Asymmetric electron energy sharing in strong-field double ionization of helium
aa r X i v : . [ phy s i c s . a t o m - ph ] J u l Asymmetric electron energy sharing in strong-field double ionization of helium
Yueming Zhou, Qing Liao and Peixiang Lu ∗ Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China (Dated: November 1, 2018)With the classical three-dimensional ensemble model, we have investigated the microscopic recol-lision dynamics in nonsequential double ionization of helium by 800 nm laser pulses at 2.0 PW /cm .We demonstrate that the asymmetric energy sharing between the two electrons at recollision plays adecisive role in forming the experimentally observed V-shaped structure in the correlated longitudi-nal electron momentum spectrum at the high laser intensity [Phys. Rev. Lett. , 263003 (2007)].This asymmetric energy sharing recollision leaves footprints on the transverse electron momentumspectra, which provide a new insight into the attosecond three-body interactions. PACS numbers: 32.80.Rm, 31.90.+s, 32.80.Fb
Nonsequential double ionization (NSDI) of atom instrong laser field has drawn extensive researches in therecent years because it provides a particular clear man-ner to study the electron-electron correlation, which isresponsible for the structure and the evolution of largeparts of our macroscopic world [1, 2]. The measure-ments of the recoil ion momentum distributions [3, 4], theelectron energy distributions [5, 6], the correlated two-electron momentum spectra [7, 8], as well as numeroustheoretical calculations [9–12] have provided convincingevidences that strong-field NSDI occurs in favor of theclassical recollision model [13]. According to this model,the first electron that tunnels out of the atom picks upenergy from the laser field, and is driven back to its par-ent ion when the field reverses its direction, and transferspart of its energy to dislodge a second electron. Thoughthe recollision model describes the NSDI process in aclear way, the details of recollision remain obscure. Forinstance, at intensities below the recollision threshold,the underlying dynamics for the intensity-independent5U p (U p is the ponderomotive energy) cutoff in the two-electron energy spectra [14–16] and the dominant back-to-back emission of the correlated electrons from NSDI ∗ Corresponding author: [email protected] of Ar [15] has not been well explored.Recently, the high resolution and high statistics exper-iments on double ionization (DI) of helium have madea great progress in unveiling the microscopic recollisiondynamics in NSDI. The finger-like structure in the cor-related longitudinal (in the direction parallel to the laserpolarization) momentum distribution from NSDI of he-lium by a 800 nm, 4.5 × W /cm laser pulses indi-cates backscattering at the nucleus upon recollision [17].At a higher intensity, 1.5 × W /cm , Rudenko etal observed a pronounced V-like shape of the correlatedtwo-electron momentum distribution [18], which is inter-preted as a consequence of Coulomb repulsion and typical(e,2e) kinematics. Theoretical studies have demonstratedthat at the relatively low laser intensity, both the nuclearCoulomb attraction [19, 20] and the final-state electronrepulsion [20, 21] contribute to this novel structure. How-ever, at the relatively high laser intensity, the roles offinal-state electron repulsion and nuclear attraction forthe V-like shape have not been examined. It is question-able whether the responsible microscopic dynamics forthe V-like shape at this high intensity is similar to thatat the relatively low intensity.In this Letter, with the classical three-dimensional(3D) ensemble model [12, 22], we examine the micro-scopic recollision dynamics in NSDI of helium by a highintensity (2.0 × W /cm ) laser pulse. We find thatthe pronounced V-like shape of the correlated electronmomentum in the direction parallel to the laser polariza-tion is a consequence of the asymmetric electron energysharing in the recollision process, whereas neither the nu-clear attraction nor the final-state electron repulsion con-tributes to the V-like shape. This is different from that atrelatively low intensity, where both the nuclear Coulombattraction and final-state electron repulsion play signifi-cant roles in forming the finger-like shape. By separat-ing the recolliding electron from the bound electron, wefind that the transverse (in the direction perpendicular tothe laser polarization) momentum spectra for these twogroups of electrons peak at different momenta. This dif-ference is ascribed to the Coulomb focusing in the trans-verse direction when the electron moves away from thecore and can be understood as a footprint of the asym-metric electron energy sharing at recollision.The 3D classical ensemble model is introduced in [12]and widely recognized as an useful approach in study-ing high-field double ionization. In this classical model,the evolution of the two-electron system is governed bythe Newton’s classical equations of motion (atomic unitsare used throughout this Letter unless stated otherwise): d r i dt = −∇ [ V ne ( r i ) + V ee ( r , r )] − E ( t ), where the sub-script i is the label of the two electrons, and E ( t ) isthe electric field, which is linearly polarized along thex axis and has a trapezoidal pulse shape with four-cycle turn on, six cycles at full strength, and four-cycleturn off. The potentials are V ne ( r i ) = − / p r i + a and V ee ( r , r ) = 1 / p ( r − r ) + b , representing the ion-electron and electron-electron interactions, respectively.The soft parameter a is set to 0.75 to avoid autoioniza-tion and b is set to 0.01 [12, 22]. To obtain the initialvalue, the ensemble is populated starting from a classi-cally allowed position for the helium ground-state energyof -2.9035 a.u. The available kinetic energy is distributedbetween the two electrons randomly in momentum space, and then the electrons are allowed to evolve a sufficientlong time in the absence of the laser field to obtain stableposition and momentum distributions [16]. Note that inthe classical model the first electrons are ionized abovethe suppressed barrier and no tunneling ionization oc-curs.Figures 1(a) and 1(b) display the correlated electronmomentum distributions in the direction parallel to thelaser polarization, where the laser intensities are 5.0 × W /cm and 2.0 × W /cm , respectively. At5.0 × W /cm , the experimental observed finger-likestructure is not reproduced (Fig. 1(a)). This is becauseof the large soft parameter employed in our calculation,which shields the nuclear potential seriously. Previousstudies have illustrated that the finger-like structure isable to be reproduced when the realistic Coulomb poten-tial or a soften potential with a smaller screening param-eter is used [19, 20].At the relatively high intensity, the overall V-like shapein the correlated momentum distribution is obvious. Incontrast to the previous experimental result [18], a clus-ter of distribution around zero momentum is clearly seen.Back analysis reveals that these events correspond to thetrajectories where DIs occur at the turn-on stage of thelaser pulse. For the soft potential employed in this Let-ter, the potential energy well for the second electron is − / √ . ≃ − . a after the first ionization [16, 19], and nonoticeable change has been found in the V-like shape. Itimplies that the nuclear attraction does not contributeto the V-like shape, which is different from that at therelatively low laser intensity [19, 20].It has been confirmed that at the relatively low inten-sity, the final-state electron repulsion plays an importantrole for the finger-like shape of the correlated electronmomentum distribution [20, 21]. In order to examinethe role of final-state electron repulsion in forming theV-shape at the high intensity, we have performed an ad-ditional calculation, in which the final-state electron in-teraction V ee ( r , r ) = 1 / p ( r − r ) + b is replaced by V ee ( r , r ) = exp [ − λr b ] /r b , where r b = p ( r − r ) + b and λ = 5 . p y + p y = 0.This behavior indicates the strong repulsion in the trans-verse direction, which is in agreement with precious stud-ies [25]. Contrarily, in Fig. 3(a) the population is clus-tered along the axes p y = 0 and p y = 0, indicatingdifferent amplitudes of transverse momenta of the twoelectrons. This difference is more clear when separatingthe bound electrons from the recolliding ones. In thebottom of Fig. 3, we display the transverse momentum( P i ⊥ = q p iy + p iz ) spectra of the recolliding (red cir-cle) and the bound (black triangle) electrons separately,where Figs. 3(c) and 3(d) correspond to the events fromFigs. 3(a) and 3(b), respectively. For the SES trajec-tories (Fig. 3(d)), the recolliding and the bound elec-trons exhibit similar transverse momentum distributions.Whereas for the AES ones (Fig. 3(c)), the differencein the distributions of the recolliding and bound elec-trons is remarkable: the spectrum of the bound electronspeaks near 0.2 a.u., while for the recolliding electrons thespectrum exhibits a maximum at 1.2 a.u. The different transverse momentum distributions for the SES and AEStrajectories imply the different three-body interactions,which can be explored by monitoring the history of theDI events.We display two sample trajectories in Fig. 4. In theleft column, the two electrons have equal energy afterrecollision (Fig. 4(a)), and achieve similar final longitu-dinal momentum (Fig. 4(c)). For the trajectory shownin the right column, the two electrons share unequal en-ergies upon recollision. The recolliding electron (solidred curve) obtains a higher energy at recollision (Fig.4(b)) but achieves a smaller final longitudinal momen-tum (Fig. 4(d)) due to the postcollision velocity [12].The time evolution of the transverse momentum is moreinteresting. As shown in the bottom of Fig. 4, for bothtrajectories the two electrons obtain similar transversemomenta with opposite directions upon recollision. Forthe SES trajectories, both electrons experience a smallsudden decrease in the transverse momenta just after rec-ollision (Fig. 4(e)). For the AES trajectory, the boundelectron suffers a much larger sudden decrease in thetransverse momentum while the transverse momentumof the recolliding electron does not change after recolli-sion (Fig. 4(f)). We ascribe the sudden decrease of thetransverse momentum to the nuclear attraction in thetransverse direction when the electron moves away fromthe core. For the SES trajectories, the two electrons leavethe core with similar momentum, thus the nuclear at-traction plays a similar role in decreasing the transversemomentum, resulting in the distribution along the diag-onal p y + p y = 0 in Fig. 3(b). For the AES trajectory,the nucleus does not effect the transverse momentum ofthe recolliding electron because it leaves the core with avery fast initial momentum. While for the bound elec-tron, it takes a longer time to leave the effective area ofthe core due to the small initial momentum, leading to asignificant decrease of the transverse momentum causedby nuclear attraction. The transverse momentum changeof the electron is determined by ∆ p ⊥ = R F ⊥ dt , where F ⊥ is the transverse force of the nuclear attraction. As-suming an electron that starts at a field zero near theregion x=2 a.u. with initial momentum υ ⊥ = 1 . υ ⊥ to 0.2 a.u.Simply speaking, in the AES trajectory, because of thedifferent initial momentum, the nuclear attraction playsdifferent roles in “focusing” the transverse momenta ofthe bound and recolliding electrons, resulting in the mo-mentum distributions in Fig. 3(c). In other words, thedifferent transverse momentum distributions of the recol-liding and bound electrons reflect the AES at recollisionand provide a new insight into the attosecond three-bodyinteractions.In conclusion, we have investigated the attosecond rec-ollision dynamics in NSDI of helium at 2.0 × W/ cm .At the high intensity, the bound electron often shares asmall part of the recolliding energy at recollision due tothe low efficacy of energy exchange at the high recolliding energy. This asymmetric energy sharing is the decisivereason for the observed V-like shape in the correlated lon-gitudinal momentum spectrum at the high laser intensity.Because of the asymmetric energy sharing recollision, thebound electron leaves the core with a small initial mo-mentum. Thus its transverse momentum is strongly fo-cused by the nuclear attraction when it moves away fromthe core. Whereas the recolliding electron leaves the coreso fast that its transverse momentum is not effected bythe nuclear attraction. The different transverse momen-tum spectra of the recolliding and bound electrons actas a signature of the asymmetric energy sharing at rec-ollision and provide a new insight into the attosecondthree-body dynamics.This work was supported by the National Natural Sci-ence Foundation of China under Grant No. 10774054,National Science Fund for Distinguished Young Scholarsunder Grant No.60925021, and the 973 Program of Chinaunder Grant No. 2006CB806006. [1] Th. Weber et al. , Nature (London)
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632 (2010).[23] S. L. Haan et al. , J. Phys. B et al. , Phys. Rev.Lett. et al. , Phys. Rev. Lett. −2 −1 0 1 2−2−1012 P / Up P x / U p / −2 −1 0 1 2P / Up −2−1012 P x / U p / FIG. 1: (color online) Correlated longitudinal electron mo-mentum distributions for NSDI of helium by 800 nm laserpulses. The intensities are (a) 0.5 PW/ cm and (b)-(d) 2.0PW/ cm . In (c) and (d), the trajectories where DI occurs atthe turn-on stage of the trapezoidal pulse are excluded. In(d), the final-state e-e repulsion is neglected by replacing thesoft Coulomb repulsion with Yukawa potential (see text fordetail). The ensemble sizes are 2 millions. −2 −1 0 1 2−2−1012 P / Up P x / U p / −2 −1 0 1 2 P / Up C oun t s ( a r b . u . ) FIG. 2: (color online) Correlated longitudinal electron mo-mentum distributions for the trajectories where the energydifference at time 0.02T after recollision is (a) larger than 2a.u. and (b) smaller than 2 a.u. (c)(d) Counts of DI trajecto-ries versus laser phase at recollision for the events in (a) and(b), respectively. The solid green curves represent laser fields.In all plots, the events where DI occurs at the turn-on stageof the trapezoidal pulse are excluded. ⊥ (a.u.) C oun t s ( a r b . u ) −1 0 1P (a.u.) ⊥ (a.u.) −1 0 1−101 P (a.u.) P y ( a . u . ) r e b e r e b (d)(c) (a) (b) FIG. 3: (color online) (a)(b) Joint-probability distributions(on logarithmic scale) of the transverse momenta (along yaxis) for the trajectories from Figs. 2(a) and 2(b), respec-tively. (c) Transverse momentum spectra of recolliding (redcycle) and bound (black triangle) electrons for the trajectoriesfrom (a). (d) The same as (c) but for the trajectories from(b). P y ( a . u . ) E ne r g y ( a . u . ) −505 P x ( a . u . ) (f)(a) (b)(d)(c)(e)(f)(a) (b)(d)(c)(e)