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We study time-delays in atomic multiphoton ionization (MPI) using the phase-sensitive detection of photoelectron vortices. Photoelectron vortices are created by MPI with counter-rotating 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+2) resonance-enhanced multiphoton ionization (REMPI) 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 3D Fourier analysis. From the energy-dependent spectral phases of the vortices, we retrieve a resonant ionization delay in 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., Comment: 11 pages, 5 figures

Since their first theoretical proposal [Ngoko Djiokap et al., Phys. Rev. Lett. 115, 113004 (2015)] and experimental demonstration [Pengel et al., Phys. Rev. Lett. 118, 053003 (2017)], free electron vortices (FEVs) have attracted considerable attention. Recently, a new class of unusually shaped FEVs, termed `reversible electron spirals', has been proposed theoretically [Strandquist et al., Phys. Rev. A 106, 043110 (2022)] for atomic single-photon ionization by two oppositely chirped and counterrotating circularly polarized (CRCP) attosecond pulses. Building on this concept, we present the first experimental demonstration of shaped FEVs created by atomic multiphoton ionization (MPI) using oppositely chirped CRCP femtosecond pulse pairs. In MPI by polarization-shaped pulses, several shaped FEVs of different rotational symmetry are superimposed resulting in the total photoelectron wave packet observed in the experiment. We employ velocity map imaging techniques to measure the photoelectron momentum distribution (PMD) and reconstruct the three-dimensional PMD by photoelectron tomography. Fourier analysis is used to decompose the measured PMD into the contributing FEVs with different rotational symmetries. The experimental results are supported by an analytical model and reproduced by numerical simulations, which provide insight into the role of resonant intermediate states. Our approach allows us to retrieve spectral information from the shaped laser field and the signatures of the MPI dynamics inscribed within the shaped FEVs., Comment: 12 pages, 6 figures

We propose a new scheme to control the shape of the Autler-Townes (AT) doublet in the photoelectron spectrum from atomic resonance-enhanced multiphoton ionization (REMPI). The scheme is based on the interference of two AT doublets created by ionization of the strongly driven atom from the ground and the resonantly excited state using tailored bichromatic femtosecond (fs) laser pulses. In this scheme, the quantum phase of the photoelectrons is crucial for the manipulation of the AT doublet. The laser polarization state and the relative optical phase between the two colors are used to manipulate the interference pattern. We develop an analytical model to describe the bichromatic REMPI process and provide a physical picture of the control mechanism. To validate the model, the results are compared to an ab initio calculation based on the solution of the 2D time-dependent Schr\"odinger equation for the non-perturbative interaction of an atom with intense polarization-shaped bichromatic fs-laser pulses. Our results indicate that the control mechanism is robust with respect to the laser intensity facilitating its experimental observation., Comment: 13 pages, 5 figures

We present a multichannel photoelectron interferometry technique based on trichromatic pulse shaping for unambiguous determination of quantum phases in multiphoton ionization (MPI) of potassium atoms. The colors of the laser field are chosen to produce three energetically separated photoelectron interferograms in the continuum. While the red pulse is two-photon resonant with the $3d$-state resulting in a (2+1) resonance-enhanced MPI (REMPI), a (1+2) REMPI occurs via the non-resonant intermediate $4p$-state with an initial green or blue pulse. We show that ionization via a non-resonant intermediate state lifts the degeneracy of photoelectron interferograms from pathways consisting of permutations of the colors. The analysis of the interferograms reveals a phase shift of $\pm \pi/2$ depending on the sign of the detunings in the (1+2) REMPI pathways. In addition, we demonstrate that the photoionization time delay in the resonant (2+1) REMPI pathway gives rise to a linear spectral phase in the photoelectron spectra. Insights into the underlying MPI processes are gained through an analytic perturbative description and numerical simulations of a trichromatic driven three level system coupled to the continuum., Comment: 17 pages, 5 figures

The coherent control of electron beams and ultrafast electron wave packets dynamics have attracted significant attention in electron microscopy as well as in atomic physics. In order to unify the conceptual pictures developed in both fields, we demonstrate the generation and manipulation of tailored electron orbital angular momentum (OAM) superposition states either by employing customized holographic diffraction masks in a transmission electron microscope or by atomic multiphoton ionization utilizing pulse-shaper generated carrier-envelope phase stable bichromatic ultrashort laser pulses. Both techniques follow similar physical mechanisms based on Fourier synthesis of quantum mechanical superposition states allowing the preparation of a broad set of electron states with uncommon symmetries. We describe both approaches in a unified picture based on an advanced spatial and spectral double slit and point out important analogies. In addition, we analyze the topological charge and discuss the control mechanisms of the free-electron OAM superposition states. Their generation and manipulation by phase tailoring in transmission electron microscopy and atomic multiphoton ionization is illustrated on a 7-fold rotationally symmetric electron density distribution., Comment: K. Eickhoff and C. Rathje contributed equally to this work

We present numerical simulations of ultrafast multiphoton ionization dynamics in a two-dimensional atomic model driven by co- and counterrotating circularly polarized single-color and bichromatic carrier envelope phase (CEP) stable ultrashort laser pulse sequences. Taking into account phase variations due to CEP fluctuations and the Gouy phase, our results accurately reproduce recently measured photoelectron momentum distributions [Pengel et al., Phys. Rev. Lett. 118, 053003 (2017), Phys. Rev. A 96, 043426 (2017); Kerbstadt et al., Nat. Comm. 10, 685 (2019), Adv. Phys. X 4, 1672583 (2019)]. The time evolution of the complex-valued electron wave function in coordinate and momentum space is calculated to study the bound state- and the vortex formation dynamics. The non-vanishing azimuthal probability current density proves the vortex nature of electron wave packets with odd-numbered rotational symmetry. Their angular momentum expectation value assumes half-integer values of 3.5 (corotating) and 0.5 (counterrotating). Knowledge of the wave function allows us to analyze the photoionization dynamics and to validate the physical pictures proposed in previous experimental studies. As an outlook, we investigate how electron vortices develop from the multiphoton- to the tunnel regime with increasing laser intensity.

Photoelectron interferograms, manifested in photoelectron angular distributions (PADs), are a high-information, coherent observable. In order to obtain the maximum information from angle-resolved photoionization experiments it is desirable to record the full, 3D, photoelectron momentum distribution. Here we apply tomographic reconstruction techniques to obtain such 3D distributions from multiphoton ionization of potassium atoms, and fully analyse the energy and angular content of the 3D data. The PADs obtained as a function of energy indicate good agreement with previous 2D data and detailed analysis [Hockett et. al., Phys. Rev. Lett. 112, 223001 (2014)] over the main spectral features, but also indicate unexpected symmetry-breaking in certain regions of momentum space, thus revealing additional continuum interferences which cannot otherwise be observed. These observations reflect the presence of additional ionization pathways and, most generally, illustrate the power of maximum information measurements of this coherent observable.

The feasibility of complete photoionization experiments, in which the full set of photoionization matrix elements are determined, using multiphoton ionization schemes with polarization-shaped pulses has recently been demonstrated [Hockett et. al., Phys. Rev. Lett. 112, 223001 (2014)]. Here we extend on our previous work to discuss further details of the numerics and analysis methodology utilised, and compare the results directly to new tomographic photoelectron measurements, which provide a more sensitive test of the validity of the results. In so doing we discuss in detail the physics of the photoionziation process, and suggest various avenues and prospects for this coherent multiplexing methodology.

We present a joint experimental and theoretical study on strong-field photo-ionization of sodium atoms using chirped femtosecond laser pulses. By tuning the chirp parameter, selectivity among the population in the highly excited states 5p, 6p, 7p and 5f, 6f is achieved. Different excitation pathways enabling control are identified by simultaneous ionization and measurement of photoelectron angular distributions employing the velocity map imaging technique. Free electron wave packets at an energy of around 1 eV are observed. These photoelectrons originate from two channels. The predominant 2+1+1 Resonance Enhanced Multi-Photon Ionization (REMPI) proceeds via the strongly driven two-photon transition $4s\leftarrow\leftarrow3s$, and subsequent ionization from the states 5p, 6p and 7p whereas the second pathway involves 3+1 REMPI via the states 5f and 6f. In addition, electron wave packets from two-photon ionization of the non-resonant transiently populated state 3p are observed close to the ionization threshold. A mainly qualitative five-state model for the predominant excitation channel is studied theoretically to provide insights into the physical mechanisms at play. Our analysis shows that by tuning the chirp parameter the dynamics is effectively controlled by dynamic Stark-shifts and level crossings. In particular, we show that under the experimental conditions the passage through an uncommon three-state "bow-tie" level crossing allows the preparation of coherent superposition states.