Chiral Electron Momentum Distribution upon Strong-Field Ionization of Atoms

TL;DR

The paper tackles generating and probing three-dimensional, globally chiral laser fields to induce chiral electron momentum distributions during strong-field ionization. It combines overlapping perpendicularly propagating two-color beams to create a time-dependent 3D field $\oldsymbol{E}(t)$ and corresponding $-$vector potential $-\boldsymbol{A}(t)$ with a defined handedness, then models argon ionization using a hybrid $SFA$+$CTS$ approach that includes non-adiabatic tunneling and Coulomb effects. By integrating over the focal volume and weighting by the position-dependent ionization probability $W(\varphi_{ac})$, the authors show that a volume-averaged momentum distribution can remain chiral, quantified by the metric $\mu_\textrm{CV}$ (e.g., $\mu_\textrm{CV}\approx 0.11$). This work establishes a benchmark for 3D chiral light fields under realistic conditions and suggests broad applications in ultrafast chiral spectroscopy, imaging, and all-optical enantiopurification, leveraging the 3D character of the driving field.

Abstract

We present a scheme to synthesize a three-dimensional laser field that produces a chiral electron momentum distribution upon strong-field ionization of atoms. Our approach employs two orthogonally propagating two-color laser beams. This results in a time-dependent three-dimensional electric field vector of the combined light field which varies for different positions within the focal volume. For each position, we conduct a simulation of the corresponding electron momentum distribution that includes non-adiabatic dynamics and Coulomb interaction after tunneling. For suitable laser parameters, only a small region of the focal volume contributes to the final momentum distribution. Thus, integrating over all position coordinates, a specific chiral laser field dominates. This leads to a volume-averaged electron momentum distribution, which is chiral, as well. This work will serve as a benchmark for future strong-field experiments aiming at the synthetization of well-defined, three-dimensional laser fields.

Figures (3)

• Figure 1: Three-dimensional laser electric field and corresponding negative vector potential. (a) shows the Lissajous curve of a three-dimensional (3D) laser electric field $\vec{E}(t)$ in light and dark orange and its projections. The arrows show the electric field vector at different instants of time. The two alternating colors mark the twelve time intervals into which the field is divided for the simulation. (b) shows the corresponding negative vector potential $-\vec{A}(t)$ in black and gray in full analogy to (a).
• Figure 2: Position-dependent three-dimensional laser fields from perpendicularly propagating CRTC and CoRTC fields. (a) shows a schematic sketch of the two laser beams crossing. One of the laser beams is a counter-rotating two-color (CRTC) field and the second beam is a co-rotating two-color (CoRTC) field as indicated by the insets in orange. In the overlapping region (focal volume) 3D laser fields emerge. The relative phase of the CRTC and CoRTC field $\varphi_{ac}$ is position-dependent (purple colorbar). The combined 3D electric field and the resulting ionization probability depend on $\varphi_{ac}$. (b) shows the approximated ionization probability $W$ for one optical cycle as a function of $\varphi_{ac}$ calculated with the ADK ionization rate (blue line) and the rate based on SFA (black crosses). (c) [(d)] shows the negative vector potential in black for $\varphi_{ac}=2.6$ [$\varphi_{ac}=5.1$] and the corresponding 3D final electron momentum distribution calculated with the combined SFA and CTS model. (c) shows the same negative vector potential as in Fig. \ref{['fig1']}(b). Please note that (c) and (d) both have two shared colorbars, one for the 3D isosurfaces and one for the 2D projections. Due to normalization, the maximum value of 1 is only reached in a very small volume (in only one or a few bins of the histogram). To ensure that the isosurfaces represent a larger (visible) volume, the highest value of the discrete scale is chosen to be 0.8.
• Figure 3: Chiral electron momentum distributions. (a) shows the same laser electric field and negative vector potential as Fig. \ref{['fig1']}(a) and \ref{['fig1']}(b). The orange dots mark the two peak electric fields and the black dots the corresponding negative vector potentials. The arrows indicate the temporal evolution. (b) shows the final electron momentum distribution for the laser field shown in (a), which is the 3D field with the highest ionization probability in the studied scenario (see $\varphi_{ac}=2.6$ in Fig. \ref{['fig3']}(b)). (c) illustrates that the distribution in (b) is chiral (see text for details and note that for an achiral distribution the histogram would be empty and the chirality value would be zero). (d) illustrates that there is a range of 3D fields contributing to ionization in full analogy to (a) if the entire focal volume contributes. To this end $\vec{E}(t)$ is calculated for all values $\varphi_{ac}$ that are indicated in Fig. \ref{['fig3']}(b). The electric field and the negative vector potential are filled into the histogram in (d) and weighted with the maximum ADK rate of the combined electric field. (e) shows the total final electron momentum distribution, which is the sum of all electron momentum distributions for the ten values of $\varphi_{ac}$. (f) shows the same as (c) for the distribution in (e). It is evident that (e) is a chiral electron momentum distribution.