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Physical Review Research

Control of attosecond photoemission time delays by quantum state interference

Divya Bharti, J. C. del Valle, Aaron Bondy, Klaus Bartschat, R. Moshammer, Anne Harth, T. Pfeifer

Published Sep 4, 2026• 0 citations
Publisher

Abstract

Scattering theory has long established that wave packets can experience time delays and advances, while developments in attosecond interferometry have made such temporal shifts experimentally accessible. They are encoded in the spectral phase of the emitted electron wave packet and are commonly accessed through interferometric techniques. Here, we report an intensity-driven reversal of the angular phase of a threshold photoelectron sideband in helium. By varying the intensity of an infrared dressing field, we control the direction of the phase change at large emission angles, which is associated with interference between partial waves near angular nodes. Solving the time-dependent Schrödinger equation within the single-active-electron approximation confirms the existence of an angular phase inversion. Our results reveal a mechanism for manipulating the angular phase structure of photoelectron wave packets over a large range via laser-induced interference.

DOI
10.1103/yjyp-kx19

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Scattering theory has long established that wave packets can experience time delays and advances, while developments in attosecond interferometry have made such temporal shifts experimentally accessible. They are encoded in the spectral phase of the emitted electron wave packet and are commonly accessed through interferometric techniques. Here, we report an intensity-driven reversal of the angular phase of a threshold photoelectron sideband in helium. By varying the intensity of an infrared dressing field, we control the direction of the phase change at large emission angles, which is associated with interference between partial waves near angular nodes. Solving the time-dependent Schrödinger equation within the single-active-electron approximation confirms the existence of an angular phase inversion. Our results reveal a mechanism for manipulating the angular phase structure of photoelectron wave packets over a large range via laser-induced interference.
When small quantum systems, atoms or molecules, absorb a high-energy photon, electrons are emitted with a well-defined energy and a highly symmetric angular distribution, ruled by energy quantization and parity conservation. These rules are based on approximations and symmetries which may break down when atoms are exposed to ultrashort and intense optical pulses. This raises the question of their universality for the simplest case of the photoelectric effect. Here we investigate photoionization of helium by a sequence of attosecond pulses in the presence of a weak infrared laser field. We continuously control the energy of the photoelectrons and introduce an asymmetry in their emission direction, at variance with the idealized rules mentioned above. This control, made possible by the extreme temporal confinement of the light-matter interaction, opens a road in attosecond science, namely, the manipulation of ultrafast processes with a tailored sequence of attosecond pulses.
We study the two-dimensional photoelectron momentum distribution in a synthesized field of an attosecond pulse and a weak infrared femtosecond pulse by solving the time-dependent Schr\"odinger equation of He atoms. The photoelectron momentum spectra reveal fruitful interference structures. With a semiclassical model, we show that some of the photoelectron interference structures come from the interference between the direct and backward-scattering electron trajectories. Those backward-scattering electrons are freed by the attosecond pulse and then are hard rescattered with parent ions by the streaking infrared field. By changing the phase delay between the attosecond pulse and the infrared laser field, we find that two kinds of backward-scattering electron trajectories will contribute to the holographic pattern. We show that backward-scattering holography can be explored with attosecond streaking experiments.
Summary form only given. Angstrom and attosecond control of free electron wave packets is one of the pinnacles of attosecond science. Orthogonally polarized two-color (OTC) laser fields allow to control the motion of field-ionizing electronic wave packets both in time and space[1]. In OTC pulses time and space are connected and thus an attosecond time scale is established in the polarization plane for both the emitted and the re-colliding wave packets[2,3].In this submission, we report on experiments that use OTC pulses for studying atomic single and double ionization. The three-dimensional momentum vector of electrons and ions created by single and double ionization of neon atoms was measured with the COLTRIMS technique as a function of the sub-cycle shape of the OTC pulses. We introduce a concept similar to attosecond streaking that allows reading sub-cycle timing information from the momentum vector of emitted electrons. The concept is then applied to gaining information about the influence of the long-range Coulomb potential on the trajectories of tunneling electrons.Fig.1 (a) shows the measured momentum distributions of electrons correlated with singly ionized neon in the polarization plane of the OTC field with relative phase Δφ between the two color components. The spectra show that the electron emission direction is sensitive to Δφ. Furthermore, the spectra feature a prominent x-shaped central structure and weaker fine-scale modulations due to wave packet interferences. To compare with simulated spectra with strong field approximation (SFA) and solving two-dimensional time-dependent Schrödinger equation (TDSE) with single active electron approximation, we conclude that Coulomb effect plays important role on the spatial distribution of released electron wave packets. In the conference, we will furthermore demonstrate control over the correlation between the two electrons emitted during double ionization upon electron recollision by tuning the shape of the electric field of the OTC pulses on the sub-cycle scale. The results of these experiments are in agreement with theoretical predictions [4].
We experimentally demonstrate that atomic orbital parity mix interferences can be temporally controlled on an attosecond time scale. Electron wave packets are formed by ionizing argon gas with a comb of odd and even high-order harmonics, in the presence of a weak infrared field. Consequently, a mix of energy-degenerate even and odd parity states is fed in the continuum by one- and two-photon transitions. These interfere, leading to an asymmetric electron emission along the polarization vector. The direction of the emission can be controlled by varying the time delay between the comb and infrared field pulses. We show that such asymmetric emission provides information on the relative phase of consecutive odd and even order harmonics in the attosecond pulse train.
Single-photon ionization of a hydrogen atom irradiated by two time-delayed isolated attosecond pulses is theoretically investigated by numerically solving the fully three-dimensional time-dependent Schr\"odinger equation. It is demonstrated that the analysis of the angular-resolved electron energy spectrum, showing a complex interference pattern, allows one to completely retrieve the difference between the energy-dependent phases of the electron wave packets generated by the two delayed attosecond pulses. Moreover, it is shown that in the case of a pair of excitation pulses with the same chirp rate, the proposed interferometric technique can be used to measure the difference between the carrier envelope phase values of two attosecond pulses.
The attosecond pump-femtosecond probe technique is widely used in electron dynamics research, with temporal resolution reaching tens of attoseconds. Here, we propose a scheme for controlling the Fano line shapes of helium doubly excited states by replacing the pump source with a pair of time-delayed attosecond pulses. We show that the interference induced by this delay provides an additional, highly effective means of controlling electron dynamics, enabling temporal resolution on the zeptosecond scale. We demonstrate that the corresponding line shapes in transient absorption spectra can shift dramatically within a time-delay variation of just a few hundred zeptoseconds. This extreme spectral modulation occurs under two key conditions: (i) when the time delay aligns with the spectral minimum of the coherently combined attosecond pulses in the frequency domain, and (ii) when the delay between the infrared probe pulse and the first attosecond pulse is held constant. This approach opens a new pathway to zeptosecond-scale control in quantum systems and demonstrates the powerful synergy between phase manipulation in both light and electron waves for achieving ultrafast spectral transformations.