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

www.nature.com/scientificreports OPEN Non-sequential double ionization with near-single cycle laser pulses A. Chen1, M. Kübel2,4, B. Bergues3,4, M. F. Kling Received: 15 February 2017 Accepted: 30 June 2017 Published: xx xx xxxx 3,4 & A. Emmanouilidou1 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-singlecycle 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. Non-sequential double ionization (NSDI) in intense near-infrared laser fields is a fundamental process with electron-electron correlation playing a key role1–3. Considerable information regarding NSDI has been obtained from kinematically complete experiments, i.e., the momenta of the escaping electrons and ions are measured in coincidence4. Most of these experiments employ multi-cycle laser pulses allowing for multiple recollisions to occur before both electrons ionize. Multiple recollisions complicate the electron dynamics and render the comparison with theory difficult. Recently, however, kinematically complete experiments succeeded in confining NSDI to a single laser cycle by using carrier-envelope phase (CEP)-controlled few- and near-single-cycle pulses5, 6. These experiments with near-single-cycle pulses allow for an easier comparison between theory and experiment. To interpret the double ionization spectra of driven Ar measured using near-single-cycle laser pulses, a simple one-dimensional (1D) classical model was put forth6–8. This model relies on the assumption that the dominant pathways of double ionization are, for small and intermediate intensities, delayed non-sequential ionization and, for higher intensities, sequential ionization. For strongly-driven Ar, intermediate intensities refer to the intensity range from 2 × 1014 W/cm2 to 4 × 1014 W/cm2. This model neglects the contribution of another major pathway of double ionization, namely, direct ionization as well as the Coulomb potential. This 1D model did not achieve a quantitative agreement with the complete set of available experimental data over the whole intensity range. Delayed ionization—also referred to as recollision-induced excitation with subsequent field ionization, RESI9, 10, and direct ionization are two main pathways of NSDI. An interesting finding of these near-single cycle experiments was that the correlated momenta components of the two escaping electrons along the direction of the laser field have a cross-shaped pattern for an intensity around 1014 W/cm2 6–8. A cross-shaped correlated electron momenta pattern due to the delayed double ionization mechanism was previously identified in the context of strongly-driven He at an intensity of 9 × 1014 W/cm2 and for a wavelength of 400 nm11. In a cross-shaped correlated electron momenta pattern the double ionization probability is the highest when the component of the momentum along the direction of the laser field is very small for one electron while it takes a wide range of values for the other electron, see the experimental correlated electron momenta at 1014 W/cm2 in Fig. 5. In the context of strongly-driven Ar, the above described 1D model attributed the cross-shaped pattern of the correlated electron momenta to the delayed pathway of double ionization7, 8. A quantum mechanical calculation, which neglects the Coulomb potential, was used to refine the contribution of the delayed pathway of double ionization to the cross-shaped correlated electron momenta pattern12. This calculation identified the key role that the symmetry of the excited state plays in the final shape of the correlated momenta. 1 Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, United Kingdom. 2Joint Laboratory for Attosecond Science, University of Ottawa and National Research Council, 100 Sussex Drive, Ottawa, Ontario, K1A 0R6, Canada. 3Max-Planck-Institut für Quantenoptik, D-85748, Garching, Germany. 4 Department für Physik, Ludwig-Maximilians-Universität, D-85748, Garching, Germany. Correspondence and requests for materials should be addressed to A.E. (email: ) Scientific REPOrts | 7: 7488 | DOI:10.1038/s41598-017-07635-5 1 www.nature.com/scientificreports/ Figure 1. Ratio of double to single ionization probability as a function of intensity. Experimental results8 are denoted by dark blue squares and light blue crosses and computed results are presented by a solid line with black circles when the focal volume effect is not accounted for and by a dashed-line with triangles when the focal volume effect is accounted for. The difference in the two experimental sets results from slightly different averaging over the focal volume8. In this work, using a three-dimensional (3D) semiclassical model, NSDI of Ar is studied when Ar is driven by 750 nm near-single-cycle laser pulses at intensities ranging from 0.85 × 1014 W/cm2 to 5 × 1014 W/cm2. In this 3D model the only approximation is in the initial state. There is no approximation during the time propagation. That is, all Coulomb forces and the interaction of each electron with the laser field are fully accounted for. Moreover, when analyzing the numerically obtained doubly-ionized events, no assumptions are made regarding the prevailing mechanism of double ionization and we use no free parameter. This is not the case for the 1D model8. In addition, the Coulomb singularity is fully accounted for using regularized coordinates13. This is an advantage over models which soften the Coulomb potential14. Previous successes of this 3D model include identifying the mechanism responsible for the fingerlike structure in the correlated electron momenta15, which was predicted theoretically16 and was observed experimentally for He driven by 800 nm laser fields17, 18. Moreover, this model was used to investigate direct versus delayed pathways of NSDI for He driven by a 400 nm laser field while achieving excellent agreement with fully ab-initio quantum mechanical calculations19. Using this model, in this work, several observables are computed for different intensities of strongly-driven Ar. These observables are the sum of the two electron momentum components along the direc (...truncated)