Double Ionization Yield Research Articles

Enhancement and suppression of nonsequential double ionization by spatially inhomogeneous fields

Using the three-dimensional classical ensemble approach, we theoretically investigate the nonsequential double ionization of argon atoms in an intense laser field enhanced by bowtie-nanotip. We observe an anomalous decrease in the double ionization yield as the laser intensity increases, along with a significant gap in the low momentum of photoelectrons. According to our theoretical analysis, the finite range of the induced field by the nanostructure is the fundamental cause of the decline in double ionization yield. Driven by the enhanced inhomogeneous field, energetic electrons can escape from the finite range of nanotips without returning. This reduces the possibility of re-scattering on the nucleus and imprints the finite size effect into the double ionization yield and momentum distribution of photoelectrons in the form of yield decline and a gap in the photoelectron-momentum distribution.

Carrier-Envelope Phase Controlling of Ion Momentum Distributions in Strong Field Double Ionization of Methyl Iodide

In strong field ionization of methyl iodide initiated by elliptically polarized few-cycle pulses, a significant correlation was observed between the carrier-envelope phases (CEPs) of the laser and the preferred ejection direction of methyl cation arising from dissociative double ionization. This was attributed to the carrier-envelope phase dependent double ionization yields of methyl iodide. This observation provides a new way for monitoring the absolute CEPs of few-cycle pulses by observing the ion momentum distributions.

Controlling electron recollision with combined linear and circular polarization

We theoretically investigate the non-sequential double ionization of Ar atoms in the combined fields of linearly polarized laser and circularly polarized laser through 3D semiclassical simulations. By partially overlapping the two time-delayed multicycle laser pulses, we construct an optical waveform whose polarization ellipticity increase slowly for consecutive optical cycles. This composite laser pulses with the time-dependent ellipticity can tunnel-ionize atoms and steer the first tunneling electron to recollision with the second bound electron through different trajectories, in which the recollision occurs with different return times of the first ionized electron. Through tuning delay time between the two laser pulses, the double ionization yields and recollision trajectories with different return times can be controlled. The time-dependent ellipticity with different delay time can enhance or suppress the probability of different return times. This work provides a scheme exploring electron dynamics in few optical cycle or even subcycle time scale in a multicycle laser field without having to be limited to near-single-cycle laser pulses.

The nonsequential double ionization of Ar atoms with different initial angular momenta irradiated by a circularly polarized laser pulse

The non-sequential double ionization process of Ar atoms with different initial angular momenta in the 500 nm circularly polarized field is investigated with a classical ensemble model. The numerical results show that, under the circularly polarized laser pulse, the double ionization yield as a function of the laser intensity for Ar atoms with different initial angular momenta exhibit an obvious Knee structure. The ionization yield in the counter-rotating case where the electronic initial rotation direction is opposite to the vector potential of the laser field, significantly higher than that in the co-rotating case where the electronic initial rotation direction is consistent with the vector potential of the laser field. Based on the classical trajectory analysis, it is found that this ionization difference comes from the angle between the direction of the electronic momentum and the force of the laser field at the single ionization instant. The angle in the counter-rotating case is greater than that in the co-rotating case, and the counter-rotating electrons are more likely to return to the parent ion for recollision. Besides, the recollision intants of Ar atoms with the different initial angular momenta are mapped to the electron momentum spectrum. This may provide a method to obtain the electron’s recollision instant of Ar atoms with different initial angular momenta.

Strong-field ionization of water. II. Electronic and nuclear dynamics en route to double ionization

We investigate the role of nuclear motion and strong-field-induced electronic couplings during the double ionization of deuterated water using momentum-resolved coincidence spectroscopy. By examining the three-body dicationic dissociation channel, D$^{+}$/D$^{+}$/O, for both few- and multi-cycle laser pulses, strong evidence for intra-pulse dynamics is observed. The extracted angle- and energy-resolved double ionization yields are compared to classical trajectory simulations of the dissociation dynamics occurring from different electronic states of the dication. In contrast with measurements of single photon double ionization, pronounced departure from the expectations for vertical ionization is observed, even for pulses as short as 10~fs in duration. We outline numerous mechanisms by which the strong laser field can modify the nuclear wavefunction en-route to final states of the dication where molecular fragmentation occurs. Specifically, we consider the possibility of a coordinate-dependence to the strong-field ionization rate, intermediate nuclear motion in monocation states prior to double ionization, and near-resonant laser-induced dipole couplings in the ion. These results highlight the fact that, for small and light molecules such as D$_2$O, a vertical-transition treatment of the ionization dynamics is not sufficient to reproduce the features seen experimentally in the strong field coincidence double-ionization data.

Saturating multiple ionization in intense mid-infrared laser fields

The interpretation of experimental data from novel mid-infrared few-cycle laser sources requires an understanding of ionization mechanisms and knowledge about related ion yields. Experimental studies have indicated sequential double ionization as the dominant process above 1014 W cm−2. These results contradict a recent prediction that in this spectral region, non-sequential processes dominate the double ionization of xenon up to intensities of about 1015 W cm−2. In either case, the ratio of doubly to singly charged xenon yield reported in previous studies has been limited to a few percent, indicating a regime well below the onset of saturation of the double ionization process. We present an experimental study of double ionization of xenon and krypton atoms exposed to intense near four-cycle pulses at 3.2 μm. Our experiments rely on the ion microscopy technique, which facilitates the detection of ions originating from a restricted region within the interaction volume, thereby reducing the impact of focal averaging. Our measurements suggest that at intensities of close to 1.2 × 1014 W cm−2, double ionization of xenon and krypton is already significantly saturated. In particular, we find a doubly to singly charged yield ratio of about 75 percent for xenon and 25 percent for krypton. We compare our results with the predictions of different models accounting for the effects of volume averaging and focal geometry. We find that in the deeply saturated regime of our experiment, the Perelomov–Popov–Terentyev theory significantly underestimates the observed double ionization yield.

Strong-field ionization of atoms with p3 valence shell: Two versus three active electrons

For a model atom with the $p^3$ valence shell we construct consistent three- and two-active electrons models enabling their direct comparison. Within these models, we study the influence of the third active electron on the double ionization yield in strong femtosecond laser fields. We reveal proportionality between double ionization signals obtained with both models in the field intensity region where non-sequential ionization dominates. We derive analytically a correspondence rule connecting the double ionization yields obtained within the three- and two-active electrons models.

Strong-field-induced single and double ionization dynamics from single and double excitations in a two-electron atom

Two-electron dynamics of an excited model atom interacting with moderately strong laser fields is analyzed in the time domain. We solve the time-dependent Schrödinger equation (TDSE) for two electrons confined to the same one-dimensional configuration space, accounting also for the electron-electron interaction. The computational method allows direct access to the time-dependent population of the relevant atomic states during and right after the interaction with a near-infrared (NIR) laser pulse. We compare the ionization dynamics of singly excited states and doubly excited states. We find that doubly-excited initial states exhibit enhanced double ionization yield, with non-trivial dynamics including contributions from direct and sequential processes, while the electrons leave the atom either back-to-back or in the same direction.

Double ionization of a three-electron atom: Spin correlation effects

We study the effects of spin degrees of freedom and wave function symmetries on double ionization in three-electron systems. Each electron is assigned one spatial degree of freedom. The resulting three-dimensional Schr\"odinger equation is integrated numerically using grid-based Fourier transforms. We reveal three-electron effects on the double ionization yield by comparing signals for different ionization channels. We explain our findings by the existence of fundamental differences between three-electronic and truly two-electronic spin-resolved ionization schemes. We find, for instance, that double ionization from a three-electron system is dominated by electrons that have the opposite spin.

Quantitative rescattering theory for nonsequential double ionization**Project supported by the National Natural Science Foundation of China (Grant No. 11274219), the Science and Technology Planning Project of Guangdong Province of China (Grant No. 180917124960522), and the Program for Promotion of Science at Universities in Guangdong Province of China (Grant No. 2018KTSCX062).

We review the recently improved quantitative rescattering theory for nonsequential double ionization, in which the lowering of threshold due to the presence of electric field at the time of recollision has been taken into account. First, we present the basic theoretical tools which are used in the numerical simulations, especially the quantum theories for elastic scattering of electron as well as the processes of electron impact excitation and electron impact ionization. Then, after a brief discussion about the properties of the returning electron wave packet, we provide the numerical procedures for the simulations of the total double ionization yield, the double-to-single ionization ratio, and the correlated two-electron momentum distribution.

Wavelength-dependent nonsequential double ionization of magnesium by intense femtosecond laser pulses

We report on a systematic investigation of wavelength scaling strong-field double ionization of Mg in intense laser fields. A significant decrease of nonsequential double ionization (NSDI) yield with increasing wavelength from 800--2000 nm is observed. Our data is well reproduced by a three-dimensional Monte Carlo simulation considering recollision impact excitation cross section. We demonstrate that the NSDI of Mg mainly occurs via the first ionic excited state ${\mathrm{Mg}}^{+*}(3p\phantom{\rule{0.16em}{0ex}}^{2}P_{3/2,1/2})$ pumped by returning electron impact process. The recollision impact direct ionization pathway plays a minor role here. The wavelength dependence of the NSDI ratio is due to the recollision energy-dependent excitation cross section as well as the electron wave packet diffusion effects, both sensitively depending on the wavelength. Our work represents a step towards strong-field double ionization experiments on Mg in the long wavelength limit and sheds light on the NSDI mechanism of alkaline-earth metal atoms.

Pulse-duration dependence of the double-to-single ionization ratio of Ne by intense 780-nm and 800-nm laser fields: Comparison of simulations with experiments

Accurate ab initio calculations of the ratio of double-to-single ionization of Ne atoms in strong laser fields are difficult due to the many-electron nature of the target. Here, with accurate total cross sections carefully evaluated by using the state-of-the-art many-electron R-matrix theory for both electron-impact ionization and electron-impact excitation of Ne+, we simulate the total double-ionization yields of Ne2+ in strong laser fields at 780 and 800 nm for pulse durations in the range from 7.5 to 200 fs based on the improved quantitative rescattering model. The corresponding single-ionization yields of Ne+ are calculated within the nonadiabatic tunneling model of Perelomov, Popov, and Terent'ev. The ratio of double-to-single ionization of Ne is then obtained from the calculated double- and single-ionization yields. By normalizing the ratio to the one calculated from solving the time-dependent Schrodinger equation for a short few-cycle pulse, we make quantitative comparisons of our results with experimental data to show that our model predicts the experimental findings very well. Finally, we analyze the pulse-duration dependence of the double-to-single ionization ratio.

Angle dependence of strong-field single and double ionization of carbonyl sulfide

We have studied, experimentally and theoretically, the ionization probability of carbonyl sulfide (OCS) molecules in intense linearly polarized 800-nm laser pulses as a function of the angle between the molecular axis and the laser polarization. Experimentally, the molecules are exposed to two laser pulses with a relative time delay. The first, weaker pulse induces a nuclear rotational wave packet within each molecule such that the ensemble exhibits preferential alignment in the laboratory frame at specific times. The second, stronger pulse induces ionization, and the variation in single and double ionization yields is measured as a function of the delay between the two pulses. The angular dependence of the ionization yield is extracted by fitting the delay-dependent yields to a sum of delay-dependent moments of the rotational wave packet's angular distribution. We compute these same angular-dependent strong-field ionization yields for OCS using time-dependent density-functional theory (TDDFT). For the single-ionization case, our measurements agree well with TDDFT calculations and with previous experiments. Furthermore, analysis of the simulated one-body density reveals that, when averaged over a laser cycle, the resulting hole is delocalized across the molecule for light polarized perpendicular to the molecular axis and mostly localized on the sulfur for parallel polarization. This suggests that preferential molecular alignment is a key parameter for controlling charge migration dynamics initiated by strong-field ionization. For double ionization, the agreement between experiment and theory is less compelling, reflecting the substantial challenges of computing double-ionization yields using TDDFT methods.

Direct and Sequential Two-Photon Double Ionization of Two-Electron Quantum Dots.

In this work we study the double ionization yields and kinetic energy spectra of a two-electron spherical quantum dot (QD) exposed in laser fields. The theoretical description is based on an ab initio nonperturbative configuration interaction theory capable of describing the two-electron QD dynamics in THz and mid-IR ultrashort laser fields. The QD's confinement potential is approximated to have a Gaussian-like spatial dependence. We have found that significant variations of the two-electron kinetic energy patterns and two-photon double ionization yields occur as we vary the QD's size. For a given laser pulse, the double ionization yield increases by orders of magnitude when the dot size is reduced. The size of the QD determines the sequential or direct character of the two-photon double ionization process. Provided that it is energetically allowed, the sequential two-photon double ionization process, requiring minimal interelectronic correlations, becomes dominant over the direct one. In the sequential regime, the corresponding two-electron kinetic energy spectrum changes from a broadened single-peaked to a doubly peaked one. Moreover, we also have identified features in the spectrum that are distinctively different than those in its atomic counterpart.

Ratios of double to single ionization of He and Ne by strong 400-nm laser pulses using the quantitative rescattering theory

We present numerical simulations of the ratio between double and single ionization of He and Ne by intense laser pulses at wavelengths of 390 and 400 nm, respectively. The yields of doubly charged ions due to nonsequential double ionization (NSDI) are obtained by employing the quantitative rescattering (QRS) model. In this model, the NSDI ionization probability is expressed as a product of the returning electron wave packet (RWP) and the total scattering cross sections for laser-free electron impact excitation and electron impact ionization of the parent ion. According to the QRS theory, the same RWP is also responsible for the emission of high-energy above-threshold ionization photoelectrons. To obtain absolute double-ionization yields, the RWP is generated by solving the time-dependent Schr\odinger equation (TDSE) within a one-electron model. The same TDSE results can also be taken to obtain single-ionization yields. By using the TDSE results to calibrate single ionization and the RWP obtained from the strong-field approximation, we further simplify the calculation such that the nonuniform laser intensity distribution in the focused laser beam can be accounted for. In addition, laser-free electron impact excitation and ionization cross sections are calculated using the state-of-the-art many-electron $R$-matrix theory. The simulation results for double-to-single-ionization ratios are found to compare well with experimental data and support the validity of the nonsequential double-ionization mechanism for the covered intensity region.

Double-electron ionization driven by inhomogeneous fields

Electron-electron correlation effects play an instrumental role in our understanding of sequential (SDI) and non-sequential double ionization (NSDI) mechanisms. Here, we present a theoretical study of NSDI driven by plasmonic-enhanced spatial inhomogeneous fields. By numerically solving the time-dependent Schr\"odinger equation for a linear reduced model of He and a double-electron time-evolution probability analysis, we provide evidence for the enhancement effects in NSDI showing that the double ionization yield at lower laser peak intensities is increased due to the inhomogeneity of the laser field. Furthermore, our quantum mechanical model, as well as classical trajectory Monte Carlo simulations, show that inhomogeneous fields are a useful tool for splitting the binary and recoil processes in the rescattering scenario.

Experimental and theoretical study on nonsequential double ionization of carbon disulfide in strong near-IR laser fields

Nonsequential double ionization (NSDI) of carbon disulfide ${\mathrm{CS}}_{2}$ in strong 800-nm laser fields is studied experimentally and theoretically. A knee structure is observed in the intensity-dependent double ionization (DI) yield in linearly polarized laser fields, which exhibits a strong dependence on the laser ellipticity. The electron momentum distributions and energy trajectories after DI in both linearly and circularly polarized laser fields are investigated by employing the two-dimensional classical ensemble method. The results clearly show the evidence of NSDI in the strong-field DI of ${\mathrm{CS}}_{2}$ molecules. It is demonstrated that, similar to that of atoms, NSDI of ${\mathrm{CS}}_{2}$ molecules is produced via laser-driven electron recollision with the ion core and presents electron-electron correlations in the process. Analysis indicates that both mechanisms in atomic strong-field NSDI, i.e., recollision impact ionization and recollision excitation with subsequent ionization, may also be contributed to NSDI of ${\mathrm{CS}}_{2}$ in strong laser fields. Further studies are no doubt necessary for a full understanding of the underlying physical mechanism of molecular strong-field NSDI, due to the multicenter character of the molecular structure and the complex molecular excited states that could be involved in the ionization.

Molecular Double Ionization Using Strong Field Few-Cycle Laser Pulses.

We study strong field double ionization of a series of organic molecules by making use of coincidence detection of fragment ions. We measure the double ionization yield as a function of pulse duration, intensity, polarization, and molecular conjugation. For conjugated molecules we find strong enhancement in the double ionization rate over what one would expect on the basis of tunneling or multiphoton ionization rates. Calculations reveal a correlation between the electronic structure of the different molecules and the observed double ionization yields, highlighting the removal of electrons from inner orbitals.

Double photoelectron momentum spectra of helium at infrared wavelength

Double photo-electron momentum spectra of the Helium atom are calculated \textit{ab initio} at extreme ultra-violet and near infrared wavelengths. At short wavelengths two-photon double ionization yields, two-electron energy spectra, and triply differential cross sections agree with results from recent literature. At the near infrared wavelength of $780\,nm$ the experimental single-to-double ionization ratio is reproduced up to intensities of $4\times 10^{14}W/cm^2$, and two-electron energy spectra and joint angular distributions are presented. The time-dependent surface flux (tSurff) approach is extended to full 3+3 spatial dimensions and systematic error control is demonstrated. We analyze our differential spectra in terms of an experimentally accessible quantitative measure of correlation.

Nonsequential double ionization with time-dependent renormalized-natural-orbital theory

Recently introduced time-dependent renormalized natural orbital theory (TDRNOT) is tested on non-sequential double ionization (NSDI) of a numerically exactly solvable one-dimensional model He atom subject to few-cycle, 800-nm laser pulses. NSDI of atoms in strong laser fields is a prime example of non-perturbative, highly correlated electron dynamics. As such, NSDI is an important "worst-case" benchmark for any time-dependent few and many-body technique beyond linear response. It is found that TDRNOT reproduces the celebrated NSDI "knee," i.e., a many-order-of-magnitude enhancement of the double ionization yield (as compared to purely sequential ionization) with only the ten most significant natural orbitals (NOs) per spin. Correlated photoelectron spectra - as "more differential" observables - require more NOs.