Multiphoton Ionization Of Atoms Research Articles

Multichromatic supercontinuum polarization shaping applied to photoelectron holography

We present a supercontinuum pulse shaping method specifically designed for the generation of polarization-tailored multichromatic femtosecond laser fields. By combining a 4f-polarization pulse shaper with a custom-made polarizer kit, we independently modulate different spectral bands of a white-light supercontinuum in amplitude, phase, and polarization. The scheme is highly modular, scalable to any number of bands supported by the input spectrum and aims at the physically motivated design of specific laser fields tailored to the relevant transitions and dynamics of the quantum system. The power and versatility of the scheme is showcased in three different scenarios based on atomic multiphoton ionization employing polarization-tailored trichromatic pulse sequences. (1) We demonstrate the creation of an -type free electron wave packet and reconstruct its 3D momentum distribution by a waveplate-free shaper-based photoelectron tomography technique. (2) We utilize the holographic properties of the wave packet to study time-resolved and phase-sensitive ultrafast dynamics of bound states. (3) We investigate the field-free time-evolution of a photoelectron wave packet in the continuum. Our results on an atomic model system demonstrate the great potential of the modular shaping scheme for a wide range of applications on more complex quantum systems, including polyatomic molecules, nanoscopic structures and solids.

Multiphoton Ionization Reduction of Atoms in Two-Color Femtosecond Laser Fields.

We report the ionization reduction of atoms in two-color femtosecond laser fields in this joint theoretical-experimental study. For the multiphoton ionization of atoms using a 400nm laser pulse, the ionization probability is reduced if another relatively weak 800nm laser pulse is overlapped. Such ionization reduction consistently occurs regardless of the relative phase between the two pulses. The time-dependent Schrödinger equation simulation results indicate that with the assisted 800nm photons the electron can be launched to Rydberg states with large angular quantum numbers, which stand off the nuclei and thus are hard to be freed in the multiphoton regime. This mechanism works for hydrogen, helium, and probably some other atoms if two-color laser fields are properly tuned.

Three-dimensional photoelectron holography with trichromatic polarization-tailored laser pulses

We present a three-dimensional (3D) photoelectron wave packet holography scheme based on polarization-tailored trichromatic femtosecond laser pulses for the determination of quantum phases in atomic multiphoton ionization (MPI). Experimentally, we combine supercontinuum polarization pulse shaping with photoelectron tomography for the reconstruction of the 3D photoelectron momentum distribution (PMD). To demonstrate the 3D photoelectron holography scheme, we superimpose a sculptured wave packet encoding a relative continuum phase with a reference wave packet. In particular, we create a sculptured angular momentum superposition wave packet by (2 + 1) resonance-enhanced MPI of potassium atoms using a counter-rotating circularly polarized bichromatic pulse sequence. The sculptured wave packet, consisting of states with different orbital angular momentum quantum numbers, interferes with the reference wave packet generated by direct three-photon ionization with a circularly polarized pulse of the third color. Depending on the circularity of the reference pulse, interference of both wave packets gives rise to 3D photoelectron holograms with c 2 or c 4 rotational symmetry in the laser polarization plane, i.e., in the azimuthal direction. In the polar direction, the azimuthal interference pattern undergoes a phase-shift revealing the relative quantum phase between the p- and f-type continuum partial waves in the sculptured wave packet. We determine the relative continuum phase by fitting the parameters of an analytical model of the hologram to the measured 3D PMD and confirm the result by direct extraction of the continuum phase difference from the polar-angle-dependent azimuthal phase-shift of the photoelectron angular distribution.

Coherent control mechanisms in bichromatic multiphoton ionization

Free electron vortices (FEVs) generated by multiphoton ionization (MPI) with ultrashort laser pulses have attracted significant attention due to their varied symmetries and unusual topological properties. We study two physical mechanisms of coherent control in atomic MPI with bichromatic polarization-shaped femtosecond laser pulses which give rise to the rich variety of FEVs. In the experiments, we combine pulse shaping of a carrier-envelope phase-stable supercontinuum with photoelectron tomography to generate and reconstruct three-dimensional photoelectron momentum distributions (PMDs). Simultaneous measurements of energetically separated photoelectrons from intraband and interband interference in a single PMD allow us to compare phase and polarization control of the angular distributions by both mechanisms. We investigate phase control in three scenarios: first, counterrotating circularly polarized pulses are employed to contrast the phase-insensitive angular momentum eigenstate created by intraband interference via frequency mixing with the phase-sensitive c 7 rotationally symmetric FEV from pure interband interference of two single-color ionization pathways. In the second scenario, we use orthogonal linearly polarized pulses to compare the phase control properties of a six-lobed angular momentum wave packet from intraband interference to those of a complex shaped interband PMD in the presence of phase fluctuations. Finally, we demonstrate phase control of a photoelectron hologram from mixed interband interference. In a (3 + 1) resonance enhanced MPI scheme, the red pump pulse induces a bound electron wave packet probed by the time-delayed blue pulse. The latter simultaneously creates a reference wave packet by three-photon ionization to form the photoelectron hologram. Rotation of the hologram with c 1 or c 5 rotational symmetry maps the time evolution of the bound wave packet. To analyze our results, we develop analytical expressions for the wave functions of intraband and interband interference in perturbative non-resonant MPI. The experiments are complemented with two-dimensional TDSE simulations to follow the FEV formation dynamics and to validate the physical pictures.

Elliptical dichroism in biharmonic ionization of atoms

In multiphoton ionization of atoms, elliptical dichroism may arise in the photoelectron angular distributions due to the interference of the possible ionization pathways. We here consider the interaction of atoms with an elliptically polarized biharmonic ($\ensuremath{\omega} + 2\ensuremath{\omega}$) field which simultaneously allows one- and two-photon ionization of the atoms. The interference between these two ionization pathways introduces contributions to the elliptical dichroism in addition to the dichroism that arises from the two-photon ionization alone. We show that these additional dichroism contributions can lead to a stronger dichroism in comparison to the one arising from two-photon ionization only. We present a relativistic analysis of the corresponding photoelectron angular distributions and discuss individual contributions to the dichroic phenomena. Detailed computations have been performed for biharmonic ionization of neutral helium atoms.

Multi-photon above threshold ionization of multi-electron atoms and molecules using the R-matrix approach

We formulate a computationally efficient time-independent method based on the multi-electron molecular R-matrix formalism. This method is used to calculate transition matrix elements for the multi-photon ionization of atoms and molecules under the influence of a perturbative field. The method relies on the partitioning of space which allows us to calculate the infinite-range free-free dipole integrals analytically in the outer region, beyond the range of the initial bound wave function. This approach is valid for an arbitrary order, that is, any number of photons absorbed both in the bound and the continuum part of the spectrum (below- and above-threshold ionization). We calculate generalized multi-photon cross sections and angular distributions of different systems (H, He, hbox {H}_{{2}}, hbox {CO}_{{2}}) and validate our approach by comparison with data from the literature.

Tunneling and multiphoton ionization of atoms in two-color linear and circular laser fields and possibility of coherent polarization control of terahertz waves

The tunneling and multiphoton ionization of atoms in an intense two-color linearly and circularly polarized laser fields are discussed in the Keldysh theory framework. We use the “imaginary-time” method, where tunneling of the photoelectron is described by the classical equations of motion but with purely imaginary “time.” Together with using of the saddle-point method, this allows to obtain the dependence of the total ionization rate and the net photoelectron current, generated due to the interaction of an intense two-color laser field with an atom, on the ratio of the second and fundamental harmonic amplitudes, their relative phase and an angle between harmonics. Application of the “imaginary-time” method also allows us to specify the parameters maximizing the net photocurrent and to determine the Coulomb correction to the ionization rate. We investigate the properties of polarization and spectral intensity of terahertz (THz) radiation and also the possibility of the coherent control of THz waves polarization in two-color scheme, through the relative phase between harmonics. We theoretically demonstrate that the amplification of THz radiation in the case of parallel co-rotating circular laser pulses is greater than for a combination of circularly and linearly polarized harmonics and provides the most promising conditions for increasing the efficiency of THz emission and coherent control of the THz beam polarization.

Orbital angular momentum superposition states in transmission electron microscopy and bichromatic multiphoton ionization

The coherent control of electron beams and ultrafast electron wave packet 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.

Multiphoton ionization of atoms in two-color laser field and coherent polarization control of terahertz waves

Within the framework of the Keldysh theory, the multiphoton ionization of atoms subjected to a perturbation by a high intensity two-color laser radiation field of an arbitrary polarization is considered. The dependence of the net photoelectron current, generated due to the interaction of an intense elliptically polarized two-color laser field with an atom, on the ratio of the second and fundamental harmonic amplitudes, their relative phase, and an angle between harmonics is found. The parameters maximizing the net photoelectron current are specified. Properties of polarization and spectral intensity of terahertz radiation and also possibility of the coherent control of terahertz waves polarization through the relative phase between harmonics in a two-color scheme are investigated. Using the ‘imaginary-time’ method, extremal subbarrier trajectories of the photoelectron moving in an elliptically polarized two-color laser field and the Coulomb correction to the total ionization rate are derived and discussed. The asymptotic expressions for the total ionization rate and the net photoelectron current obtained in the paper for the qualitative explanation of experiments on the generation of terahertz radiation in gases can be used.

Control of three-dimensional electron vortices from femtosecond multiphoton ionization

We report on the creation and manipulation of three-dimensional (3D) electron vortices from femtosecond multiphoton ionization of atoms. Vortex-shaped photoelectron momentum distributions arise from the superposition of two time-delayed free-electron wave packets with different magnetic quantum numbers. In the experiment, pairs of time-delayed counter-rotating circularly polarized (CRCP) femtosecond laser pulses, generated from a polarization-shaped supercontinuum source, are used to ionize potassium atoms. The resulting 3D electron vortices are reconstructed tomographically from a set of velocity map imaging measurements. By variation of the time delay, the helicity, and the spectral bandwidth of the CRCP pulse sequence, we control the radial vortex shape. Absorption of another photon in the continuum changes the ${c}_{6}$ azimuthal symmetry of the threshold vortex into ${c}_{8}$ for above-threshold ionization. Electron vortices from nonperturbative excitation show ${c}_{4}$ azimuthal symmetry and a $\ensuremath{\pi}$-phase jump in the polar direction. Determination of the relative phase of the superposition state allows us to reconstruct a free-electron wave function.

Circular dichroism in photoelectron images from aligned nitric oxide molecules.

We have used velocity map photoelectron imaging to study circular dichroism of the photoelectron angular distributions (PADs) of nitric oxide following two-color resonance-enhanced two-photon ionization via selected rotational levels of the A 2Σ+, v'=0 state. By using a circularly polarized pump beam and a counter-propagating, circularly polarized probe beam, cylindrical symmetry is preserved in the ionization process, and the images can be reconstructed using standard algorithms. The velocity map imaging set up enables individual ion rotational states to be resolved with excellent collection efficiency, rendering the measurements considerably simpler to perform than previous measurements conducted with a conventional photoelectron spectrometer. The results demonstrate that circular dichroism is observed even when cylindrical symmetry is maintained, and serve as a reminder that dichroism is a general feature of the multiphoton ionization of atoms and molecules. The observed PADs are in good agreement with calculations based on parameters extracted from previous experimental results obtained by using a time-of-flight electron spectrometer.

Crossover from tunneling to multiphoton ionization of atoms

We present a theory illuminating the cross-over from strong-field tunnelling ionization to weak-field multiphoton ionization in the interaction of a classical laser field with a hydrogen atom. A simple formula is derived in which the ionization amplitude appears as a product of two separate amplitudes. The first describes the initial polarization of the atom by virtual multiphoton absorption and the second the subsequent tunnelling out of the polarized atom. Tunnelling directly from the ground state and multiphoton absorption without tunnelling appear naturally as the limits of the theory.

Strong-field atomic ionization in an elliptically polarized laser field and a constant magnetic field

Within the framework of the quasistationary quasienergy state (QQES) formalism, the tunneling and multiphoton ionization of atoms and ions subjected to a perturbation by a high intense laser radiation field of an arbitrary polarization and a constant magnetic field are considered. On the basis of the exact solution of the Schr\odinger equation and the Green's function for the electron moving in an arbitrary laser field and crossed constant electric and magnetic fields, the integral equation for the complex quasienergy and the energy spectrum of the ejected electron are derived. Using the ``imaginary-time'' method, the extremal subbarrier trajectory of the photoelectron moving in a nonstationary laser field and a constant magnetic field are considered. Within the framework of the QQES formalism and the quasiclassical perturbation theory, ionization rates when the Coulomb interaction of the photoelectron with the parent ion is taken into account at arbitrary values of the Keldysh parameter are derived. The high accuracy of rates is confirmed by comparison with the results of numerical calculations. Simple analytical expressions for the ionization rate with the Coulomb correction in the tunneling and multiphoton regimes in the case of an elliptically polarized laser beam propagating at an arbitrary angle to the constant magnetic field are derived and discussed. The limits of small and large magnetic fields and low and high frequency of a laser field are considered in details. It is shown that in the presence of a nonstationary laser field perturbation, the constant magnetic field may either decrease or increase the ionization rate. The analytical consideration and numerical calculations also showed that the difference between the ionization rates for an $s$ electron in the case of right- and left-elliptically polarized laser fields is especially significant in the multiphoton regime for not-too-high magnetic fields and decreases as the magnetic field increases. The paper generalizes the results obtained earlier [V. M. Rylyuk, Phys. Rev. A 86, 013402 (2012)].

L. V. Keldysh’s “Ionization in the Field of a Strong Electromagnetic Wave” and modern physics of atomic interaction with a strong laser field

Basic premises, approximations, and results of L.V. Keldysh’s 1964 work on multiphoton ionization of atoms are discussed, as well as its influence on the modern science of the interaction of atomic–molecular systems with a strong laser field.

High-intensity laser-atom interactions

Following a historical introduction on the nature of light and its interaction with matter, a survey is given of the development of lasers capable of delivering short pulses of very intense radiation. The peak intensities of these laser pulses are so high that the corresponding laser fields can compete with, or even dominate, the Coulomb field in governing the dynamics of atomic systems. As a result, new phenomena, known as multiphoton processes, can occur. An outline is given of the basic properties found in the study of three important multiphoton processes. Firstly, the multiphoton ionization of atoms and the phenomenon of “above-threshold ionization”. Secondly, the emission by atoms of high-order harmonics of the frequency of the driving laser and their use to generate laser pulses having durations in the attosecond range. Thirdly, laser-assisted electron-atom collisions. A review is then given of the main non-perturbative methods which have been used to perform theoretical studies of multiphoton processes.

50 years of optical tunneling

The special issue ‘Fifty years of optical tunneling’ celebrates the fifty-year-anniversary of the seminal paper by L V Keldysh, ‘Ionization in the field of astrong electromagnetic wave’, published in November 1964 in Russian [1] andthen, in May 1965, in its English translation [2].When a laser field interacting with an atom is weak, the conventional per-turbation theory allows us to understand and describe almost everything. But whatshould one do if the energy of the electron oscillations in the laser field exceedsthe photon energy and approaches the electron binding energy? What if thestrength of the laser electric field starts to approach the strength of the Coulombfield that binds an electron inside an atom?In other words, what should one do when the conventional perturbation theoryis no longer applicable? Here is a short answer: one should go and read theKeldysh paper.It provides both the mathematical tools and the physical picture for inter-preting the mathematical results. It provides the fundamental understanding of thevery rich dynamics that can be triggered by intense laser field. It also shows thedeep connection between multi-photon ionization of atoms and molecules and themultiphoton valence-conduction band transitions inside dielectrics, a connectionwhich we are now beginning to appreciate more and more.Reviewing the Russian literature of the late 19th century, Eugene-Melchiorde Vogue (1848–1910), a French diplomat and literary critic, wrote in his ‘LeRoman Russe’: ‘…Nous sommes tous sortis du Manteau de Gogol’. Similar isthe relationship between the theory of intense laser-atom interaction and theKeldysh paper. The fundamental papers by V S Popov and coworkers [3], ANikishov and V Ritus [4], H Reiss [5], F Faisal [6], N Manakov and L Rapoport[7], and many other papers too numerous to list here, are all deeply linked to theKeldysh paper.Simply said, the Keldysh paper has laid down the foundation for the wholefield of intense-field laser-atom interaction and the many things that have fol-lowed. Paraphrasing Plato: ‘… good theory gives soul to the Universe, wings tothe mind, flight to the imagination, and charm and gaiety to life and toeverything’.Virtually all effects that have been discovered in this field can be interpretedwithin the Keldysh theory, or within its modifications. And when a new experi-mental observation seems to belay its predictions (see e.g. [8]), the initial surprise(see e.g. [9]), usually followed by a flurry of experimental and theoretical activity,often culminates in a clear physical picture that, once again, grows out of themasterpiece painted by Keldysh’s bold brush.In 1964, the laser had just been invented. Multi-photon ionization, analyzed inthe Keldysh paper in detail, had not yet been observed—but followed shortly [10].Optical tunneling—one of the key outcomes of the Keldysh analysis, wouldremain out of reach for another two decades [11]. Above-threshold ionization,

Density‐matrix theory of quantum dynamics under a strong external field switched on nonadiabatically

Quantum time‐evolution equations for the density matrix are formulated in the unrestricted Hartree–Fock approximation, with an emphasis on the nonperturbative effect due to a sudden or gradual onset of a strong external field. Numerical simulations are performed for ideal Fermi gas around a square‐well potential which is switched on dynamically. When the switching is fast enough, an oscillatory motion of the particle is induced by a nonadiabatic transition at the Landau–Zener crossing point, which is most clearly seen in a small‐size system. When the switching is sufficiently slow, the simulation corroborates the adiabatic theorem. It is shown that the Anderson's infrared catastrophe in a metal is strongly enhanced by the nonperturbative effect. The Keldysh formula of atomic multiphoton ionization can also be derived from the nonperturbative term in the density‐matrix equation, indicating a wide applicability of the present theory. © 2014 Wiley Periodicals, Inc.

Circular Dichroism in Laser-Assisted Short-Pulse Photoionization

A remarkable effect of circular dichroism, i.e., a difference in photoelectron spectra produced by right and left circularly polarized light in two-color multiphoton ionization of atoms, is predicted for the case when the atom is ionized by an extreme ultraviolet or x-ray femtosecond pulse in the field of a strong infrared laser pulse, both pulses being circularly polarized. We show that the sidebands formed in the spectra exhibit different circular dichroism often of different signs both in angle-resolved and angle-integrated experimental conditions. The effect can be used for detecting and measuring circular polarization of x rays in a spectral range where other methods are not effective.

Qualitatively different theoretical predictions for strong-field photoionization rates

We give examples showing that two well-known versions of the S-matrix theory, which describes a nonresonant multiphoton ionization of atoms and ions in intense laser fields, lead to qualitatively different results. The latter refer not only to total ionization rates, but also to energy distributions of photoelectrons, for instance in a polarization plane of the laser field. It should be possible to make an experiment testing predictions of both theories in the near future.

Multiphoton ionization of atoms by a two-color laser pulse

The probability of multiphoton ionization of atoms in a laser radiation field containing an additional second harmonic is calculated by the imaginary time method [9, 10]. The conditions are found when the second-harmonic contribution to the ionization of atoms dominates over that of the first harmonic. It is shown that the average momentum of photoelectrons ejected from atoms depends on the phase shift between the first and second harmonics and their mutual polarization. The obtained asymptotic expressions can be used for the qualitative explanation of experiments on generation of terahertz radiation from the optical breakdown region in gas in the focus of a femtosecond laser.