Three-dimensional Semiclassical Model Research Articles

General model and toolkit for the ionization of three or more electrons in strongly driven molecules using an effective Coulomb potential for the interaction between bound electrons

We formulate a general three-dimensional semiclassical model for the study of correlated multielectron escape during fragmentation of molecules driven by intense infrared laser pulses. We do so in the context of triple ionization of strongly driven HeH2+. Our model fully accounts for the singularity in the Coulomb potentials of a recolliding electron with the core and a bound electron with the core as well as for the interaction of a recolliding electron with a bound electron. This model also accounts for the magnetic field of the laser pulse. To avoid artificial autoionization, our model employs effective potentials to treat the interaction between bound electrons. We focus on triple and double ionization as well as frustrated triple and frustrated double ionization. In these processes, we identify and explain the main features of the sum of the kinetic energies of the final ion fragments. We find that frustrated double ionization is a major ionization process, and we identify the different channels and hence different final fragments that are obtained through frustrated double ionization. Also, we discuss the differences between frustrated double and triple ionization. Published by the American Physical Society 2024

Singularity in the electron-core potential as a gateway to accurate multielectron ionization spectra in strongly driven atoms

We demonstrate a general three-dimensional semiclassical model as a powerful technique for the study of correlated multi-electron escape in atoms driven by infrared laser pulses at intensities where electron-electron correlation prevails. We do so in the context of triple ionization of strongly driven Ne. We show that a drawback of other current quantum mechanical and classical models of triple ionization is that they soften the Coulomb potential of each electron with the core. The model we employ fully accounts for the singularity in the Coulomb potentials of a recolliding electron with the core and a bound electron with the core as well as for the interaction of a recolliding with a bound electron. Our model treats approximately only the interaction between bound electrons through the use of effective potentials. These effective potentials ensure that no artificial autoionization takes place as a result of the full treatment of the electron-core potential. We demonstrate the accuracy of our model by obtaining triple ionization distributions of the sum of the final electron momenta which we find to be in very good agreement with experiments. Also, we explain the main features of these momenta distributions in terms of the prevalent pathways of correlated three-electron escape in Ne. We also show that the different ionization pathways prevailing in three-electron escape in strongly driven Ne versus Ar give rise to different momenta distributions in these two atoms.

General model and toolkit for the ionization of three or more electrons in strongly driven atoms using an effective Coulomb potential for the interaction between bound electrons

We formulate a three-dimensional semi-classical model to address triple and double ionization in three-electron atoms driven by intense infrared laser pulses. During time propagation, our model fully accounts for the Coulomb singularities, the magnetic field of the laser pulse and for the motion of the nucleus at the same time as for the motion of the three electrons. The framework we develop is general and can account for multi-electron ionization in strongly-driven atoms with more than three electrons. To avoid unphysical autoionization arising in classical models of three or more electrons, we replace the Coulomb potential between pairs of bound electrons with effective Coulomb potentials. The Coulomb forces between electrons that are not both bound are fully accounted for. We develop a set of criteria to determine when electrons become bound during time propagation. We compare ionization spectra obtained with the model developed here and with the Heisenberg model that includes a potential term restricting an electron from closely approaching the core. Such spectra include the sum of the electron momenta along the direction of the laser field as well as the correlated electron momenta. We also compare these results with experimental ones.

Triple ionization and frustrated triple ionization in triatomic molecules driven by intense laser fields

We formulate a three-dimensional semi-classical model to treat three-electron escape dynamics in a strongly-driven linear triatomic molecule, HeH$_{2}^{+}$. Our model includes the Coulomb singularities. Hence, to avoid unphysical autoionization, we employ two criteria to switch off the Coulomb repulsive force between two bound electrons and switch it on when the motion of one electron is mostly determined by the laser field. We investigate triple and "frustrated" triple ionization. In the latter process two electrons escape while one electron remains bound in a Rydberg state. We find that two pathways prevail in "frustrated" triple ionization, as in "frustrated" double ionization. We also find that the electron that remains in a Rydberg state is more likely to be attached to He$^{2+}$ compared to H$^{+}$. Our results indicate that in triple and "frustrated" triple ionization electronic correlation is weak. Moreover, we compute the sum of the kinetic energies as well as the angular patterns of the final ion fragments in triple and "frustrated" triple ionization. These patterns suggest that the fragmenting molecule deviates from its initial linear configuration.

Signatures of magnetic-field effects in nonsequential double ionization manifesting as backscattering for molecules versus forward scattering for atoms

For two-electron diatomic molecules, we investigate magnetic field effects in non-sequential double ionization where recollisions prevail. We do so by formulating a three-dimensional semi-classical model that fully accounts for the Coulomb singularities and for magnetic field effects during time propagation. Using this model, we identify a prominent signature of non-dipole effects. Namely, we demonstrate that the recolliding electron back-scatters along the direction of light propagation. Hence, this electron escapes opposite to the direction of change in momentum due to the magnetic field. This is in striking contrast to strongly-driven atoms where the recolliding electron forward-scatters along the direction of light propagation. We attribute these distinct signatures to the different gate that the magnetic field creates jointly with a soft recollision in molecules compared to a hard recollision in atoms. These two different gates give rise, shortly before recollision, to different momenta and positions of the recolliding electron along the direction of light propagation. As a result, we show that the Coulomb forces from the nuclei act to back-scatter the recolliding electron in molecules and forward-scatter it in atoms along the direction of light propagation.

Enhancing frustrated double ionization with no electronic correlation in triatomic molecules using counter-rotating two-color circular laser fields

We demonstrate significant enhancement of frustrated double ionization (FDI) in the two-electron triatomic molecule D$_{3}^{+}$ when driven by counter-rotating two-color circular (CRTC) laser fields. We employ a three-dimensional semiclassical model that fully accounts for electron and nuclear motion in strong fields. For different pairs of wavelengths, we compute the probabilities of the FDI pathways as a function of the ratio of the two field-strengths. We identify a pathway of frustrated double ionization that is not present in strongly-driven molecules with linear fields. In this pathway the first ionization step is "frustrated" and electronic correlation is essentially absent. This pathway is responsible for enhancing frustrated double ionization with CRTC fields. We also employ a simple model that predicts many of the main features of the probabilities of the FDI pathways as a function of the ratio of the two field-strengths.

Fingerprints of slingshot non-sequential double ionization on two-electron probability distributions

We study double ionization of He driven by near-single-cycle laser pulses at low intensities at 400 nm. Using a three-dimensional semiclassical model, we identify the pathways that prevail non-sequential double ionization (NSDI). We focus mostly on the delayed pathway, where one electron ionizes with a time-delay after recollision. We have recently shown that the mechanism that prevails the delayed pathway depends on intensity. For low intensities slingshot-NSDI is the dominant mechanism. Here, we identify the differences in two-electron probability distributions of the prevailing NSDI pathways. This allows us to identify properties of the two-electron escape and thus gain significant insight into slingshot-NSDI. Interestingly, we find that an observable fingerpint of slingshot-NSDI is the two electrons escaping with large and roughly equal energies.

Sub-cycle attosecond control in frustrated double ionization of molecules

We demonstrate sub-cycle control of frustrated double ionization (FDI) of the two-electron triatomic molecule when driven by two orthogonally polarized two-color laser fields, where a weak mid-infrared laser field is employed to probe the FDI process triggered by a strong near-infrared laser field. We use a three-dimensional semi-classical model that fully accounts for the electron and nuclear motion in strong fields. We analyze the FDI probability and the distribution of the momentum of the escaping electron along the polarization direction of the mid-infrared laser field. These observables when considered in conjunction bear clear signatures of sub-cycle control of FDI. We find that the momentum distribution of the escaping electron has a striking hive-shape with features that can accurately be mapped to the time that one of the two electrons tunnel-ionizes at the start of the break-up process. This mapping distinguishes consecutive tunnel-ionization times within a cycle of the mid-infrared laser field but not tunnel-ionization times differing by an integer number of cycles.

Double ionization of neon in elliptically polarized femtosecond laser fields

We present a joint experimental and theoretical investigation of the correlated electron momentum spectra from strong-field double ionization of neon induced by elliptically polarized laser pulses. A significant asymmetry of the electron momentum distributions along the major polarization axis is reported. This asymmetry depends sensitively on the laser ellipticity. Using a three-dimensional semiclassical model, we attribute this asymmetry pattern to the ellipticity-dependent probability distributions of recollision time. Our work demonstrates that, by simply varying the ellipticity, the correlated electron emission can be two-dimensionally controlled and the recolliding electron trajectories can be steered on a subcycle time scale.

Non-dipole recollision-gated double ionization and observable effects

Using a three-dimensional semiclassical model, we study double ionization for strongly driven He fully accounting for magnetic field effects during the propagation in time. For linearly and slightly elliptically polarized laser fields, we show that recollisions and the magnetic field combined act as a gate. This gate favors more transverse—with respect to the electric field—initial momenta of the tunneling electron that are opposite to the propagation direction of the laser field. In the absence of non-dipole effects, the transverse initial momentum is symmetric with respect to zero. We find that this asymmetry in the transverse initial momentum gives rise to an asymmetry in a double ionization observable.

Controlling electron-electron correlation in frustrated double ionization of triatomic molecules with orthogonally polarized two-color laser fields

We demonstrate the control of electron-electron correlation in frustrated double ionization (FDI) of the two-electron triatomic molecule D$_{3}^{+}$ when driven by two orthogonally polarized two-color laser fields. We employ a three-dimensional semi-classical model that fully accounts for the electron and nuclear motion in strong fields. We analyze the FDI probability and the distribution of the momentum of the escaping electron along the polarization direction of the longer wavelength and more intense laser field. These observables when considered in conjunction bear clear signatures of the prevalence or absence of electron-electron correlation in FDI, depending on the time-delay between the two laser pulses. We find that D$_{3}^{+}$ is a better candidate compared to H$_{2}$ for demonstrating also experimentally that electron-electron correlation indeed underlies FDI.

Non-sequential double ionization with near-single cycle laser pulses

A three-dimensional semiclassical model is used to study double ionization of Ar when driven by a near-infrared and near-single-cycle laser pulse for intensities ranging from 0.85 × 1014 W/cm2 to 5 × 1014 W/cm2. Asymmetry parameters, distributions of the sum of the two electron momentum components along the direction of the polarization of the laser field and correlated electron momenta are computed as a function of the intensity and of the carrier envelope phase. A very good agreement is found with recently obtained results in kinematically complete experiments employing near-single-cycle laser pulses. Moreover, the contribution of the direct and delayed pathways of double ionization is investigated for the above observables. Finally, an experimentally obtained anti-correlation momentum pattern at higher intensities is reproduced with the three-dimensional semiclassical model and shown to be due to a transition from strong to soft recollisions with increasing intensity.

Recollision as a probe of magnetic-field effects in nonsequential double ionization

Fully accounting for non-dipole effects in the electron dynamics, double ionization is studied for He driven by a near-infrared laser field and for Xe driven by a mid-infrared laser field. Using a three-dimensional semiclassical model, the average sum of the electron momenta along the propagation direction of the laser field is computed. This sum is found to be an order of magnitude larger than twice the average electron momentum along the propagation direction of the laser field in single ionization. Moreover, the average sum of the electron momenta in double ionization is found to be maximum at intensities smaller than the intensities satisfying previously predicted criteria for the onset of magnetic field effects. It is shown that strong recollisions are the reason for this unexpectedly large value of the sum of the momenta along the direction of the magnetic component of the Lorentz force.

Nonsequential double ionization of the aligned hydrogen molecule in strong field

This paper studies the nonsequential double ionization (NSDI) process of diatomic molecules aligned parallel and perpendicular to an intense linearly polarized laser field by using a three-dimensional semiclassical model. With this model, it achieves insight into the ion momentum distribution under the combined influence of a two-centre Coulomb potential and an intense laser field, and this result shows the significant influence of molecular alignment on the ratio between double and single ionization rate. Careful investigations show that the NSDI process for different alignment molecules has a close relation to the laser intensity and the different bounding electron distribution has a significant influence on the final ion momentum distribution.

Compression and localization of an atomic cloud in a time dependent optical lattice

We analyze a method of compressing a cloud of cold atoms by dynamic control of a far off-resonance optical lattice. We show that by reducing the lattice spacing either continuously or in discrete steps while cooling the atoms with optical molasses large compression factors can be achieved. Particle motion in the time-dependent lattice is studied numerically using a three-dimensional semiclassical model. Two experimentally realistic models are analyzed. In the first we continuously vary the lattice beam angles to compress atoms initially in a Gaussian distributed cloud with standard deviation of 250 µm into a single site of a two-dimensional lattice of area A ∼ 35 × 35λ2, with λ the wavelength of the lattice beams. This results in an optical depth for an on-resonant probe beam >80 which is an increase by a factor of about 1800 compared to the uncompressed cloud. In the second approach we use a discrete set of lattice beam angles to decrease the spatial scale of the cloud by a factor of 500, and localize a few atoms to a single lattice site with an area A ≲ λ2.

Corrections to Vibrational Transition Probabilities Calculated from a Three-Dimensional Model

Corrections to the collision-induced vibration transition probability calculated by Hansen and Pearson from a three-dimensional semiclassical model are examined. These corrections come from the retention of higher order terms in the expansion of the interaction potential and the use of the actual value of the deflection angle in the calculation of the transition probability. It is found that the contribution to the transition cross section from previously neglected potential terms can be significant for short range potentials and for the large relative collision velocities encountered at high temperatures. The correction to the transition cross section obtained from the use of actual deflection angles will not be appreciable unless the change in the rotational quantum number is large.