Sub-cycle pulse control of holographic and non-holographic electron interferences

TL;DR

This work demonstrates that sub-cycle laser pulses profoundly control strong-field intracycle interference in helium photoelectron momentum distributions. By combining 3D TDSE simulations within the SAE framework and a classical-trajectory model, it links interference patterns—forward-scattering holography, backscattering holography, and time double-slit—to pulse duration, carrier-envelope phase, and envelope shape, all through the lens of intrinsic chirp. Shorter pulses shorten recollision times via blueshifted instantaneous frequency, expanding or contracting fringe spacings across FSH, BSH, and TDS, while envelope choice can counteract or enhance these effects. The results offer a route to tailor attosecond electron dynamics and facilitate ultrafast holographic imaging by temporally shaping sub-cycle fields. $FSH$, $BSH$, and $TDS$ patterns emerge as sensitive probes of sub-cycle waveform control in strong-field ionization of helium, with potential extensions to more complex targets.

Abstract

We investigate the influence of sub-cycle laser pulses on holographic and non-holographic intracycle interferences by analyzing the photoelectron momentum distributions of helium using TDSE simulations supported by classical trajectory calculations. The results show that the forward-scattering holographic (FSH), backward-scattering holographic (BSH), and time double-slit (TDS) structures are found to be highly sensitive to the pulse duration, carrier-envelope phase (CEP), and temporal envelope in the sub-cycle regime. Sub-cycle pulses with CEP values of $0^\circ$ and $90^\circ$ selectively enhance or suppress distinct features, isolating holographic patterns and enhancing BSH fringes. Classical analysis reveals that the intrinsic chirp inherent to sub-cycle fields shortens the recollision time for scattering trajectories, thereby increasing the fringe spacing in FSH and BSH patterns, while simultaneously enlarging the ATI peak spacing associated with TDS interference. Pulse envelope variations, even at fixed FWHM duration, further reshape the fringe spacings by modifying the instantaneous frequency and vector potential slope near ionization times. These results demonstrate that sub-cycle pulses enable precise temporal control of holographic interference, offering new opportunities for probing and manipulating attosecond electron dynamics.

Figures (13)

• Figure 1: Temporal profiles of the laser electric field $\mathbf{E}(t)$ (dashed curve, left-axis) and instantaneous frequency $\omega(t)$ (solid curve, right-axis) for different envelope functions defined in Eq. \ref{['laser_envlp']} for FWHM durations: (a) $\tau = 0.5T_0$, and (b) $\tau = 1.0T_0$. The laser pulses are of $800$ nm wavelength with peak intensity $I_0 = 5\times 10^{14}$ W$/$cm$^{2}$, and CEP $\phi_0 = 0^\circ$. Here, $T_0\ (= 2\pi/\omega_0)$ denotes one laser cycle.
• Figure 2: Half-cycle and single-cycle laser fields with CEP $\phi_0 = 0^\circ$ and corresponding TDSE-simulated PMDs of helium. The temporal profiles of the laser electric field $\mathbf{E}(t)$ (red solid curve, left-axis) and vector potential $\mathbf{A}(t)$ (blue dashed curve, right-axis) for Gaussian-enveloped pulses with FWHM $\tau:$ (a) $0.5T_0$ and (b) $1.0T_0$. The corresponding PMDs are shown in (c) and (d), respectively.
• Figure 3: Similar to Fig. \ref{['fig2']}, but with CEP $\phi_0 = 90^\circ$. (a) and (b) shows the temporal profiles of the electric field $\mathbf{E}(t)$ and its corresponding vector potential $\mathbf{A}(t)$ for laser pulses with FWHM $\tau = 0.5T_0$ and $1.0T_0$, respectively. The corresponding PMDs of helium atom are shown in (c) and (d), respectively.
• Figure 4: Variation in stripe density of the FSH structure. (a) Schematic illustration of underlying mechanism contributing to the observed FSH structure. The half-cycle laser field $\mathbf{E}(t)$ (red solid curve) with CEP $\phi_0 = 0^\circ$ and the corresponding vector potential $\mathbf{A}(t)$ (blue dashed curve) are shown. The shaded quarter-cycle indicates the ionization times of the direct and forward-scattering trajectories. (b) PMDs showing the spider-leg-like FSH interference pattern obtained from the classical-trajectory based model (CTM). (c) PMADs for different pulse durations, extracted from the TDSE-simulated PMDs of helium. (d) Average peak widths (PWs) of PMADs-calculated using TDSE and CTM methods for different pulse durations.
• Figure 5: (a) Classical ionization times $T_{ion}$ of the direct (DT) and scattering trajectories (STs) as a function of the polar angle $\theta$. (b) The recollion time $\Delta T$ of STs, defined as the difference between the ionization time $T_{ion}$ and the rescattering time $T_{rec}$ for different pulse durations. All data points are extracted at a fixed final momentum $p = 0.5$ a.u. from the classical model based PMDs.