Time-resolving the birth of photoelectrons in strong-filed ionization with an isolated attosecond pulse

Abstract

To time-resolve attosecond electronic dynamics in general photoionization processes, the technique that retrieves the phase of emitted electronic wave packets without intercepting the interactions is essential. Here, we theoretically demonstrate a scheme that uses isolated attosecond pulses (IAPs) to achieve this goal. Our approach utilizes the coherent interference between the electronic wave packets of interest and the one produced by a subsequent IAP. It is shown that the photoelectron spectral phase that has eluded direct detection so far can be fully recovered from observable photoelectron spectra without perturbing the electron-release process under investigation. By further performing a time-frequency-like analysis on the photoelectron energy spectra with the spectral phase, we reveal the birth processes of photoelectrons in time and the association between electronic energy and birth time in strong-field ionization driven by circularly polarized laser pulses. The present work explores a promising application of IAPs for ultrafast measurement and opens a viable venue for investigating electronic dynamics with quantum phase information.

Figures (6)

• Figure 1: The ionization scenario induced by the chirped IAP with $\mathcal{E}_0=0.01\ \mathrm{a.u.}$, $\omega_0=3\ \mathrm{a.u.}$, $\tau_\mathcal{E}=30\ \mathrm{a.u.}$, and $\beta=-40$. (a) The angle-resolved PES (normalized to the maximum, in linear color scale). The dashed line indicates $\varphi_k=0$. (b) The PES cut at $\varphi_k=0$ and the spectral phases. (c) The theoretically exact and retrieved wave packets and their phases. See text for details.
• Figure 2: The SFI scenarios driven by the circularly polarized pulses. (a1)--(a3) The angle-resolved PES (normalized to the maximum, in linear color scale) induced by the driving pulses. (b1)--(b3) The PES cut at $\varphi_k=0$. The PES multiplied by factors are for better visibility. (c1)--(c3) The exact and retrieved wave packets and the corresponding amplitudes at $\varphi_k=0$. (d1)--(d3) The angle-resolved BTDs (normalized to the maximum, in linear color scale), where the circles located at $\varphi_k=0.275\pi,\ 0.0528\pi,\ \mathrm{and}\ 0.0361\pi$ indicate the overall maxima, respectively, and the solid contours indicate $99\%$ of the maxima. The vertical and horizontal dashed lines indicate $\varphi_k=0$ and $\tau_0=0$, respectively. From top to bottom, the laser parameters of the driving pulses are $\mathcal{E}_0=0.03$, $0.045$, and $0.05\ \mathrm{a.u.}$, $\omega_0=0.16$, $0.1139$, and $0.05695\ \mathrm{a.u.}$, and $\tau_\mathcal{E} \equiv 7\ \mathrm{o.c.}$, respectively, while those of the IAPs are $\mathcal{E}_0=0.01$, $0.01$, and $0.015\ \mathrm{a.u.}$, $\omega_0=0.88$, $0.88$, and $1.2\ \mathrm{a.u.}$, and $\tau_\mathcal{E} = 25,\ 25,\ \mathrm{and}\ 15\ \mathrm{a.u.}$, respectively. Note that the same IAP is applied for the first and second rows.
• Figure 3: The energy-time representations of photoelectrons in different ionization scenarios (see text), based on GT (top row) and SST (bottom row). The solid curves in the upper panels indicate the $y$ components of the circularly polarized driving pulses. The shadows and solid curves in the lower panels indicate the profiles of the corresponding BTDs and PES at selected momentum directions, respectively. In (b0), the dotted curve shows the profile of the instantaneous pulse intensity and the dash-dotted line the instantaneous pulse frequency minus $I_\mathrm{p}$. All distributions are normalized to the corresponding maxima and displayed in logarithmic color scale. The laser parameters for the columns from left to right are the same as those in Figs. \ref{['fig:xuv']}(a), \ref{['fig:sfi']}(a1), \ref{['fig:sfi']}(a2), and \ref{['fig:sfi']}(a3), respectively.
• Figure 4: Comparison of the birth-time distributions obtained from the exact and retrieved wave packets for four ionization scenarios. Panels (a)--(d) correspond to the scenarios that are discussed in the first to the last columns of Fig. \ref{['fig:sst']}, respectively.
• Figure 5: Comparison of the ETR distributions based on the Gabor transform of the exact (top row) and retrieved (bottom row) wave packets. The four ionization scenarios from left to right correspond to those discussed in the first to the lase columns of Fig. \ref{['fig:sst']}, respectively.