Exploring photoelectron angular distributions emitted from molecular dimers by twodelayed intense laser pulses

Václav Hanus,1, 2, ∗ Sarayoo Kangaparambil,1 Seyedreza Larimian,1 Martin Dorner-Kirchner,1

Xinhua Xie (谢新华),1, 3 Andrius Baltuška,1 and Markus Kitzler-Zeiler1, †

1Photonics Institute, Technische Universität Wien, 1040 Vienna, Austria, EU2Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, Budapest, Hungary, EU

3SwissFEL, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland

We describe the results of experiments and simulations performed with the aim of extending pho-toelectron spectroscopy with intense laser pulses to the case of molecular compounds. Dimer framephotoelectron angular distributions generated by double ionization of N2-N2 and N2-O2 van derWaals dimers with ultrashort, intense laser pulses are measured using four-body coincidence imag-ing with a reaction microscope. To study the influence of the first-generated molecular ion on theionization behavior of the remaining neutral molecule we employ a two-pulse sequence comprisingof a linearly polarized and a delayed elliptically polarized laser pulse that allows distinguishing thetwo ionization steps. By analysis of the obtained electron momentum distributions we show thatscattering of the photoelectron on the neighbouring molecular potential leads to a deformation androtation of the photoelectron angular distribution as compared to that measured for an isolatedmolecule. Based on this result we demonstrate that the electron momentum space in the dimer casecan be separated, allowing to extract information about the ionization pathway from the photoelec-tron angular distributions. Our work, when implemented with variable pulse delay, opens up thepossibility of investigating light-induced electronic dynamics in molecular dimers using angularlyresolved photoelectron spectroscopy with intense laser pulses.

INTRODUCTION

A powerful method for tracing molecular dynamics in-duced by a pump pulse is to observe the evolution ofthe angular distributions of photoelectrons emitted bysingle- or few-photon ionization during a delayed probepulse [1, 2]. If combined with coincidence imaging of thephotoion momenta, this technique allows for the mea-surement of molecular frame photoelectron angular dis-tributions (MFPADs) of a single molecule, which canprovide unique insight into the intra-molecular dynamicswith femtosecond resolution [3]. This method can also beimplemented with an intense, elliptically polarized laserpulse as the ionizing probe [4–9]. In that case, the rotat-ing electric field vector of the probe pulse can be exploitedfor mapping laser-sub-cycle time to electron momentum,a concept known as angular streaking [9–14]. When dis-tortions of the such obtained MFPADs due to the parention’s Coulomb potential [5, 7], the field-driven electronicdynamics [6], or the nuclear dynamics [9, 13] that takeplace concomitantly with the photoelectron emission areproperly accounted for, molecular dynamics can be ex-tracted from them with sub-femtosecond resolution.

The next frontier in ultrafast intense laser science isto extend existing methods that are now routinely ap-plied to isolated molecules, to the study of dynamics inmore complicated systems such as molecules in a com-pound. This effort is motived by the fact that mostmolecular processes in nature or technical applicationsdo not take place within a single molecule isolated in vac-uum but between different molecules. A famous exam-ple for such an inter-molecular process is proton coupled

electron transfer [15], which is of key importance in biol-ogy, chemistry, and technology. A widely used approachto study photoinduced inter-molecular processes in fem-tosecond pump-probe experiments is to use small molec-ular van der Waals clusters and dimers as model systems[1, 2]. In recent years, atomic and molecular dimers havealso found increasing attention in experiments that studytheir ionization and fragmentation dynamics when drivenby a strong laser fields [16–29]. It was demonstrated thatthe analysis of the momenta of photoions or photoelec-trons emitted during ionization-fragmentation of dimerscan provide detailed insight into, e.g., the ionization dy-namics [30], the structural deformation induced by thestrong-field interaction [26], the influence of a nearbycharge on the dissociation behaviour of molecules [27],or into laser-sub-cycle electron transfer processes [29]. Acommon finding of these studies is that during multi-ple ionization the nearby charge from the neighbouringion can have a decisive impact on the further ionizationand/or fragmentation dynamics of the partner molecule.

In this Article we describe experiments and simulationsperformed with the aim of investigating to what extentphotoelectron angular distributions (PADs) measuredwith a strong, elliptically polarized laser field can be usedto extract structural and dynamical information frommolecules bound in a hetero-dimer complex. To this endwe studied with a reaction microscope [9, 13, 14, 31, 32]the PADs from sequential double ionization of N2-N2 andN2-O2 dimers during two delayed intense laser pulses incoincidence with the photoions ejected during subsequentfragmentation of the dimers. Our main concern was tounderstand which information about the laser-molecule

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interaction is contained in the measured PADs and howthis information can be extracted. The double-pulse ap-proach in combination with the coincidence measurementpermitted us to reconstruct PADs in the dimer frameof reference (referred to as DFPADs) specifically for thesecond ionization step. This allowed us to identify theinfluence of a nearby molecular ion on the ionization andfragmentation behaviour of a neutral molecule in mea-sured DFPADs.

From our measurements we find that the nearby chargeof the first-created molecular ion mainly leads to a rota-tion of the measured photoelectron angular distributionas compared to the isolated molecule case, whereas itsoverall shape is to a large degree preserved. Thus, oneof the results of this study is that DFPADs can, withadaptations, be read in a similar way as MFPADs. Fur-thermore, by applying methods based on angular streak-ing developed previously [9, 13, 14] and with the supportfrom semi-classical trajectory simulations we are able toshow that the dominant process underlying the rotationis scattering of the second-emitted electron on the neigh-bouring molecular ion as it is driven away by the stronglaser field. This finding adds to the emerging evidence forthe key importance of laser-sub-cycle electron scatteringdynamics in strong-field driven dimers [29] and clusters[33].

EXPERIMENTS

The reaction microscope used in our experiments tomeasure in coincidence the momenta of two molecularions and two electrons emerging from the interaction ofa sequence of two intense laser pulses with a cold jet ofmolecules generated by ultrasonic expansion of N2 andO2 gas is described elsewhere [9, 13, 14]. The laser pulsesused in the experiments had both a central wavelengthof 790 nm and a duration of about 25 fs. Since thegas is strongly cooled during the ultrasonic expansion,molecular dimers, as the pre-cursors of a quantum fluid,may be formed during the ultrasonic expansion [31, 32].When these dimers interact with the intense laser pulses,each molecule in the dimer might become singly ionized,leading to Coulomb explosion of the doubly ionized dimercomplex. The signatures of these Coulomb explosions areshown in the photoion-photoion coincidence (PIPICO)histogram in Fig. 1(a) as the sharp lines. These linesreflect the momentum conservation between the two ex-ploding fragment ions and therefore are clear signaturesexistence of a certain molecular species in the cold gas jet.The histogram in Fig. 1(a) shows that in our experimentN2-N2, O2-O2 and N2-O2 dimers were formed during theultrasonic expansion and Coulomb exploded during theinteraction with the strong laser pulses. The laser inter-action took place in an ultra-high vacuum chamber (basepressure 0.9×10−10 mbar). Ions and electrons emerging

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FIG. 1. (a) Measured photoion-photoion coincidence(PIPICO) distributions obtained by application of both thepump and probe pulses. Indicated are the three dimer speciesthat are generated and detected in our experiment. (b) Ki-netic energy distributions (KER) that result from Coulombexplosions initiated by laser double ionization of the threedimer species shown in (a) when both the pump and probelaser pulses were applied. (c) Schematic representation of theexperiment. A linearly polarized and an elliptically polarizedpulse delayed by 33 ps each remove one electron (cyan andpink electric field-vector traces) from one of the two moleculesin the dimer. Depicted is the example of a dimer consistingof an N2 molecule with σ-geometry of the highest occupiedmolecular orbital (HOMO) and an O2 molecule with a π-geometry of the HOMO. (d) Measured electron momentumdistribution in the laser polarization plane for N2 after in-teraction with the double-pulse sequence. The distributionsfor the dimers look similar. The narrow elongated structurein the cyan box corresponds to electrons emitted during thelinearly polarized pulse, for which electron emission happensdominantly along the laser polarization axis [cf. cyan spherein panel (c)]. The arc segment-shaped parts in the pink boxesare due to electron emission in the elliptically polarized de-layed pulse [cf. pink sphere in panel (c)].

from the interaction volume were guided by weak elec-tric (19 V/cm) and magnetic fields (12 G) to two separateposition-sensitive detectors. From the time-of-flight andimpact position of each detected particle its momentumright after the laser interaction was calculated.

We optimized the expansion conditions for a high pro-duction rate of N2-O2 dimers in the jet, since we wereinterested in the influence of the molecular species onthe ionization and fragmentation dynamics. Hence, O2was set to have lower abundance in the gas jet as com-pared to N2. This led to low yield of O2-O2 dimers and,thus, to low statistic in their DFPADs. Therefore, in thefollowing, we will not discuss angularly resolved data forO2-O2 dimers.

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FIG. 2. Measured molecular frame and dimer frame photoelectron angular distributions (MFPADs respectively DFPADs)with statistical error bars for the (a) N2 molecule, (b) N2-N2 dimer and (c) N2-O2 dimer. The lines are to guide the eyeand represent fits to the measured data. Depicted are the angular distributions of the second electron released during theelliptically polarized pulse. For the DFPAD in (c) the electrons for both orientations of the N2-O2 dimer were superposed. Themolecular respectively dimer axes, retrieved from the ions’ momenta, are aligned horizontally, which coincides with the majoraxis of the polarization ellipse, see the cartoon between (b) and (c), which also depicts the clockwise rotation of the electricfield vector.

During Coulomb explosion of a dimer into two chargedmolecular ions with masses m1,2, the electrostatic poten-tial energy is released as kinetic energy of the two ionswith momenta pi. The kinetic energy released (KER)during this explosion, EKER =

∑i p

2i /(2mi), is a precise

measure of the intermolecular distance, Rd = 1/EKER, ofthe dimer [34]. The measurement revealed, cf. Fig. 1(b),that EKER is the largest for the O2-O2 dimer, hence itexhibits the smallest intermolecular distance of 5.94 a.u.The smallest energy release was measured for the N2-N2dimer, corresponding to a van der Waals bond length of7.18 a.u. An intermediate distance of Rd = 6.66 a.u. wasmeasured for the heteronuclear dimer N2-O2.

The KER distributions in Fig. 1(b) were obtainedwhen both laser pulses of the double-pulse sequence wereused for Coulomb exploding the dimers. As we will de-scribe in detail below, the combined use of a linearly po-larized pump pulse and a preceding circularly polarizedprobe pulse, delayed to the pump by 33 ps, cf. sketchin Fig. 1(c), allowed us to distinguish the two possi-ble ionization sequences that can initiate the fragmen-tations leading to the KER distributions in Fig. 1(b).These two possibilities are: (i) both ionization eventstake place within the duration of one of the two appliedpulses (i.e., within a few tens of femtoseconds), (ii) oneionization event takes place during the pump pulse, thesecond one during the probe pulse (delay about 33 ps).Exploiting this opportunities we found that the measuredKER distributions corresponding to the two possibilitiesagree within experimental errors [not shown in Fig. 1(b)].This indicates that the dimers’ bond stretch dynamics isnegligible during the 33 ps delay. Thus, the most likelyscenario is that the potential energy curves of the singly

charged dimers are binding and of very similar shapes asthose of the neutral dimers.

Because in a two-body Coulomb explosion the two par-ticles are ejected back-to-back, the measured ions’ mo-menta p1 = −p2 directly reflect the orientation of thedimer axis in the laser focus at the time of interaction,provided the explosion happens much faster than the ro-tational dynamics that might be induced during the laserinteraction [35]. As for the large size and mass of thedimers this is well fulfilled, the dimer axis and therewithDFPADs can be reconstructed from the measured elec-tron and ion momenta.

DOUBLE-PULSE APPROACH TO DISTINGUISHTHE TWO IONIZATION STEPS

Our goal was to measure the DFPAD generated byan elliptically polarized laser pulse when one of the twomolecules in the dimer was ionized by a preceding pulse.For such measurement it is necessary to discriminate thefirst emitted from the second emitted electron in the de-tected electrons. This discrimination cannot be simplymade based on the flight times of the two electrons de-tected in coincidence, as the first detected could be thesecond emitted electron and vice versa. Therefore, weemployed a technique that exploits the different shapeof the electron momentum distributions produced by lin-early and elliptically polarized laser pulses [36]: Elec-trons released in linearly polarized light exhibit smallmomenta perpendicular to the light polarization direc-tion and therefore cover regions in an electron momen-tum distribution that are dominantly aligned along the

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polarization axis. In contrast, electrons released in ellip-tically polarized light are angularly streaked and covermomentum regions with large perpendicular momentumthat resemble circle segments [9, 12, 13]. Thus, it be-comes possible to minimize the momentum space overlapbetween two electrons released in a two-pulse sequenceconsisting of a linearly polarized pump laser pulse anda delayed, elliptically polarized probe pulse, when dur-ing each pulse only one electron is emitted, cf. sketchin Fig. 1(c). In our experiments the helicity of the el-liptically polarized probe pulse was chosen such that theelectric field vector rotates clockwise in the electron mo-mentum plane. The delay between the two pulses was setconstant to 33.3 ps in order to ensure that the pulses donot overlap and that the prompt alignment of dimers orpossible revivals of the alignment are avoided [20, 37, 38].

The pulse peak intensities of the two pulses were chosenas 4× 1014 W cm−2 for both pulses. The intensities werecalibrated in situ using the proton distribution from thedissociation of hydrogen, H2, from the background gas inthe ultra-high vacuum chamber [39]. For these intensi-ties, chosen because they are typical for strong-field ex-periments that investigate laser-ionization, an optimiza-tion of the ellipticity that produced minimal overlap ofthe two electron momentum distributions from each pulseyielded E⊥/E‖ = 0.6. Here, E⊥ and E‖ are the laserpeak field strengths perpendicular and parallel to themain axis of the polarization ellipse of the ellipticallypolarized pulse, which was aligned with the polarizationdirection of the linearly polarized laser pulse. Through-out the Article this axis is assumed along the horizon-tal direction. The electron momentum distribution mea-sured with these pulse sequences is shown in Fig. 1(d)exemplary for N2. The distributions for the dimers looksimilar.

Provided that all ions and electrons are detected incoincidence, as was done in our experiment, the double-pulse approach enables the selection of dimer fragmen-tation events when the first electron was exclusively re-leased by the pump pulse and the second electron exclu-sively by the probe pulse. To reconstruct the MFPADsrespectively DFPADs corresponding to the second ioniza-tion step, we separated the measured electron momentumdistributions in the laser polarization plane into three re-gions using pe,⊥, the electrons’ momentum perpendicu-lar to the polarization direction of the linear pulse, asthe decisive parameters, see colored boxes in Fig. 1(d).Electrons with |pe,⊥| ≤ 0.3 a.u. [cyan box in Fig. 1(d)]were considered to be emitted during the linearly polar-ized first pulse. Electrons with |pe,⊥| > 0.3 a.u. [pinkboxes in Fig. 1(d)] were considered to be emitted duringthe elliptically polarized second pulse. We only consid-ered those coincidence events, where one of the two elec-trons was in the cyan-bordered momentum region andthe other electron in one of the two pink-bordered re-gions. All other coincidence events were discarded. This

separation works perfectly only for negligible overlap ofthe electron momentum distributions due to the linearand elliptical pulse, respectively. In practice, a smalloverlap of the wings of two momentum distributions isunavoidable. Three main types of systematic errors re-sulting from this overlap can be distinguished: (i) Theelectron emitted during the elliptical pulse is emittedwith |pe,⊥| ≤ 0.3 a.u., (ii) the electron emitted duringthe linear pulse is emitted with |pe,⊥| > 0.3 a.u., (iii)both electrons are emitted during the elliptical pulse, onewith |pe,⊥| > 0.3 a.u., the other one with |pe,⊥| ≤ 0.3 a.u.By fitting the three main lobes in the electron momen-tum distributions [that all have a similar shape as theone in Fig. 1(d)] with three Gaussians and exploiting co-incidence arguments, we found that only case (iii) canresult in noteworthy errors. However, even for this casethis is only problematic, when the first emitted electronreaches |pe,⊥| > 0.3 a.u. and the second emitted only|pe,⊥| ≤ 0.3 a.u. But as the first emission happens mostlikely during the onset and rising slope of the pulse, whilethe second emission is expected to happen around itspeak, even this error has a small probability. In sum, wefound that the double-pulse method with well-chosen rel-ative peak intensities, as it is the case in our experiment,is relatively insensitive to the unavoidable overlap of thewings of the electron momentum distributions.

From the coincidence events that remained after de-manding that the first electron was emitted during thelinear pulse (with |pe,⊥| ≤ 0.3 a.u.) and the second oneduring the elliptical pulse (with |pe,⊥| > 0.3 a.u.), wefurthermore discarded those events where the ejectiondirection of the ionic fragments was perpendicular to themajor axis of the polarization ellipse: We only consid-ered those coincidence events where the internuclear axisin the case of molecules, respectively the intermolecularaxis in the case of dimers, were oriented within an angleof ±45◦ to the major axis of the polarization ellipse. Theorientation of the molecules/dimers was calculated fromthe fragment ions’ momentum vectors p1 = −p2. Thereason for this selection was motivated by our recent workRef. [29] in which we found that the ionization behaviourof a dimer is strongly influenced by laser-driven electronscattering and transfer processes between the two entitiesof the dimer. To investigate the influence of such electronscattering processes with the double-pulse method, thedimer axis should be roughly aligned along the dominantionization direction where the field strength is largest,i.e., the major axis of the polarization ellipse. If thedimers’ axes were aligned perpendicular to this direction(i.e., along the minor axis), scattering of the ionizing elec-tron on the opposing molecular entity is expected to beof less importance. Again, all coincidence events wherethe dimers/molecules were not aligned within ±45◦ tothe major axis were discarded.

For the remaining coincidence events, one of the twodetected ions (either N+, N+2 , or O

+2 , depending on the

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molecule/dimer considered) was taken as the referencefragment ion and its momentum vector was rotated, to-gether with the electron momentum vectors, into the pos-itive horizontal axis. Then, we calculated for the elec-trons in the pink boxes in Fig. 1(d), that are attributedto emissions during the elliptically polarized probe laserpulse, the angle between the reference ion and the elec-tron momentum vector, denoted by α in the following.Plotting the electron yield as a function of α yielded,finally, the MFPADs/DFPADs shown in Fig. 2.

As for the N2 molecule and the N2-N2 dimer thetwo ions are indistinguishable, we mirrored the MF-PADs/DFPADs about the vertical axis. The same wasdone for the N2-O2 dimer in Fig. 2(c), yielding a DFPADwhere both orientations (N2 ejected to the right, and N2ejected to the left) are superposed. A DFPAD for theN2-O2 dimer, where the electron and ion momenta wererotated together such that the momentum vector of N2exclusively points to the right, is shown in Fig. 3(e) andwill be discussed in detail below.

ANALYSIS OF MEASURED DIMER-FRAMEPHOTOELECTRON ANGULARDISTRIBUTIONS (DFPADS)

To understand the information contained in DFPADs,we first compare them to the more familiar case of anMFPAD measured for a Coulomb exploding doubly ion-ized molecule. Fig. 2(a) shows the MFPAD for theN2 molecule measured with the double-pulse sequence,where the first ionization event takes place during thelinearly polarized pump pulse and the second one dur-ing the elliptically polarized probe pulse. Figs. 2(b) and2(c) show the DFPADs for the N2-N2 and N2-O2 dimersmeasured with exactly the same pulse sequence. TheMFPAD features a symmetric shape about the symme-try axis along α = 85◦, with α the angular coordinate.The small ca. 5◦-rotation from α = 90◦ that would beexpected in angular streaking for an elliptically polar-ized pulse with its major axis of the polarization ellipsealong α = 0◦, may be attributed to the influence of theCoulomb field on the emitted electron [7]. In contrastto the symmetric MFPAD, the DFPADs feature a non-symmetric shape about the α = 85◦ axis: For the upperhemisphere, α = [0◦, 180◦], the DFPADs contain a largernumber of events in the range α < 90◦. This asymmetryis even more pronounced in the DFPAD measured forN2-O2 shown in Fig. 2(c).

To explain the reason for the different shapes of theMFPAD and the DFPADs depicted in Fig. 2 we turn todiscussing the differences in the binding potentials fromwhich the second electron is detached. The photoelec-tron distributions plotted in Fig. 2 reflect the angulardependence of the second ionization step. In a simplifiedpicture we can assume that the second electron, at the

instant of its emission, is bound in a potential well thatis defined by two positive charge centres. In the case of amolecule these centres are close to each other and thereis no considerable barrier between them, see the sketchin Fig. 3(a). When the electron tunnels through the field-suppressed barrier it directly reaches the continuum. Ifthe two centres are further apart, as it is the case for adimer, two situations can be distinguished: The electroncan be either released from the down-field or the up-fieldwell. An electron released from the down-field can tun-nel directly to the continuum similar to the molecularcase sketched in Fig. 3(a). In contrast, when an electrontunnels from the up-field well, as sketched in Figs. 3(c)and 3(d), there is a possibility that the electron, as itis driven away by the laser electric field, scatters on thedown-field charge centre.

In the following we will show by an in-depth analysis ofthe measured DFPADs, supported by results of semiclas-sical trajectory Monte Carlo simulations, that the asym-metry in the measured DFPADs in Figs. 2(b) and 2(c) isindeed caused by scattering of electrons released from theup-field well on the opposing charge center. To guide ouranalysis, we simulate the momentum distribution of theelectron that is emitted during the elliptically polarizedpulse from a model binding potential by tunnel ionizationand subsequently is driven by the combined forces due tothe laser electric field and a binding potential situated atsome distance R from the electron’s parent binding po-tential. The neighbouring binding potential mimics thepositively charged ion created by ionization during thepreceding linearly polarized pump pulse. The electronreleased during the linear pulse is not simulated and itis assumed that this electron has already left the inter-action volume. This is perfectly justified given the delayof 33 ps between the two pulses. Thus, the potential feltby the ionizing and laser-driven electron has a Coulombdouble-well shape. To avoid numerical problems due tothe Coulomb singularity we used soft-core potentials ofthe form

V (r) = −2∑

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where is A the Coulomb softening parameter that wasset to 0.1 for all calculations, and r is the position of thesimulated electron. At position R1 the singly chargedneighbouring ion is situated, at R2 is the parent ion ofthe electron. The separation R = |R1 −R2| of the twoions was chosen as R = 2.46 a.u. for the N2 molecule andR = 6.66 a.u. for the N2-O2 dimer. At every instant ti ofthe discrete temporal mesh the starting position of theelectron, r0, i.e., the tunnel exit sketched in Figs. 3(a,c,d),was calculated by numerically solving the equation

V (r0) + r0 ·E(ti) = −|Ip| (2)

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FIG. 3. (a)-(d) Results of simulations detailed in the text and explanatory sketches. The grey line in (b) shows the simulatedangular distribution of photoelectrons emitted from a molecular-type potential depicted in (a). The assumed internucleardistance of 2.46 a.u. corresponds to that of neutral N2. The red line in (b) shows the photoelectron angular distribution whenthe electrons tunnel from the up-field potential well towards the left. This situation, depicted in (c) with a red circle indicatingthe tunneling electron, occurs when the laser electric field vector points to right (as indicated by an arrow). The green line in(b) shows the angular distribution for the opposite case, sketched in (d), when the electric field vector points to the left and theelectron (green circle) is ejected to the right. (e) Measured angular distribution of the photoelectron emitted from the N2-O2dimer during the elliptically polarized probe pulse. The black line shows the data when the dimer is oriented such that N2is on the right side. For clarity, only one representative statistical error bar is shown (around 90◦). The red line is added forreference and shows the angular distribution of the non-oriented dimer, duplicated from Fig. 2(c). See text for further details.

instant of the temporal grid a trajectory was launched atthe position r0(ti) with a probability given by the molecu-lar ADK ionization theory [40]. As the sole purpose of thesimulations was to obtain a qualitative understanding ofthe ionization behaviour and the subsequent laser-drivenfree electron dynamics rather than obtaining quantitativeagreement with the measured data, we used, for the sakeof simplicity, the parameters of the helium atom in theADK formula, where the Ip was adapted to that of themolecules. The trajectories were propagated in three di-mensions for an elliptically polarized laser pulse with thesame parameters as in the experiments using the Runge-Kutta integration scheme. The helicity of the ellipticallypolarized laser pulse was, as in the experiments, assumedclockwise. From the final momentum value ṙ∞ of eachtrajectory at time t→∞ (long after the pulse) the elec-tron momentum distribution was obtained by binning alllaunched trajectories.

The simulation for the molecular-type potential withthe shorter internuclear distance resulted in a symmet-ric MFPAD with its symmetry axis around α = 85◦ [seegray line in Fig. 3(b)], similar to the measured MFPADin Fig. 2(a). This case also applies to the dimer-casewhen the potoelectrons are emitted from the down-fieldpotential well, as in both cases the electrons tunnel di-rectly into the continuum [cf. Fig. 3(a)]. In contrast, thesimulated angular distribution of photoelectrons emitted

from the up-field potential well of the dimer-like poten-tial with the larger intermolecular separation features astronger rotation and a clearly visible distortion, in agree-ment with the measurement, cf. Fig. 3(b). The angu-lar distribution in Fig. 3(b) is separated into two cases:The red line shows the DFPAD for electrons emitted tothe left, the green line for electrons emitted to right [cf.the sketches Figs. 3(c) and (d)]. In both cases the DF-PAD in Fig. 3(b) shows a strong rotation. The simulatedphotoelectron momentum distributions from which theMFPAD and the green-colored half of the DFPAD inFig. 3(b) are calculated are shown in Figs. 4(a) and 4(b),respectively.

The simulations, thus, predict a stronger rotation anddistortion of the angular distributions of photoelectronsemitted from the upper potential [red and green lines inFig. 3(b)] as compared to photoelectrons emitted fromthe lower potential well [gray line in Fig. 3(b)]. By adetailed analysis of the electrons’ trajectories we foundthat the dominant reason for this stronger rotation isthat the photoelectrons emitted from the up-field poten-tial well, scatter off the neighbouring potential well asthey are driven away by the strong laser field. To visual-ize this process we show in Figs. 4(c) and 4(d) the tempo-ral evolution of an example trajectory in real space andin momentum space, respectively. The green dot depictsthe trajectory’s starting conditions (space and momen-

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.)(d)

FIG. 4. Simulated electron momentum distributions in thepolarization plane for the molecular model potential shown inFig. 3(a) and the dimer model potential shown in Fig. 3(d),reproduced for convenience in the inset. The data in (a) wereused to plot the grey distribution in Fig. 3(b), while the datain (b) were used for the green distribution in Fig. 3(b). (c, d)Example trajectory (blue line) of an electron tunneling fromthe up-field site of the model dimer in position space (c) andmomentum space (d). The green dot marks the beginning ofthe trajectory while the red dot marks the final momentumvalue, indicated both in (b) and (d). The color density in (c)depicts the Coulomb potential of the doubly charged dimer.The dashed arrow in (b) denotes the clockwise rotation of thelaser electric field vector.

tum). The red dot indicates the final momentum [alsoindicated in Fig. 4(b)]. For trajectories that make up thered half of the simulated DFPAD in Fig. 3(b) the situ-ation is reversed and the trajectories emitted from theright well scatter on the left potential well. Thus, basedon our semiclassical trajectory simulations we attributethe rotation and distortion of the measured DFPADs inFigs. 2(b) and (c) to scattering of photoelectrons emit-ted from the up-field potential well on the charge in theopposing potential well of the partner molecule in thedimer.

INFORMATION RETRIEVAL FROM THEDFPADS

We now turn to discussing the information that is con-tained in DFPADs measured with strong, elliptically po-larized laser fields and how it can be extracted. It wasshown above that a DFPAD can be quite different fromthe corresponding MFPAD. Specifically we have shownthat the nearby presence of a molecular ion results in

a notable rotation and deformation of the photoelectronangular distribution from the dimer. In the followingwe will show for the example of the heterodimer N2-O2that, despite the distortions that are introduced by thepresence of the neighbouring molecular ion in the DF-PAD, it is still possible to extract from it detailed in-formation about the ionization process in the ellipticallypolarized pulse and the nature of the distortion due tothe neighouring ion.

To start the discussion, we note that double ionizationand fragmentation of the N2-O2 dimer in the pump-probescheme of our experiment can proceed via two pathways.In the first pathway, the N2 molecule is ionized duringthe linearly polarized pump pulse and subsequently theO2 molecule becomes ionized by the elliptically polarizedprobe pulse, see Equ. (3). During the second pathwaythe sequence of ionization is reversed, see Equ. (4).

N2-O2 → N+2 -O2→ N+2 -O

+2 (3)

N2-O2 → N2-O+2→ N+2 -O

+2 (4)

In both pathways the ionization process during the pumppulse takes place within a neutral dimer. The ionizationdynamics of the second molecule during the probe pulse,in contrast, takes place in the vicinity of a molecularion. The presence of this ion may modify the ionizationprocess of the second molecule. Which ionization stepwill be modified more strongly by the presence of theneighbouring ion as compared to the neutral case, theone of O2 or of N2?

To explore this question, one should evaluate the prob-ability ratio of pathways (3) and (4). Is it possible toextract this ratio from the angular distribution of thesecond electron that is emitted from the heteromoleculardimer? As we will show in the following, the answer tothis question is yes. In our experiment we measure theelectrons and ions emitted in coincidence. Therefore, wecan display the PAD in the dimer frame, which results ina DFPAD. The crucial point is, however, that for a het-erodimer, the DFPAD can be further refined by not onlyfixing the dimer-axis along the, e.g., horizontal, axis, butalso by orienting the dimer with respect to the molecularspecies. While in Fig. 2(c) the orientations (N2 ejectedto the left/right or O2 ejected to the left/right) were notconsidered and therefore Fig. 2(c) is a superposition ofboth cases, the DFPAD displayed in Fig. 3(e) is plottedsuch that N2 is always ejected to the right.

Under this condition the oriented DFPAD can be sepa-rated into two halves by resorting to the concept of angu-lar streaking [9, 10, 13]. For the clockwise helicity of theelliptical laser field used in our experiment electrons arestreaked into the upper half [colored in red in Fig. 3(e)]when the laser electric field vector points from O2 to N2,cf. sketch in Fig. 3(c). In contrast, the green-coloredlower half in Fig. 3(e) corresponds to electrons that areemitted when the laser field vector points from N2 to O2,cf. sketch in Fig. 3(d). If we compare the shapes of the

8

two halves in the oriented DFPAD in Fig. 3(e) we no-tice that they are distinctly different. To highlight thisdifference we overlaid in Fig. 3(e) the non-oriented DF-PAD from Fig. 2(c) by a red line. By comparison of theoriented DFPAD with this red line it becomes obviousthat the upper, red-colored half comprises of significantlymore electrons. Thus, we can conclude that obviously thesecond ionization step happens with a higher probabilitywhen the laser electric field vector points from O2 site toN2 [sketch in Fig. 3(c)]. This does, however, not implythat the second electron is more likely emitted from O2 inthe down-field well of the dimer. Thus, to quantify theprobability ratio and to determine how many electronsare emitted from O2 respectively N2, it is not simplypossible to integrate the upper and lower halves of theDFPAD in Fig. 3(e).

The reason is that for dimers the laser field driven tra-jectories of the emitted electrons are strongly influencedby the potential of the neighbouring molecular ion, aswe have discussed above. Consquently, electrons thatare emitted when the electric field vector points into acertain direction may not be detected under an angle of90◦ to the field direction, as it is predicted by angularstreaking based on the strong-field approximation (SFA)[41, 42] that neglects the influence of any ionic poten-tial on the final momentum of the photoelectron. Butdue to scattering on the neighbouring molecular ion, inparticular electrons from the up-field potential well maybe streaked into a distinctively different direction. Thisleads to deformations, but mainly to a global rotation ofthe overall DFPAD as compared to the SFA prediction.This was clearly shown by the results of our simulations,cf. Fig. 3(b). Based on the finding described above thatthe dominant deviation from the SFA prediction is a rota-tion of the angular distribution of photoelectrons emittedfrom the up-field potential well along the clockwise rota-tion of the laser electric field vector, we can, however,separate the scattered from the non-scattered electrons.

To understand the rotation due to scattering, we turnto the simulated results in Fig. 3(b). This figure showsthat electrons that are emitted from the down-field po-tential well directly into the continuum (gray line), willonly be marginally affected by the Coulomb binding po-tential. The overall effect is that they, when emitteddominantly around the peaks of the laser field along themain axis of the laser polarization ellipse (at 0◦ and180◦), will be deflected only by a few degrees furtheralong the laser field vector rotation direction (clockwisein our case) than the 90◦ predicted by the SFA. As aconsequence, their PAD shows peaks around 85◦ and265◦. In contrast, electrons that are emitted from theup-field potential well are scattered on the neighbouringwell, leading to a much larger rotation of the angular dis-tribution. Our model, which reproduced the measuredDFPADs reasonably well, predicts that the additionalrotation due to scattering is about 40◦, such that the an-

gular distribution of these electrons shows peaks around50◦ and 230◦, see red and green lines in Fig. 3(b). Basedon these values we divide each half of the DFPAD inFig. 3(e) into two segments using 60◦ respectively 240◦

as the borders. This results in the four segments de-noted I to IV, indicated by darker and lighter red andgreen shading in Fig. 3(e). We note that the scatteredand non-scattered regions in the DFPAD certainly over-lap to some extent. It is therefore intrinsically impossibleto unequivocally disentangle these regions using sharpangular limits. As a result, precise quantitative resultscannot be expected from such a division of the DFPAD.The purpose of the analysis described below is, however,not to provide quantitative results, but to demonstrate apossible approach to disentangling different processes inmeasured DFPADs. We think that this approach couldbe extended to a qualitative level using a more advanceddivision of the DFPAD.

In the following we discuss how the regions I to IVdefined by the sharp angular limits can be used to es-timate the emission percentage of the second electronfrom the up-field and down-field potential wells. Andsubsequently, how from this information an estimate forthe branching ratio between pathways (3) and (4) canbe obtained. Region I in the upper half of the DF-PAD corresponds to electrons that were scattered aftertheir release from the up-field potential well in the situa-tion depicted in Fig. 3(c). Thus, they can be attributedto emission from N2. Electrons in region II were notscattered. Therefore, they were emitted from the down-field well, i.e., from O2. With the same logic, region IIIcontains scattered electrons emitted from O2, while re-gion IV corresponds to non-scattered electrons emittedfrom N2. With this assignment, it is now simple to es-timate the percentage of the two pathways described byEqus. (3) and (4): Regions I and IV contain electronsemitted from N2 during the probe pulse (second ioniza-tion step), thus, represent pathway (4). Regions II andIII contain electrons emitted from O2 during the secondionization step and, thus, represent pathway (3). By in-tegrating the numbers in these regions we obtain that54% of the total counts are due to pathway (3), whileonly 46% of all events follow pathway (4). We emphasizeonce more that these numbers are of no specific value.It is the demonstration of an approach that we are in-terested in rather than obtaining an exact result. Wehave, however, checked by small variations of the angu-lar limits in the DFPAD that the numbers are relativelyrobust with respect to the specific choice of the limits.Hence, despite the intrinsic uncertainties we would liketo conclude that in our experiment the pathway when theO2 is ionized in the second ionization step is somewhatmore likely. This can be interpreted such that the twoionization steps are not completely independent of eachother.

Which factors could be responsible for this ionization

9

behaviour? An ionization process that favors electronemission from a specific potential well in a molecule ex-posed to a strong field is enhanced ionization (EI) [37, 43].It has been shown that this molecular ionization processtakes place in almost the same manner also in dimers[23]. However, EI favors electron emission from the up-field well, while in our experiment the more probableelectron emission from O2 takes place for the down-fieldwell. Thus, EI cannot be hold responsible for the ion-ization dynamics observed in our experiment. A morelikely reason for the observed preponderance of pathway(3) is the influence of the structure of the heteromolec-ular dimer on the ionization probability during the two-step double-ionization in our double-pulse experiment.The ionization probability of an isolated molecule with agiven valence electron configuration and binding energydepends mainly on the orientation of the molecule withrespect to the laser field. If two molecules are boundtogether by van der Waals forces, a number of differentdimer configurations become possible [22, 44], for exam-ple T-shaped, X-shaped, parallel, linear, etc. Thus, notonly the valence structure of the two molecules and theirdifferent ionization potentials, but also the dimer geome-try determines which dimers from the randomly orientedensemble in the utrasonic gas jet are preponderantly ion-ized. Therefore, in a double pulse scheme, particularlywhen the two pulses have different polarization states, asin our experiment, the probability of a particular path-way is determined by many convoluted parameters. Adetailed analysis of the hypothesis that the dimer struc-ture is responsible for the slightly favorable ionization ofO2 during the second ionization step is, however, beyondthe present work and must be left for future work.

SUMMARY

In summary, we described the results of experimentsand simulations performed with the aim of exploringwhether and how information extraction from laser-generated photoelectron angular distributions (PADs), astandard method in atomic and molecular physics, canbe extended to the case of molecular compounds. Tothis end we have studied strong-field double-ionization ofhomo- and heteromolecular dimers of O2 and N2 formedby van der Waals binding forces. To distinguish the twoionization steps we applied two delayed ultrashort intenselaser pulses, where the first pulse was linearly polarizedand the second one elliptically polarized. In combinationwith four-body coincidence imaging using a reaction mi-croscope this allowed us to measure dimer-frame photo-electron angular distributions (DFPADs). By a detailedanalysis of the DFPAD for the heteromolecular O2-N2dimer we showed that the PAD of a molecular dimer isdeformed and rotated as compared to the PAD of an iso-lated molecule. With the help of simulations we showed

that these distortions are mainly due to scattering of elec-trons emitted from the up-field potential well on the po-tential of the molecular ion formed during the first ioniza-tion step. Building on this finding, we demonstrated thatby dividing the DFPAD into regions that mainly containscattered electrons, and regions containing mainly non-scattered electrons, it becomes possible to overcome thecomplications due to the DFPAD-distortion and to ex-tract information about the ionization pathway.

The results of our study point to a promising possibil-ity of extracting information about bound electron dy-namics induced by a pump pulse from a DFPAD. Suchextraction has been the subject of many works on iso-lated molecules [3–9, 45]. The underlying principle ofthese efforts is that the angular ionization probability re-flects the intra-molecular bound electron density. Thus,the bound electronic dynamics becomes encoded in themeasured MFPAD. In turn, by a time-resolved measure-ment of the MFPAD it becomes possible to obtain insightinto the electronic dynamics in molecules.

Our work investigates the case of molecular dimers andshows that the resulting DFPAD contains valuable infor-mation about the electronic dynamics during laser-dimerinteraction. Moreover, we demonstrate a possible routeto extract this information. Thus, if the DFPADs aremeasured with a variable delay between the first and sec-ond ionization step (rather than only for one value of thedelay as in our work), the femtosecond evolution of dy-namics in dimer-molecules induced by the pump pulsecan be extracted.

This work was supported by the Austrian Science Fund(FWF), Grants No. P28475-N27 and P30465-N27.

∗ vaclav.hanus@tuwien.ac.at† markus.kitzler-zeiler@tuwien.ac.at

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Exploring photoelectron angular distributions emitted from molecular dimers by two delayed intense laser pulsesAbstract Introduction Experiments Double-pulse approach to distinguish the two ionization steps Analysis of measured dimer-frame photoelectron angular distributions (DFPADs) Information retrieval from the DFPADs Summary Acknowledgments References