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Mauser and coworkers discussed in a series of papers an ansatz how to split the Dirac equation and the wave function appearing therein into a part related to a free moving electron and another part related to a free moving positron. This ansatz includes an expansion of these quantities into orders of the reciprocal of the speed of light $$\epsilon = 1/c$$ ϵ = 1 / c . In particular, in Mauser (VLSI Design 9:415, 1999) it is discussed how to apply this expansion up to the second order in the reciprocal of the speed of light $$\epsilon $$ ϵ . As an expansion of this analysis, we show in this work how all three well-known terms that appear in an expansion of the Dirac equation in second order on the reciprocal of the speed of light, namely, a relativistic correction to the kinetic energy, the Darwin term, and the spin-orbit interaction, can be found using the ansatz of Mauser—and doing so, we close a gap between this ansatz to approximate the Dirac equation and other approximative results found using the Foldy–Wouthuysen transformation.

Using the Ehrenfest theorem, two possibilites are regarded to calculate momentum expectation values. They lead to different quantum probability and flux densities being illustrated with numerical results from a model for coupled electron-nuclear motion.

We theoretically study the ionization enhancement of the diatomic molecular ion ${\mathrm{H}}_{2}{}^{+}$ at two critical internuclear distances $R$, using orthogonal two-color laser fields. The polarization of the fundamental infrared laser field and a weak second-harmonic field is parallel and perpendicular to the molecular axis, respectively. It is observed that adding the second-harmonic field raises slightly the first ionization peak at the smaller critical $R$, whereas it enhances the second one at the larger critical $R$ significantly. We further analyze the observable evidence which distinguishes two underlying mechanisms responsible for the enhanced ionization of ${\mathrm{H}}_{2}{}^{+}$: (i) the resonant excitation along with the coherent interference of the ionizing wave packets from the $1s{\ensuremath{\sigma}}_{g}$ and $2p{\ensuremath{\sigma}}_{u}$ states and (ii) the easier ionization from the up-field site of the molecule.

We investigate the effect of the molecular alignment of nitric oxide (NO) on nonadiabatic tunnel ionization of degenerate valence π± orbitals in strong circularly polarized laser fields and on spin polarization of photoelectrons. Our numerical study shows that not only for the alignment parallel to the laser propagation axis [Liu, K.; Barth, I. Phys. Rev. A 2016, 94, 043402] but also for arbitrary alignment angles except for perpendicular alignment, the counter-rotating molecular orbital with respect to the circular polarization of the laser field projected on the plane perpendicular to the molecular axis is ionized more easily. Due to the nonadiabatic effect and the nodal structure of the valence 2π± orbitals of NO, the ionization maxima for the 2π- and 2π+ orbitals in right circularly polarized laser fields are obtained for the molecular orientations at the polar angles of around 60∘ and 120∘, respectively. Considering the spin-orbital entanglement in the doubly degenerate electronic ground state of NO,...

The nonadiabaticity of quantum tunneling through an evolving barrier is relevant to resolving laser-driven dynamics of atoms and molecules at an attosecond timescale. Here, we propose and demonstrate a novel scheme to detect the nonadiabatic behavior of tunnel ionization studied in an attoclock configuration, without counting on the laser intensity calibration or the modeling of the Coulomb effect. In our scheme, the degree of nonadiabaticity for tunneling scenarios in elliptically polarized laser fields can be steered continuously simply with the pulse ellipticity, while the critical instantaneous vector potentials remain identical. We observe the characteristic feature of the measured photoelectron momentum distributions, which matches the distinctive prediction of nonadiabatic theories. In particular, our experiments demonstrate that the nonadiabatic initial transverse momentum at the tunnel exit is approximately proportional to the instantaneous effective Keldysh parameters in the tunneling regime, as predicted theoretically by Ohmi, Tolstikhin, and Morishita [Phys. Rev. A 92, 043402 (2015)PLRAAN1050-294710.1103/PhysRevA.92.043402]. Our study clarifies a long-standing controversy over the validation of the adiabatic approximation and will substantially advance studies of laser-induced ultrafast dynamics in experiments.

Based on the Ehrenfest theorem, the time-dependent expectation value of a momentum operator can be evaluated equivalently in two ways. The integrals appearing in the expressions are taken over two different functions. In one case, the integrand is the quantum mechanical flux density j̲ , and in the other, a different quantity j̃ ̲ appears, which also has the units of a flux density. The quantum flux density j̲ is related to the probability density ρ via the continuity equation, and j̃ ̲ may as well be used to define a density ρ̃ that fulfills a continuity equation. Employing a model for the coupled dynamics of an electron and a proton, we document the properties of the densities and flux densities. It is shown that although the mean momentum derived from the two quantities is identical, the various functions exhibit a very different coordinate and time-dependence. In particular, it is found that the flux density j̃ ̲ directly monitors temporal changes in the probability density, and the density ρ̃ carries information about wave packet dispersion occurring in different spatial directions.

We theoretically investigate the deformation of atomic p_{±} orbitals driven by strong elliptically polarized (EP) laser fields and the role it plays in tunnel ionization. Our study reveals that different Stark effects induced by orthogonal components of the EP field give rise to subcycle rearrangement of the bound electron density, rendering the initial p_{+} and p_{-} orbitals deformed and polarized along distinctively tilted angles with respect to the polarization ellipse of the EP field. As a consequence, the instantaneous tunneling rates change such that for few-cycle EP laser pulses the bound electron initially counterrotating (corotating) with the electric field is most likely released before (after) the peak of the electric field. We demonstrate that with a sequential-pulse setup one can exploit this effect to spatially separate the photoelectrons detached from p_{+} and p_{-} orbitals, paving the way towards robust control of spin-resolved photoemission in laser-matter interactions.

We demonstrate a scheme to produce coherent extreme ultraviolet and soft x-ray radiation with subpetahertz temporal helicity modulation, based on the high harmonic generation from current-carrying orbitals driven by intense linearly polarized laser fields. It is found that the electronic angular momentum of the orbitals oscillates periodically in femtosecond scale in the driving field. This so-far undescribed phenomenon is qualitatively interpreted and attributed to the laser-induced energy shift of orbitals. Consequently, the polarization of the harmonic radiation switches periodically in the temporal domain between left and right elliptical polarizations, and the frequency of the helicity modulation reaches subpetahertz. By varying the intensity of the laser field, the modulation frequency can be continuously controlled. This light source will serve as a potential tool to detect and manipulate the ultrafast dynamics in magnetic materials and chiral media.

Quantum particles can penetrate potential barriers by tunneling (1). If that barrier is rotating, the tunneling process is modified (2,3). This is typical for electrons in atoms, molecules or solids exposed to strong circularly polarized laser pulses (4,5). Here we measure how the transmission probability through a rotating tunnel depends on the sign of the magnetic quantum number m of the electron and thus on the initial sense of rotation of its quantum phase. We further show that the electron keeps part of that rotary motion on its way through the tunnel by measuring m-dependent modification of the electron emission pattern. These findings are relevant for attosecond metrology as well as for interpretation of strong field electron emission from atoms and molecules (6-13) and directly demonstrates the creation of ring currents in bound states of ions with attosecond precision. In solids, this could open a way to inducing and controlling ring-current related topological phenomena (14)., 19 pages, 6 figures, Nature Physics accepted

For an arbitrary nonstationary wave function of a nonrelativistic closed many-body system consisting of arbitrary interacting particles, the general expressions for the time-dependent one-particle probability and flux densities in the center-of-mass frame without applying Born–Oppenheimer approximation are obtained. Even the wave function for the translation is additionally introduced; it disappears in the center-of-mass frame automatically. It is shown that for the rotational ground state the time-dependent probability and flux densities of an arbitrary particle in the center-of-mass frame are isotropic. It means that the angular dependence is absent but these densities depend on radius and time. More importantly, it is shown that the angular components of the time-dependent flux density vanish. With these statements, one can calculate the radial component of the radius- and time-dependent electronic flux density within the Born–Oppenheimer approximation via the continuity equation. Application of this theory to the pulsating or exploding “quantum bubble” of the vibrating or dissociating Na2 molecule in the rotational ground state, respectively, is found elsewhere in this issue.

Bohm developed the Bohmian mechanics (BM), in which the Schr\"odinger equation is transformed into two differential equations: A continuity equation and an equation of motion similar to the Newtonian equation of motion. This transformation can be executed both for single-particle systems and for many-particle systems. Later, Kuzmenkov and Maksimov used basic quantum mechanics for the derivation of many-particle quantum hydrodynamics (MPQHD) including one differential equation for the mass balance and two differential equations for the momentum balance, and we extended their analysis in a prework [K. Renziehausen, I. Barth, Prog. Theor. Exp. Phys. 2018, 013A05 (2018)] for the case that the particle ensemble consists of different particle sorts. The purpose of this paper is to show how the differential equations of MPQHD can be derived for such a particle ensemble with the differential equations of BM as a starting point. Moreover, our discussion clarifies that the differential equations of MPQHD are more suitable for an analysis of many-particle systems than the differential equations of BM because the differential equations of MPQHD depend on a single position vector only while the differential equations of BM depend on the complete set of all particle coordinates., Comment: 27 pages

The tunneling site of the electron in a molecule exposed to a strong laser field determines the initial position of the ionizing electron and, as a result, has a large impact on the subsequent ultrafast electron dynamics on the polyatomic Coulomb potential. Here, the tunneling site of the electron of ${{\mathrm{H}}_{2}}^{+}$ ionized by a strong circularly polarized (CP) laser pulse is studied by numerically solving the time-dependent Schr\"odinger equation. We show that the electron removed from the down-field site is directly driven away by the CP field and the lateral photoelectron momentum distribution (LPMD) exhibits a Gaussian-like distribution, whereas the corresponding LPMD of the electron removed from the up-field site differs from the Gaussian shape due to the Coulomb focusing and scattering by the down-field core. Our current study presents the direct evidence clarifying a long-standing controversy over the tunneling site in ${{\mathrm{H}}_{2}}^{+}$ and raises the important role of the tunneling site in strong-field molecular ionization.

Aside from technological applications, steering non-equilibrium currents in electronic matter delivers information on the system electric and magnetic properties and their relation to electronic correlation and the underlying symmetry of the electrons’ confinement. This theoretical study demonstrates that optical vortices are a versatile tool for spatio-temporal generation of charge currents via resonant and stimulated Raman-type processes for semi-conductor-based nanostructures as well as for atoms, thereby the orbital angular momentum associated with the optical vortex plays a key role.

In the first part of this paper, the many-particle quantum hydrodynamics (MPQHD) equations for a system containing many particles of different sorts are derived exactly from the many-particle Schr\"odinger equation. It includes the derivation of the many-particle continuity equations (MPCE), many-particle Ehrenfest equations of motion (MPEEM), and many-particle quantum Cauchy equations (MPQCE) for any of the different particle sorts and for the total particle ensemble. The new point in our analysis is that we consider a set of arbitrary particles of different sorts in the system. In MPQCEs, there appears a quantity called pressure tensor. In the second part of this paper, we analyze two versions of this tensor in depth -- the Wyatt pressure tensor and the Kuzmenkov pressure tensor. There are different versions because there is a gauge freedom for the pressure tensor similar to that for potentials. We find that the interpretation of all quantities contributing to the Wyatt pressure tensor is understandable but for the Kuzmenkov tensor, it is difficult. Furthermore, the transformation from Cartesian coordinates to cylindrical coordinates for the Wyatt tensor can be done in a clear way, but for the Kuzmenkov tensor, it is rather cumbersome., Comment: 52 pages; Improvements in second version: Refs. [50] - [55] were added. In addition, among other, minor improvements, we decided to rename the many-particle Bohmian equations of motion into many-particle quantum Cauchy equations of motion because this renaming simplifies the interpretation of these equations

The ionization of the prealigned nitric oxide molecule by strong circularly polarized laser fields is studied via theoretical simulations of the spin-resolved photoelectron momentum distributions by solving numerically the three-dimensional time-dependent Schr\"odinger equation. Due to the spin-orbit entanglement in the ground state of nitric oxide and the sensitivity of the tunnel ionization of its doubly degenerate valence $2{\ensuremath{\pi}}_{\ifmmode\pm\else\textpm\fi{}}$ orbitals carrying opposite electron ring currents to the sense of the laser-field rotation, the momentum-resolved spin-polarized photoelectrons are produced. We show that the spin polarization exhibits strong dependence on the kinetic energy as well as the emitting angle of the photoelectron. In addition to the laser control, the momentum gate in strong-field experiments would enable full control of the spin polarization.

Recollision experiments have been very successful in resolving attosecond scale dynamics. However, such schemes rely on the single atom response, neglecting the macroscopic properties of the interaction and the effects of using multi-cycle laser fields. In this paper we perform a complete spatio-spectral analysis of the high harmonic generation process and resolve the distribution of the subcycle dynamics of the recolliding electron. Specifically, we focus on the measurement of ionization times. Recently, we have demonstrated that the addition of a weak, crossed polarized second harmonic field allows us to resolve the moment of ionization (Shafir, 2012) [1] . In this paper we extend this measurement and perform a complete spatio-spectral analysis. We apply this analysis to reconstruct the ionization times of both short and long trajectories showing good agreement with the quantum path analysis.

We investigate the strong-field ionization from p± orbitals driven by circularly polarized laser fields by solving the two-dimensional time-dependent Schrodinger equation in polar coordinates with the Lagrange mesh technique. Enhancement of ionization is found in the deep multiphoton ionization regime when the helicity of the laser field is opposite to that of the p electron, while this enhancement is suppressed when the helicities are the same. It is found that the enhancement of ionization is attributed to the multiphoton resonant excitation. The helicity sensitivity of the resonant enhancement is related to the different excitation-ionization channels in left and right circularly polarized laser fields.

We show how laser control over both electronic and hole dynamics in aligned molecules can be used to shape polarization of attosecond pulses produced via high harmonic generation driven by two-color, linearly polarized laser fields.

In previous works, it was predicted that electronic and nuclear ring currents in degenerate excited states of atomic and molecular systems persist after the end of driven circularly polarized atto- or femtosecond laser pulses on relatively long time scales, often on pico- or nanosecond time scales, before spontaneous emission occurs. Although this conclusion is true in the center of mass frame, it is not true in the laboratory frame, where the translation has to be considered. In this theoretical work, the analytic formulas for the ring current densities, electric ring currents, mean ring current radii, and induced magnetic fields at the ring center, depending on the translational wavepacket widths, are derived. It shows that the ring currents and the corresponding induced magnetic fields in the laboratory frame persist on shorter timecales due to spreading of translational wavepackets. The electronic ring currents in 2p(±) orbitals of the hydrogen-like systems decay on the femtosecond time scale, but the corresponding nuclear ring currents with giant induced magnetic fields (for example up to 0.54 MT for (7)Li(2+)) and very small mean ring current radii on the femtometer scale decay on the very short, zeptosecond time scale, according to the Heisenberg uncertainty principle. The theory is also applied to ring currents in many-electron atoms and ions as well as to nuclear ring currents in pseudorotating molecules. For example, in the first triply degenerate pseudorotational states |v(1)l(±1)> of the tetrahedral molecule OsH(4), the ring currents of the heavy central nucleus Os decay on the attosecond time scale.

We design a circularly polarized laser pulse in the infrared frequency and femtosecond time domains, for excitation of the OsH(4) molecule in its first excited pseudorotational state of the triply-degenerate bend. The OsH(4) molecule need not be pre-oriented. After excitation, the central nucleus Os carries out pseudorotation about the axis parallel to the direction of propagation of the laser pulse. This pseudorotation causes a strong electric ring current with a value I=1.53 e fs(-1). The mean value of the radius of the ring current is very small, R=0.0031 a(0), where a(0) is the Bohr radius. According to the Biot-Savart law (|B(R=0)| ~I/R)), this nuclear ring current induces the strongest magnetic field predicted so far in molecules, with a central peak absolute value |B(R=0)| =623 T. To monitor the effect, we propose an IR-pump-X-ray-probe versus an X-ray-probe-only experiment, at the K- and L-edges of X-ray ionization. The results are based on the general quantum theory of excitations of pseudorotations in tetrahedral molecules AB(4), driven by a circularly polarized laser pulse.

Common myth suggests synchronicity and unidirectionality of nuclear and electronic fluxes. Accurate quantum dynamics simulations of the vibrating model system, aligned H2+, confirm this rule, but with exceptional opposite behaviours during short periods in the attosecond time domain. The ratio of electronic versus nuclear fluxes increases systematically, from small to large amplitude nuclear motions. Visualization of the electronic and nuclear densities and flux densities reveals that this is due to broader dispersion of electronic wavepackets compared to nuclear ones. The accurate results validate an efficient general method for quantum calculations of the fluxes in terms of densities, not flux densities.

We present hydrogen bonds with toroidal densities of the protons, called toroidal hydrogen bonds, in systems with cylindrical symmetry e.g. triatomic molecules AHB or ions AHB+ or AHB–. These may be prepared by excitation of the degenerate bending vibrations and related pseudorotation such that the hydrogen atom (or the corresponding proton) is no longer located on the symmetry axis between atoms A and B, but – classically speaking – it rotates around that axis. Quantum mechanically, the toroidal hydrogen bond is represented by an excited nuclear eigenstate with nuclear wavefunction and corresponding nuclear density which have toroidal shapes around the central nodal line which conincides with the AB symmetry axis. The properties of these bonds are analyzed, including the pseudorotational angular momentum. Toroidal hydrogen bonds may be excited by means of circularly polarized infrared (IR) laser pulses. The results are demonstrated exemplarily for the oriented model system FHF–, by means of combined quantum chemistry calculations of the potential energy and dipole surfaces (adapted from L. González, G. Pérez-Hernández, J. González-Vázquez, (2008), submitted), calculations of the vibrational and pseudorotational states in the frame of Watson’s isomorphic Hamiltonian for linear molecules (J. K. G. Watson, Mol. Phys. 19 (1970) 465), and quantum dynamics simulations of the laser driven nuclear dynamics, analogous to recent applications to CdH2 (I. Barth, J. Manz, P. Sebald, Chem. Phys. 346 (2008) 89).

Circularly polarized laser pulses may excite state selective unidirectional toroidal electric ring currents around the axis of oriented linear molecules. These in turn induce state selective magnetic fields. Quantum simulations for AlCl show that these effects are about one or even more than three orders of magnitudes larger than those which may be prepared in oriented planar molecules such as Mg-porphyrin, by means of either circularly polarized laser pulses, or by traditional magnetic fields, respectively.

A circularly polarized infrared (IR) laser pulse which propagates along the axis of a pre-aligned linear polyatomic molecule may excite unidirectional pseudorotations corresponding to excitation of the molecular bend and rotation of the bent molecule around that axis. This preparation and spinning a molecular top is, in part, analogous to the generation of unidirectional electron circulation in molecules by means of circularly polarized ultraviolet (UV) laser pulses [I. Barth, J. Manz, Angew. Chem. 118 (2006) 3028; Angew. Chem., Int. Ed. 45 (2006) 2962], allowing to apply similar methods for the laser driven wavepacket dynamics. It is demonstrated here by means of quantum simulations of the laser driven wavefunction Ψ(t) of the model system 114CdH2(X1Σg+), where Ψ(t) is expanded in terms of vibrational eigenfunctions Ψvl which are labeled by quantum numbers v,l=(vs=0,vbl,va=0) for the vibrations (v) including the symmetric stretch (s), bend (b), antisymmetric stretch (a), and for the pseudorotation (l). The corresponding vibrational and pseudorotational eigenenergies and matrix elements for the model 114CdH2 are adapted as approximations from accurate values which have been determined previously, for simulations of high resolution IR spectra. These dipole matrix elements and related selection or propensity rules imply dominant ladder climbing vbl=00→11→22→⋯ or 00→1-1→2-2→⋯, i.e., sequential populations of the states with increasing quantum numbers for the bends and pseudorotations vbl, where l=+vb or l=-vb depending on the right (+) or left (-) circular polarization of the IR laser pulse, respectively.

Koopmans’ picture predicts that the ith ionisation potential IP i is approximately equal to the negative orbital energy −e i of the molecular orbital ϕ i occupied by the single active electron (SAE), which is ionised, IP i = −e i . The corresponding time-dependent extension describes ionisation in terms of the time-dependent orbital ϕ i (t) which is occupied by the SAE starting from the Extended Hartree–Fock (EHF) wavefunction. The Time-Dependent EHF-SAE theory for singlet states is developed, beyond previous TDHF-SAE approaches. Applications are demonstrated for ionisation of (z-)aligned H , by means of linearly (z-)polarized laser pulses in the domain of dominant single photon ionisation.

Applying the concept of quantum hydrodynamics on a hydrogen atom, one can derive an equation of motion which describes the time derivative of the mass current density for the relative motion of the electron and the proton. Since this derivation can be performed with the Ehrenfest theorem, we call this equation the Ehrenfest equation of motion. As quantum hydrodynamics is consistent with Schrodinger's quantum mechanics, the stationary s-wave functions satisfy both the Schrodinger equation and the Ehrenfest equation of motion. It is the purpose of this paper to prove that the stationary s-wave functions satisfy the Ehrenfest equation of motion. From the quantum hydrodynamical point of view, this result for s-wave functions can be interpreted that the Coulomb force density that attracts the electron to the proton is compensated by a quantum force density that is related to the dispersion of the probability density.

We show that ionization of noble gas atoms by strong infrared circularly polarized laser field under standard exerimental conditions can yield electrons with up to 100% spin polarization in energy resolved measurements. Spin polarization arises due to the interplay of the electron-core entanglement and the sensitivity of ionization in circularly polarized fields to the sense of electron rotation in the initial state., 10 pages, 2 figures

We compare results of the recent experiment by Herath et al. [T. Herath, L. Yan, S. K. Lee, and W. Li, Phys. Rev. Lett. 109, 043004 (2012)] on strong-field nonadiabatic tunneling in circularly polarized laser fields with the original predictions of our theory [I. Barth and O. Smirnova, Phys. Rev. A 84, 063415 (2011)] that stimulated these experiments. We show that the theory and experiment are in very good agreement. We also explain why the initial comparison performed by Herath et al. [T. Herath, L. Yan, S. K. Lee, and W. Li, Phys. Rev. Lett. 109, 043004 (2012)] has suggested quantitative discrepancies with our theory. We confirm that these seeming discrepancies are removed with an accurate application of our theoretical model. We suggest an experiment for unique determination of the ionization preference of valence orbitals ${p}_{+}$ or ${p}_{\ensuremath{-}}$.

In contrast to theoretical predictions based on adiabatic tunneling picture, the accurate analytical ionization rates for p+ and p- orbitals in circularly polarized laser fields differ by an order of magnitude for typical experimental conditions.

We consider selectivity of strong-field ionization in circularly polarized laser fields to the sense of electron rotation in the laser polarization plane in the initial state. We show that, in contrast to the textbook examples of one-photon ionization and bound-state excitations with increase in the electron angular momentum, and also in contrast to the well-studied ionization of Rydberg atoms in microwave fields, which all prefer corotating electrons, optical tunneling selectively depletes states where the electron initially rotates against the laser field. We also show that key assumptions regarding adiabaticity of optical tunneling may quickly become inaccurate in typical experimental conditions.

A full quantum treatment shows that coupled electronic and nuclear fluxes exhibit a strong sensitivity to a small mass change in a vibrating molecule. This has been exemplified with the existing isotopes of H{sub 2}{sup +} as well as few fictitious ones. We find that the fluxes undergo a significant change as one goes from one isotope of reduced mass {mu} to another. Other well-defined observables are likewise affected. It turns out that as a general rule, the heavier the isotope, the larger the flux, the smaller the dispersion, and the longer the revival period. While we were able to confirm analytically that the time at the first turning point scales as {radical}({mu}) and that the revival period changes linearly with {mu}, the mechanism of other observables remains subtle as the result of quantum interference highlighted by the pronounced difference observed on the dispersion pattern.

Quantum dynamics simulations of double proton transfer (DPT) in the model porphine, starting from a nonequilibrium initial state, demonstrate that a switch from synchronous (or concerted) to sequential (or stepwise or successive) breaking and making of two bonds is possible. For this proof of principle, we employ the simple model of Smedarchina, Z.; Siebrand, W.; Fernández-Ramos, A. J. Chem. Phys. 2007, 127, 174513, with reasonable definition for the domains D for the reactant R, the product P, the saddle point SP2 which is crossed during synchronous DPT, and two intermediates I = I(1) + I(2) for two alternative routes of sequential DPT. The wavepacket dynamics is analyzed in terms of various properties, from qualitative conclusions based on the patterns of the densities and flux densities, until quantitative results for the time evolutions of the populations or probabilities P(D)(t) of the domains D = R, P, SP2, and I, and the associated net fluxes F(D)(t) as well as the domain-to-domain (DTD) fluxes F(D1,D2) between neighboring domains D1 and D2. Accordingly, the initial synchronous mechanism of the first forward reaction is due to the directions of various momenta, which are imposed on the wavepacket by the L-shaped part of the steep repulsive wall of the potential energy surface (PES), close to the minimum for the reactant. At the same time, these momenta cause initial squeezing followed by rapid dispersion of the representative wavepacket. The switch from the synchronous to sequential mechanism is called indirect, because it is mediated by two effects: First, the wavepacket dispersion; second, relief reflections of the broadened wavepacket from wide regions of the inverse L-shaped steep repulsive wall of the PES close to the minimum for the product, preferably to the domains I = I(1) + I(2) for the sequential DPT during the first back reaction, and also during the second forward reaction, etc. Our analysis also discovers a variety of minor effects, such as direct switch of the mechanisms, as well as damped oscillations in the net fluxes and populations due to compensations of partially overlapping DTD fluxes.

We demonstrate that coupled electronic and nuclear fluxes in molecules can strongly depend on the initial state preparation. Starting the dynamics of an aligned ${\mathrm{D}}_{2}{}^{+}$ molecule at two different initial conditions, the inner and the outer turning points, we observe qualitatively different oscillation patterns of the nuclear fluxes developing after 30 fs. This corresponds to different orders of magnitude bridged by the time evolution of the nuclear dispersion. Moreover, there are attosecond time intervals within which the electronic fluxes do not adapt to the nuclei motion depending on the initial state. These results are inferred from two different approaches for the numerical flux simulation, which are both in good agreement.

Circularly polarized re-optimized π laser pulses may induce electronic and/or nuclear ring currents in model systems, from one-electron atomic ions till molecules which should have three-, four-, or higher-fold axes of rotations or reflection-rotations, in order to support doubly or more degenerate, complex-valued eigenstates which support these ring currents. The ring currents in turn induce magnetic fields. The effects are about two orders of magnitude larger than for traditional ring currents which are induced by external magnetic fields. Moreover, the laser pulses allow to control the strengths and shapes of the ring currents and, therefore, also the induced magnetic fields. We present a survey of the development of the field, together with new quantum simulations which document ultrafast switchings of magnetic fields. We discuss various criteria such as strong ring currents with small radii, in order to generate huge magnetic fields, approaching 1,000T, in accord with the Biot–Savart law. Moreover, we consider various methods for monitoring the fields, and for applications, in particular ultrafast deflections of neutrons by means of quantum switching of the ring currents and induced magnetic fields.

It is predicted that oriented BeO molecules would give rise to unprecedentedly strong, unidirectional electric ring current and an associated magnetic field upon excitation by a right or left circularly polarized laser pulse into the first excited degenerate singlet state. The strong toroidal electric ring current of this state is dominated by the ring current of the 1π± orbital about the molecular axis. Our predictions are based on the analysis of the orbital composition of the states involved and are substantiated by high level electronic structure calculations and wavepacket simulations of the laser-driven orientation and excitation dynamics. Luis.Serrano@uv.es