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

www.nature.com/scientificreports OPEN Fingerprints of slingshot nonsequential double ionization on two-electron probability distributions G. P. Katsoulis & A. Emmanouilidou* 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. Non-sequential double ionization (NSDI) of atoms driven by intense laser fields is a fundamental process which has attracted considerable theoretical and experimental interest1–23. The three-step model underlies NSDI1. First, one electron tunnels through the field-lowered Coulomb potential. This tunnel-ionizing electron can return to the core and transfer energy to the other electron. For high intensities, the main pathway of NSDI is the direct one. The recolliding electron transfers energy to the other electron that suffices for both electrons to ionize following recollision. For low intensities, the delayed pathway of NSDI prevails. The recolliding electron transfers energy to the bound electron, however, this energy is sufficient for only one of the two electrons to ionize following recollision. As a result of the energy transferred, the other electron transitions to an exited state of the remaining ion. Until recently, the delayed pathway of NSDI was generally accepted as being equivalent to recollision-induced excitation with subsequent field ionization (RESI)7,22. According to RESI, the electron that transitions to an excited state after recollision, ionizes later in time at extrema of the laser field. It does so mainly with the assistance of the field. However, recently, we have shown that RESI is not always the most important mechanism of the delayed pathway of NSDI. We did so by employing a three-dimensional semiclassical model24. Several classical and semiclassical models have been employed in recent years to describe processes in strong fields23,25–27, for a review see ref. 28. When He is driven by near-single-cycle pulses of 400 nm wavelength, we have shown that a new mechanism overtakes RESI in the delayed pathway of NSDI29, at small intensities below the recollision threshold. We labeled this mechanism slingshot-NSDI. We have shown that in slingshot-NSDI, following the transition of an electron to an excited state, due to the attractive force that the nucleus exerts to this electron, the electron subsequently undergoes a Coulomb slingshot motion. This slingshot motion we identify in the context of Coulomb forces is reminiscent of the slingshot motion, in the context of gravitational forces, that a spacecraft undergoes altering its motion around a planet. During Coulomb slingshot the electron ionizes mostly around the second extremum of the field with the assistance of both the nucleus and the laser field. Due to the electron that ionizes last undergoing slingshot motion, the two electrons escape opposite to each other along the direction of the laser field. This anti-correlated two-electron escape has previously been attributed to multiple recollisions, a mechanism that was put forth in the context of RESI30–34. This pattern of two-electron escape has been found to prevail NSDI of several atoms driven by intense long duration pulses. It has been the object of many theoretical and experimental studies30–37. Hence, slingshot-NSDI offers an alternative explanation to multiple recollisions. Here, we show that anti-correlated two-electron escape is not the only feature that distinguishes slingshot-NSDI from the other NSDI pathways. The main NSDI pathways, which are considered in the current Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, United Kingdom. *email: Scientific Reports | (2019) 9:18855 | https://doi.org/10.1038/s41598-019-55066-1 1 www.nature.com/scientificreports www.nature.com/scientificreports/ study, are the direct pathway, RESI and the double delayed pathway. In the latter pathway both electrons ionize with a delay following recollision. We show that slingshot-NSDI has very distinct fingerprints in both energy and angular two-electron probability distributions. These features can be observed experimentally. Hence, this study paves the way for identifying slingshot-NSDI by kinematically complete experiments that employ near-single-cycle pulses where control of carrier envelope phase (CEP) is achieved34,38–40. Method We consider He driven by a near-single-cycle laser pulse at intensities 5 × 1014 W/cm2 and 7 × 1014 W/cm2 at 400 nm. Both intensities are below the recollision threshold, which corresponds to an intensity of 8.6 × 1014 W/ cm2. The latter corresponds to the maximum energy of the electron returning to the core being equal to the energy needed to transition to the first excited state of the remaining ion. The maximum energy of the electron returning to the core is 3.17  20/(4ω 2)1, which is equal to 23.7 eV at 5 × 1014 W/cm2 and 33.1 eV at 7 × 1014 W/cm2; 0 and ω are the strength and frequency of the field. We use a laser field of the form 2  → t   (t) = 0 exp−2 ln2  cos(ωt + ϕ)ẑ ,  τ    (1) where φ is the CEP, and τ = 2 fs is the full-width-half-maximum of the pulse duration in intensity. We employ atomic units, unless otherwise stated. We use a three-dimensional (3D) semiclassical model that is formulated in the framework of the dipole approximation24. Previous successes of this model include verifying that electron backscattering from the nucleus accounts for the finger-like structure in NSDI of He driven by long laser pulses at higher intensities 24. This finger-like structure was predicted theoretically14 and obtained experimentally15,16. Moreover, it was explained in a classical framework24,41. In addition, using this 3D model, we investigated the direct versus the delayed pathway of NSDI for He driven by a long duration laser pulse at 400 nm42. For intensities ranging from below- to above-the-recollision threshold, we achieved excellent agreement with fully ab-initio quantum mechanical calculations. In addition, using this model we obtained very good agreement with experimental results for several observables of NSDI for Ar when driven by near-single-cycle laser pulses at 800 nm43. These observables were obtained as a functi (...truncated)