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Physical Review A

Signatures beyond the rotating-wave approximation in retrieving the photoionization time delay from an ω−2ω interferometric method

Mingqing Liu, Xinqiang Wang, Lijuan Jia, Peiguang Yan, Wei‐Chao Jiang

Published Jul 7, 2023• 8 citations
Publisher

Abstract

We propose a protocol to retrieve the photoionization time delay that employs a pair of oppositely circularly polarized attosecond extreme ultraviolet pulses with frequencies $\ensuremath{\omega}$ and $2\ensuremath{\omega}$. By numerically solving the three-dimensional time-dependent Schr\"odinger equation, we observe an oscillation in the energy-resolved photoionization time delay encoded in the relative optical phase between $\ensuremath{\omega}$ and $2\ensuremath{\omega}$ pulses when the emission asymmetry of the photoelectron is maximal. Our results show that this oscillation arises from the interference between two one-photon ionization pathways from the ground state due to the broad bandwidth effect of an ultrashort pulse: the absorption of one left-handed circularly polarized photon and the emission of one right-handed circularly polarized photon. The latter is regarded as a consequence of the breakdown of the rotating-wave approximation (RWA). We compare the perturbation theory with and without RWA and demonstrate that photon emission plays a crucial role in retrieving photoionization time delay. Our study enriches the underlying physics of attosecond spectroscopy and provides a framework for accurately measuring photoionization time delays in atoms and molecules.

DOI
10.1103/physreva.108.013102

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We propose a protocol to retrieve the photoionization time delay that employs a pair of oppositely circularly polarized attosecond extreme ultraviolet pulses with frequencies \ensuremathω\ensuremath{\omega}\ensuremathω and 2\ensuremathω2\ensuremath{\omega}2\ensuremathω. By numerically solving the three-dimensional time-dependent Schr"odinger equation, we observe an oscillation in the energy-resolved photoionization time delay encoded in the relative optical phase between \ensuremathω\ensuremath{\omega}\ensuremathω and 2\ensuremathω2\ensuremath{\omega}2\ensuremathω pulses when the emission asymmetry of the photoelectron is maximal. Our results show that this oscillation arises from the interference between two one-photon ionization pathways from the ground state due to the broad bandwidth effect of an ultrashort pulse: the absorption of one left-handed circularly polarized photon and the emission of one right-handed circularly polarized photon. The latter is regarded as a consequence of the breakdown of the rotating-wave approximation (RWA). We compare the perturbation theory with and without RWA and demonstrate that photon emission plays a crucial role in retrieving photoionization time delay. Our study enriches the underlying physics of attosecond spectroscopy and provides a framework for accurately measuring photoionization time delays in atoms and molecules.
We study time delays in atomic multiphoton ionization (MPI) using the phase-sensitive detection of photoelectron vortices. Photoelectron vortices are created by MPI with counterrotating circularly polarized (CRCP) ultrashort double-pulse sequences. The vortices are characterized by a spiral-shaped photoelectron momentum distribution (PMD) resulting from the Ramsey-type interference of the partial photoelectron wave packets created by each pulse. The slope of the spiral arms encodes the time delay between the partial wave packets with interferometric precision. We study the ionization time delay in the 1+21+21+2 resonance-enhanced multiphoton ionization of potassium atoms using femtosecond CRCP white-light supercontinuum pulses. Pairwise interference of the partial wave packets with a reference wave packet gives rise to vortices of different rotational symmetry, which are superimposed to form the total PMD. The PMD is reconstructed tomographically and decomposed into the vortices using three-dimensional Fourier analysis. From the energy-dependent spectral phases of the vortices, we retrieve a resonant ionization delay on the order of 1 fs, much shorter than the pulse duration. Our results demonstrate the power of photoelectron vortices for the accurate determination of photoionization time delays and open up new perspectives for photoelectron chronoscopy including the measurement of ionization delays on the attosecond timescale.
Abstract Attosecond chronoscopy is central to the understanding of ultrafast electron dynamics from gas to condensed phase with attosecond temporal resolution. It has, however, not yet been able to determine the timing of individual partial waves, and steering their contribution has been a substantial challenge. Here, we develop a polarization-skewed attosecond chronoscopy to reveal their roles from the angle-resolved photoionization phase shifts in rare gas atoms. By scanning the relative polarization angle between an extreme-ultraviolet attosecond pulse train and a phase-locked near-infrared laser field serving as a partial wave meter, we break the cylindrical symmetry and observe an emission direction dependent phase shift in the photoionized electron momenta. The experimental observations are well supported by numerical simulations using the R-matrix with time-dependence method, and by analytical analysis using the soft-photon approximation. Our symmetry-resolved, partial-wave analysis identifies the transition rate and phase shifts of each individual ionization pathway in the attosecond photoelectron emission dynamics. Our findings provide critical insights into the ubiquitous attosecond optical timer and the underlying attosecond photoionization dynamics, thereby offer new perspectives for the control, manipulation, and exploration of ultrafast electron dynamics in complex systems.
We present an interferometric method for studying the Rabi dynamics in atoms by employing an $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ extreme ultraviolet pulse pair generated from the seeded free-electron laser. By solving the time-dependent Schr\"odinger equation (TDSE) for hydrogen atoms, we study the photoelectron spectrum that emerges when the $\ensuremath{\omega}$ pulse triggers Rabi oscillations between the ground state and the first excited state. The interference between the one-photon and two-photon ionization pathways in the photoelectron signal gives access to the phase difference between the one- and two-photon transition amplitudes. Compared to the cases without Rabi oscillations, an additional $\ensuremath{\pi}$ phase jump is observed in the energy domain. Based on perturbation theory, we demonstrate that this phase jump directly reflects the ultrafast buildup of Rabi oscillations in the time domain. The present $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ scheme can be generalized and applied to other more complex atoms or molecules provided that the populations of bound states can be efficiently and coherently modulated using the free-electron laser.
We theoretically propose a bicircular two-color interferometry to retrieve the resonant photoionization time delay (RPTD) of atomic hydrogen, which can be described by the energy derivative of amplitude phase difference between single- and two-photon ionization pathways. Our results reveal that the RPTD can be well retrieved from the maximal asymmetry of photoelectron momentum distributions in the perturbative and nonperturbative regimes. In the perturbative regime, the RPTD can be characterized by perturbation theory, which demonstrates a decreasing trend with the increasing energy in counter-rotating pulse configurations, while in the co-rotating case, which exhibits pronounced oscillatory characteristics. These oscillations originate from quantum interference between photoelectron wave packets generated through direct single-photon ionization processes and those mediated by resonant excitation pathways caused by the broad spectral bandwidth of ultrashort laser pulses. In the nonperturbative regime, we develop the strong-field nonperturbation theory (SFNPT) by taking the population depletion and Stark energy shift of the ground state into account, which shows a good agreement with the numerical solution of the time-dependent Schrödinger equation. The RPTD shows a smoothly increasing characteristic as photoelectron energy increases for the counter-rotating and co-rotating cases, which differs remarkably from the case in the perturbative regime. Our SFNPT model unveils that this abnormal phenomenon can be attributed to the population depletion of the ground state. Our proposed bicircular two-color interferometry approach provides an avenue for exploring the resonant time delays in atomic photoionization and observing their nonperturbative characteristics.
Attosecond chronoscopy enables the exploration of correlated electron dynamics in real time. One key observable of attosecond physics is the determination of "time zero" of photoionization, the time delay with which the wave packet of the ionized electron departs from the ionic core. This observable has become accessible by experimental advances in attosecond streaking and reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) techniques. In this Letter, we explore photoionization time delays by strong extreme ultraviolet fields beyond the linear-response limit. We identify novel signatures in time delays signifying strong coupling between atoms and light fields and the light-field dressing of the ion. As a prototypical case, we study the interelectronic coherence and entanglement in helium driven by a strong extreme ultraviolet field. By the numerical solution of the time-dependent Schrödinger equation in its full dimensionality, we show that the time delay of the photoionized electron allows one to monitor the ultrafast variations of coherence dynamics and entanglement in real time.
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.