödinger equation in one dimension and employing a virtual detector at the tunnel exit that there is a nonvanishing positive time delay between the electric field maximum and the instant of ionization. Moreover, we find a nonzero exit momentum in the direction of the electric field. To extract proper tunneling times from asymptotic momentum distributions of ionized electrons, it is essential to incorporate the electron's initial momentum in the direction of the external electric field.