Two-photon Double Ionization Of Helium Research Articles

Nonlinear scaling in photon momentum transfer caused by two-electron effects

The photon momentum transfer in the two-photon double ionization of helium is theoretically studied based on the $ab\phantom{\rule{4pt}{0ex}}initio$ calculations. A nonlinear dependence of the transferred momentum on the photon energy is identified at relatively small photon energies. As expected, the linear dependence is recovered with the slope approaching 1.60 when the photon energy becomes sufficiently large. With a semianalytical model including the Coulomb screen effect in the two-electron ground state, we can qualitatively reproduce the nonlinear dependence and find that it is mainly contributed by the fast electron. However, compared with the results from the $ab\phantom{\rule{4pt}{0ex}}initio$ calculations, the quantitative discrepancies at relatively small photon energies can be accounted for only by the electron correlation in the intermediate state. The present study reveals the vital roles played by the two-electron effects for the complicated photon momentum transfer process in the few-photon and few-electron systems.

Angular distribution parameters in two-photon double ionization of helium beyond the dipole approximation

We study nondipole effects in the two-photon double ionization of helium by solving the full-dimensional time-dependent Schr\"odinger equation (TDSE). The angular distributions of the photoelectrons in TDSE calculations are parametrized by several angular distribution parameters. The electron correlation effects are revealed and discussed by analyzing angular distribution parameters of the photoelectrons. Compared with the linearly polarized laser, the values of dipole angular parameters for circularly polarized laser pulses in the nonsequential double-ionization regime are closer to the pure dipole emission of the one-photon single ionization, which indicates a weaker electron correlation for circular pulses. For the nondipole angular parameters, in the sequential double-ionization regime, we find that the parameters show peak structures from the sequential ionization channel over the energy sharing between two electrons and these peak positions are slightly shifted by the electron correlation. In general, due to the nondipole effects, the angular distributions of photoelectrons are shifted towards the direction of laser propagation, due to the transfer of the photon linear momentum.

Laser-assisted two-color two-photon double ionization of helium atoms

Correlated momentum and kinetic energy distributions of two photoelectrons in laser-assisted two-color two-photon double ionization of helium are investigated by numerically solving a one-plus-one dimensional time-dependent Schrödinger equation (TDSE). We find that the weak assisting laser field can act as an energy transferring field, resulting in burst of double ionization triggered by the intense extreme ultraviolet (XUV) pulse. More importantly, the participation of the laser photon into the double ionization reshapes the correlation patterns in the momentum and kinetic energy distributions. The laser photon can be absorbed by any one of the two electrons, providing two channels that induces destructive interference in the correlated momentum and kinetic energy distributions, which is never found in previous work.

Understanding two-photon double ionization of helium from the perspective of the characteristic time of dynamic transitions

By using the B-spline numerical method, we investigate a two-photon double-ionization (TPDI) process of helium in a high-frequency laser field with its carrier frequency ranging from 1.6 to 3.0 a.u. and the pulse duration ranging from 75 to 160 attoseconds. We found that there exists a characteristic time tc for a TPDI process, such that the pattern of energy distribution of two ionized electrons presents a peak or two, depending respectively on whether the pulse duration is shorter or longer than tc. Especially, when the pulse duration is larger than tc, the TPDI spectrum shows a double-peak structure which is attributed to the fact that most of the electron–electron Coulomb interaction energy is acquired by a single electron during their oscillation around the nucleus before the two electrons leave, and hence the double-peak structure cannot be identified as a signal of sequential ionization. Additionally, if the carrier frequency is less than the ionization energy of He+, i.e. that carrier frequency is in the so called correlated region, tc is not a fixed value, and it increases as the carrier frequency decreases; while if the carrier frequency is greater than the ionization energy of He+, i.e. the carrier frequency is in the so called non-correlated region, tc is fixed at about 105 attoseconds. We further found that, for a helium-like ion in its ground state, the characteristic time for when the carrier frequency is larger than the ionization energy of the second electron has a key relation with the Coulomb interaction energy between the two electrons, which can be expressed as , a type of quantum mechanical uncertainty relation between time and energy. In addition, this relation can be attributed to the existence of a minimal evolution time from the ground state to a double ionization state with two electrons carrying different energies. These results may shed light on a deeper understanding of many-electron quantum dynamical processes.

Observing electron-correlation features in two-photon double ionization of helium

By numerically solving the time-dependent Schr\odinger equation for helium in its full dimensionality, we determine the joint momentum spectrum along the polarization direction $P({k}_{1z},{k}_{2z})$ for two-photon double ionization (TPDI). We identify features uniquely attributable to dynamical correlation effects in the double continuum. We show that some of the correlation signatures persist in integrated measures, in particular the emission asymmetry, that should become accessible with upcoming XUV light sources. We also compare with predictions of analytic models for TPDI which neglect such final-state correlations.

Doubly-excited state effects on two-photon double ionization of helium by time-delayed, oppositely circularly-polarized attosecond pulses

We study two-photon double ionization (TPDI) of helium by a pair of time-delayed (non-overlapping), oppositely circularly-polarized attosecond pulses whose carrier frequencies are resonant with 1Po doubly-excited states. All of our TPDI results are obtained by numerical solution of the two-electron time-dependent Schrödinger equation for the six-dimensional case of circularly-polarized attosecond pulses, and they are analyzed using perturbation theory (PT). As compared with the corresponding nonresonant TPDI process, we find that the doubly-excited states change the character of vortex patterns in the two-electron momentum distributions for the case of back-to-back detection of the two ionized electrons in the polarization plane. The doubly-excited states also completely change the structure of fixed-energy, two-electron angular distributions. Moreover, both the fixed-energy and energy-integrated angular distributions, as well as the two-electron energy distributions, exhibit a periodicity with time delay τ between the two attosecond pulses of about 69 as, i.e. the beat period between the doubly-excited state and the He ground state. Using PT we derive an expression for an angle-integrated energy distribution that is sensitive to the slower beat period ∼1.2 fs between different doubly-excited states as well as to the long timescale ∼17 fs of autoionization lifetimes. However, with our current computer codes we are only able to study numerically the time-dependent phenomena occurring on an attosecond time scale.

Correlation dynamics in double photoionization of excited helium atom by a single ultrashort XUV pulse

SynopsisWe study single- and two-photon double ionization of helium by short XUV pulses by numerically solving the time-dependent Schrödinger equation in full dimensionality within a finite element discrete variable representation scheme. We discuss the joint energy and angular distributions, identify sequential and non-sequential contributions in the double ionization by ultrashort pulse, and track the dynamics of the ionization process in distinct double ionization regimes.

Two-photon double ionization of helium by chirped few-cycle attosecond pulses: From nonsequential to sequential regime**Project supported by the National Natural Science Foundation of China (Grant Nos. 11322437 and 11574010) and the National Basic Research Project of China (Grant No. 2013CB922402).

The two-photon double ionization (TPDI) dynamics of helium by chirped attosecond pulses are theoretically studied by solving the two-electron time-dependent Schrödinger equation in its full dimensions. We show that both the differential and the total double ionization probability can be significantly controlled by adjusting the chirp. The dependence of the TPDI on the chirp can be quite different for different photon energies, relying on the central photon energy being in the sequential region, nonsequential region, or translation region. The physics which lead to the chirp dependence for different photon energies are addressed. Present findings are well reproduced by a model based on the second-order time-dependent perturbation theory.

Ab-initio validation of a simple heuristic expression for the sequential-double-ionization contribution to the double ionization of helium by ultrashort XUV pulses

SynopsisWe study two-photon double ionization of helium by short XUV pulses by numerically solving the time-dependent Schrodinger equation in full dimensionality within a finite-element discrete-variable-representation scheme. Based on the emission asymmetries in joint photoelectron angular distributions, we identify sequential and non-sequential contributions to two-photon double ionization for ultrashort pulses whose spectrum overlaps the sequential (ħω > 54.4 eV) and non-sequential (39.5 eV < ħω < 54.4 eV) double-ionization regimes.

Probing time-ordering in two-photon double ionization of helium on the attosecond time scale

We show that time ordering underlying time-dependent quantum dynamics is a physical observable accessible by attosecond streaking. We demonstrate the extraction of time ordering for the prototypical case of time-resolved two-photon double ionization of helium by an attosecond XUV pulse. The Eisenbud–Wigner–Smith time delay for the emission of a two-electron wavepacket and the time interval between subsequent emission events can be unambiguously determined by attosecond streaking. The delay between the two emission events sensitively depends on the energy, pulse duration, and angular distribution of the emitted electron pair. Our fully-dimensional ab initio quantum mechanical simulations provide benchmark data for experimentally accessible observables.

Distinction between sequential and direct ionization in two-photon double ionization of helium

This paper aims to shed some light on the role of the direct, or nonsequential, ionization channel in the regime in which the sequential channel is open in two-photon double ionization (TPDI) of helium. In this regime the sequential channel dominates any direct contribution unless the laser pulse is of very short duration, in which case their distinction is hard to draw. Based on both a simple model and full solutions of the time-dependent Schr\"odinger equation, we aim to provide evidence of direct double ionization by identifying a term proportional to the pulse duration in the double ionization yield. Indeed, such a term is identified in the energy-differential yield. When it comes to the total double ionization probability, however, it turns out that the net first-order contribution is negative. The nature of the negative first-order contribution is discussed, and we argue that it is of correlated origin.

Control of two-photon double ionization of helium with intense chirped attosecond laser pulses

We study the two-photon double-ionization process of the helium atom by solving numerically the nonrelativistic, time-dependent Schr\odinger equation in its full dimensionality. We investigate with intense chirped attosecond laser pulses of 23.5-nm wavelength the two-photon absorption near and above the sequential threshold. We show how it is possible by adjusting the chirp parameter to control the electronic transitions inside the atom, thereby reinforcing or weakening the ionization process. Attosecond chirped laser pulses offer a promising way to probe and control the two-photon double ionization of helium when compared with attosecond transform-limited pulses.

Comparison study of electron correlation in one-photon and two-photon double ionization of helium

Based on ab initio time-dependent calculations for helium, we study the joint angular distribution (JAD) of the two electrons ionized by absorbing one or two photons. On the JAD plane for the equal energy sharing case, one can identify a common symmetric ejection mode with respect to the laser polarization for three different processes, i.e., one-photon double ionization, two-photon nonsequential ionization, and sequential double ionization. In this symmetric ejection case, the two ejected electrons strongly favor a particular interelectron angle. We show that this angle can mimic the electron correlation strength in these double-ionization processes. The interelectron angle in the three types of double ionization is found to be obviously different.

Nuclear-recoil differential cross sections for the two-photon double ionization of helium

The time-dependent close-coupling method is used to calculate fully differential cross sections for the two-photon double ionization of the He($1{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}^{e}$) ground state at a photon energy of 44 eV and the He($1s2s{\phantom{\rule{0.16em}{0ex}}}^{1,3}{S}^{e}$) excited states at a photon energy of 34 eV. The total and triple-differential cross sections for the ground state are in good agreement with available calculations. We also used the time-dependent close-coupling method to calculate fully differential nuclear-recoil cross sections of He${}^{2+}$ for the two-photon double ionization of He in the ground and excited states at the same photon energies. The nuclear-recoil differential cross sections of He${}^{2+}$ for the ground state are in good agreement with the measurements recorded with a reaction microscope at the free-electron laser facility in Hamburg (FLASH).

Two-photon double ionization of helium: investigating the importance of correlation in the final state

AbstractIn this paper, we present theoretical results for the process of non-sequential two-photon double ionization of helium at the photon energy 42 eV. Our approach is based on solving the time-dependent Schrödinger equation in a B-spline based numerical framework. Information about the process is obtained by extracting the double-ionized component by means of uncorrelated final states. The total (generalized) cross section for the process is extracted, as well as differential cross sections resolved in electron energies and ejection angles. We focus on the impact the final-state correlation has on the accuracy of the cross sections.

Closure approximation in the theory of two-photon double ionization of atoms

We consider two-photon double ionization of helium with 100, 200, and 400 eV excess energy. We focus on the case of ultrashort pulses and develop an approach to calculate the two-photon transition matrix elements within the lowest order of the time-dependent perturbation theory. It is shown, that in the subfemtosecond regime the intermediate Green's function can be successfully evaluated by means of the closure approximation.

Two-photon double ionization of helium by attosecond laser pulses: Evidence of highly correlated electron motion

We apply a recently developed ab initio numerical framework to investigate the angular distributions of the emitted electrons in the immediate proximity of the threshold for the two-photon double ionization of helium. Provided one of the electrons is emitted perpendicular to the laser polarization direction, it is found that the angular distribution of the other electron is characterized by three lobes. The results are similar to those recently reported for the corresponding process in the hydrogen negative ion [R. Nepstad and M. F\o{}rre, Phys. Rev. A 84, 021402(R) (2011)], and provide further evidence of highly correlated electron dynamics in the vicinity of the double ionization threshold.

A master equation approach to double ionization of helium

It is demonstrated how a numerical approach based on absorbing boundaries may be used to describe the process of non-sequential two-photon double ionization of helium. Contrary to any method based on solving the Schrödinger equation alone, this numerical scheme is able to reconstruct the remaining particles as one particle is absorbed. This may be used to distinguish between single and double ionization. A model of reduced dimensionality, which describes the process at a qualitative level, has been used. The results have been compared with a more conventional method in which the time-dependent Schrödinger equation is solved and the final wavefunction is analysed in terms of projection onto eigenstates of the uncorrelated Hamiltonian, i.e. with no electron–electron interaction included in the final states. It is found that the two methods indeed produce the same total cross sections for the process.

Two-photon double ionization of helium: Evolution of the joint angular distribution with photon energy and two-electron energy sharing

Ab initio calculations of two-photon double ionization of helium with photon energies varying from the nonsequential regime to well above the double-ionization threshold are presented. A systematic study of the joint angular distributions of the two ionized electrons at different energy sharing shows that the role of electron correlations is imprinted in the joint angular distribution. In particular, a rather general pattern is identified in the nonsequential regime that is independent of photon energy, pulse length, and energy sharing between the two electrons. Interestingly, the same distribution pattern is found for the equal-energy-sharing case, even when the photon energy is well above the double-ionization threshold. In the case of an extremely uneven energy sharing, the distribution pattern changes drastically as the photon energy is increased. In particular, when the photon energy is greater than the second-ionization threshold, the dominant emission mode of the two electrons switches gradually from ``back to back'' to ``side by side.'' Finally, the joint angular distribution is found to provide clear evidence of the role of electron correlations in the initial state.

Universal features in sequential and nonsequential two-photon double ionization of helium

We analyze two-photon double ionization of helium in both the nonsequential ($\ensuremath{\hbar}\ensuremath{\omega}&lt;{I}_{2}\ensuremath{\approx}54.4 \mathrm{eV}$) and sequential ($\ensuremath{\hbar}\ensuremath{\omega}&gt;{I}_{2}$) regime. We show that the energy spacing $\ensuremath{\Delta}E={E}_{1}\ensuremath{-}{E}_{2}$ between the two emitted electrons provides the key parameter that controls both the energy and the angular distribution and reveals the universal features present in both the nonsequential and sequential regime. This universality, i.e., independence of $\ensuremath{\hbar}\ensuremath{\omega}$, is a manifestation of the continuity across the threshold for sequential double ionization. For all photon energies considered, the energy distribution can be described by a universal shape function that contains only the spectral and temporal information entering second-order time-dependent perturbation theory. Angular correlations and distributions are found to be more sensitive to the value of $\ensuremath{\hbar}\ensuremath{\omega}$. In particular, shake-up interferences have a large effect on the angular distribution. Energy spectra, angular distributions parametrized by the anisotropy parameters ${\ensuremath{\beta}}_{j}$, and total cross sections presented in this paper are obtained by fully correlated time-dependent ab initio calculations.