Time-resolved study of resonant interatomic Coulombic decay in helium nanodroplets
A. C. LaForge, R. Michiels, Y. Ovcharenko, A. Ngai, J. M. Escartin, N. Berrah, C. Callegari, A. Clark, M. Coreno, R. Cucini, M. Di Fraia, M. Drabbels, E. Fasshauer, P. Finetti, L. Giannessi, C. Grazioli, D. Iablonskyi, B. Langbehn, T. Nishiyama, V. Oliver, P. Piseri, O. Plekan, K. C. Prince, D. Rupp, S. Stranges, K. Ueda, N. Sisourat, J. Eloranta, M. Pi, M. Barranco, F. Stienkemeier, T. Moeller, M. Mudrich
TTime-resolved study of resonant interatomic Coulombic decay in helium nanodroplets
A. C. LaForge,
1, 2, ∗ R. Michiels, Y. Ovcharenko, A. Ngai, J. M. Escart´ın, N. Berrah, C.Callegari, A. Clark, M. Coreno, R. Cucini, M. Di Fraia, M. Drabbels, E. Fasshauer, P.Finetti, L. Giannessi,
5, 9
C. Grazioli, D. Iablonskyi, B. Langbehn, T. Nishiyama, V. Oliver, P. Piseri, O. Plekan, K. C. Prince, D. Rupp, S. Stranges, K. Ueda, N. Sisourat, J.Eloranta, M. Pi,
16, 17
M. Barranco,
16, 17
F. Stienkemeier, T. M¨oller, † and M. Mudrich ‡ Department of Physics, University of Connecticut, Storrs, Connecticut, 06269, USA Physikalisches Institut, Universit¨at Freiburg, 79104 Freiburg, Germany Institut f¨ur Optik und Atomare Physik, Technische Universit¨at, 10623 Berlin, Germany Institut de Qu´ımica Te`orica i Computacional, Universitat de Barcelona,Carrer de Mart´ı i Franqu`es 1,08028 Barcelona, Spain. Elettra-Sincrotrone Trieste, 34149 Basovizza, Trieste, Italy Laboratoire Chimie Physique Mol´eculaire, Ecole Polytechnique F´ed´erale de Lausanne, 1015 Lausanne, Switzerland CNR - Istituto di Struttura della Materia, 00016 Monterotondo Scalo, Italy Department of Physics and Astronomy, Aarhus University, 8000 Aarhus C, Denmark Nazionale di Fisica Nucleare - Laboratori Nazionali di Frascati, Via E. Fermi 40, 00044 Frascati, Roma, Italy Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan Dipartimento di Fisica and CIMaINa, Universit`a degli Studi di Milano, 20133 Milano, Italy Department of Chemistry, University Sapienza, 00185 Rome, Italy Sorbonne Universit´e, CNRS, Laboratoire de Chimie Physique Mati`ere et Rayonnement, UMR 7614, F-75005 Paris, France Department of Chemistry and Biochemistry, California State University at Northridge, Northridge, CA, 91330, USA Departament FQA, Facultat de F´ısica, Universitat de Barcelona, Barcelona, 08028, Spain Institute of Nanoscience and Nanotechnology (IN2UB),Universitat de Barcelona, Barcelona, 08028, Spain (Dated: September 4, 2020)When weakly-bound complexes are multiply excited by intense electromagnetic radiation, energycan be exchanged between neighboring atoms through a type of resonant interatomic Coulombicdecay (ICD). This decay mechanism due to multiple excitations has been predicted to be relativelyslow, typically lasting tens to hundreds of picoseconds. Here, we directly measure the ICD timescalein resonantly excited helium droplets using a high resolution, tunable, extreme ultraviolet free-electron laser. Over an extensive range of droplet sizes and laser intensities, we discover the decayto be surprisingly fast, with decay times as fast as 400 femtoseconds, and to only present a weakdependence on the density of the excited states. Using a combination of time dependent densityfunctional theory and ab initio quantum chemistry calculations, we elucidate the mechanisms ofthis ultrafast decay process where pairs of excited helium atoms in one droplet strongly attract eachother and form merging void bubbles which drastically accelerates ICD.
INTRODUCTION
Short-wavelength free-electron lasers (FELs) are well-suited for studying light-matter interactions, due to theirhigh intensity and ultrashort pulse duration, where manyphotons can be absorbed in a system within a few fem-toseconds. For condensed systems, the complexity ofinteratomic processes makes gaining a thorough under-standing of the ionization mechanisms and dynamics te-dious, if not impossible. On the other hand, free, weakly-bound nanosystems such as van der Waals (vdW) clus-ters, can be used to study such interatomic interactionsin a well-controlled manner. In particular, the study ofvdW clusters irradiated by intense FEL radiation has ledto the observation of numerous interatomic processes [1–3].A novel type of interatomic process known as inter-atomic Coulombic decay (ICD) [4] has been widely stud-ied in weakly-bound systems [5, 6]. In cases where local Auger decay is energetically forbidden, an excited atomor molecule releases its excitation energy by transferringit to a neighboring atom or molecule, which can resultin its ionization. In general, ICD is a prominent de-cay mechanism in a multitude of systems, specificallythose of biological relevance [7–10]. One of the factorsdetermining the importance of ICD in a nanosystem isits decay time, which is directly linked to its efficiency.With the advent of seeded FELs and the availabilityof intense, tunable extreme ultra-violet (XUV) radia-tion [11, 12], new types of resonant ICD [13] have beenobserved in vdW clusters [14–17] where energy is ex-changed between neighboring excited atoms. Addition-ally, similar resonant-type ICDs were observed by syn-chrotron radiation in mixed vdW clusters where energywas exchanged between species [18–20].He nanodroplets have served as model systems forstudying interatomic processes induced by one pho-ton [19–27] and multiple photons [14, 15, 17, 28], due a r X i v : . [ phy s i c s . a t m - c l u s ] S e p U V t i m e d e l a y ( p s )
Electron kinetic energy (eV)
I C D e x p e r i m e n t I C D s i m u l a t i o n2 P I e x p e r i m e n t 2 P I s i m u l a t i o n I C D f i t
Electron intensity (arb. units)
U V t i m e d e l a y ( p s )a )b )
Figure 1. a) Time-resolved electron kinetic energy distribu-tions of resonantly excited He droplets centered around theICD peak (top panel) and the two-photon ionization (2PI)signal (bottom panel). b) Projection of the intensity of theICD peak (blue circles) and the 2PI signal (red squares) asa function of XUV-UV pump-probe delay. The experimentaldata is fitted with a convoluted exponential decay function(gray line). The red and blue lines show the results of a MCsimulation (see text for details). The droplet size was 76,000atoms and the excitation photon energy was 21.6 eV. to their simple electronic structure and extremely weakatom-atom interactions. Moreover, beyond being a test-bench for studying atomic and binary interatomic pro-cesses, He nanodroplets are quantum fluid clusters, whichexhibit unique features such as voids, or “bubbles”,around impurities [29–31], which can freely move aboutthe droplet owing to its superfluid state [32].Here, we report on time-resolved measurements of res-onant ICD in He droplets. The process is initiated byan XUV pulse tuned to the resonant 1s2p droplet band( hν = 21.6 eV) [33]. This creates multiple excited atoms in the droplet which can decay via ICD, i. e. the en-ergy from one excited He atom, He ∗ , is transferred to an-other He ∗ , which is then ionized. A second, time-delayedUV pulse can directly ionize the excited atom(s) in thedroplet thereby interrupting and halting any interatomicdecay processes. Over an extensive range of droplet sizesand laser pulse energies, the decay mechanism was foundto be much faster than predicted by theory [13]. Evenmore surprising, the decay rate is nearly independent ofthe number of excited atoms per droplet, although the-ory predicts a very strong dependence on the internu-clear distance. To understand the discrepancies, the ex-perimental results were modelled using a combination oftime-dependent density-functional theory (TDDFT) [34]and ab initio calculations of the doubly excited He ∗ -He ∗ pair potentials as well as the ICD widths. We discoveredthat the ICD dynamics are largely determined by theattractive interaction of closely-spaced He ∗ atoms andby the formation of bubbles around them. The latterstrongly accelerates the ICD via the merging of overlap-ping bubbles. The results show that interatomic pro-cesses in condensed phase nanosystems are governed bya complex set of relaxation mechanisms which can resultin ultrafast autoionization. EXPERIMENT
This work was performed at the Low Density Matterendstation [35] of the seeded FEL FERMI, in Trieste,Italy. The FEL photon energy (21 . µ J to 50 µ J, was determined upstream by gasionization, taking the nominal reflectivity of the opti-cal elements in the beam transport system into account.The diameter of the FEL focus was 250 µ m FWHM. TheUV probe pulse was obtained from a frequency-tripled(-doubled) Ti:Sapphire laser ( hν (cid:48) = 4.8 (3.2) eV) with apulse energy of 50 (200) µ J with a focus diameter of250 µ m FWHM. A tin filter of 160 µ m thickness was usedto suppress higher order harmonic radiation. The crosscorrelation between the FEL and the probe laser was200 fs FWHM, measured by resonant two-photon ioniza-tion of He. A supersonic gas jet of He nanodroplets wasproduced by expansion of high pressure He gas througha pulsed, cryogenically cooled Even-Lavie nozzle. Byvarying the expansion conditions (backing pressure andnozzle temperature), the mean cluster size was varied inthe range of (cid:104) N (cid:105) = 10 -10 He atoms. The nanodropletbeam was perpendicularly crossed by the FEL and UVbeams at the center of a velocity map imaging spectrom-eter [35]. The electron kinetic energy distributions werereconstructed using the Maximum Entropy Legendre Re-construction method [36].
RESULTS AND DISCUSSION
Fig. 1 a) shows the distributions of electron kinetic en-ergy E e emitted by resonantly excited He droplets as afunction of the delay between XUV pump and UV probelaser pulses. The mean droplet size was (cid:104) N (cid:105) = 76 , . × W/cm . Atlow kinetic energies (0 < E e < t < ∗ from the XUV-excited 1s2p state to the 1s2s state [31].At higher kinetic energies (15 < E e <
18 eV), reso-nant multiphoton ICD is observed according to the re-action [13–15](He ∗ + He ∗ )He N − → (He + + e ICD + He)He N − . Here, He N denotes the He droplet and e ICD is the ICDelectron. A discussion of the electronic states which initi-ate this type of ICD is given in Appendix 1. Since ICD isa binary process, at least two excited atoms are requiredper droplet.The intensities of photoelectrons (red squares) andICD electrons (blue circles), depicted in Fig. 1 b), dis-play opposing trends in their time evolution: the 2 PIsignal is enhanced at delays 0 < ∆ t < . ∗ population through photoionizationby the UV probe pulse, thereby suppressing the ICD.As the pump-probe delay is increased, ICD can proceedbefore the He ∗ are photoionized and the e ICD yield is re-plenished. Thus, the rise of the e ICD yield reflects thetimescale of the ICD. To quantify this process, the ICDsignal was fitted with a function [gray line in Fig. 1 b)]accounting for the exponential rise as well as the tem-poral overlap of two Gaussian pulses near time zero. Athorough discussion of this fitting procedure is given inAppendix 2. Fig. 1 b) also shows the ICD (blue line) and2 PI (red line) data from a Monte Carlo (MC) simulationas discussed later in the text. Additional data and fits fordifferent experimental parameters are given in Appendix3. To systematically investigate the dynamics of ICD inHe nanodroplets, pump-probe delay dependencies over awide range of He droplet sizes and XUV intensities wererecorded. The latter controls the He ∗ excitation probabil-ity (photon flux × absorption cross section) and therebythe mean distance between He ∗ in a droplet. Due to thestrong coupling between the FEL power, droplet size,and collective auto-ionization (CAI) effects [17], only alimited range of excitation probabilities (0.1-1 %) showed E x p e r i m e n t S i m u l a t i o n S i m u l a t i o n N
H e ~ 1 0 f i x e d S i m u l a t i o n N H e ~ 1 0 f i x e d Effective ICD decay time (ps)ICD efficiency, 2*eICD/nHe*(%)
E x c i t a t i o n p r o b a b i l i t y , F p * s a b s ( % )a )b ) Figure 2. a) Effective ICD decay time and b) ICD effi-ciency plotted as a function of the excitation probability (redsquares). MC simulation results for the specific experimentalconditions, droplet size and FEL intensity, are shown as bluedots. Additionally, to show the general trend in the simu-lations on the FEL intensity, the results for fixed small andlarge droplets are shown as black and gray lines, respectively. a clearly distinguishable ICD peak, despite the broadrange of droplet sizes and FEL intensities available. Asthe FEL intensity increases, multiple excited atoms mayinteract, leading to decay by CAI and formation of ananoplasma [15]. In the transition from ICD to CAI, theICD peak broadens and shifts to lower energies due to theformation of a collective Coulomb potential, and eventu-ally becomes dominated by low-energy thermal electronsfrom the nanoplasma [17].Similar to what is shown in Fig. 1 b), each ICD de-lay dependence is fitted with a function to determine thetime constant of the e ICD evolution. The resulting ICDtimes, τ ICD , and e ICD yields are respectively plotted asred symbols in Fig. 2 a) and b) as a function of the ex-citation probability. The corresponding MC simulationresults are shown as blue dots. The e ICD yield is deter-mined from the total number of detected electrons andthe He ∗ photoionization cross section [37]. It is normal-ized to the number of He ∗ atoms in the droplet and mul-tiplied by two to account for the fact that two excitationsproduce one ICD electron. The resulting ICD efficiencyrises from 0.09 to 0.32 in the given range of He ∗ excitationprobability, while τ ICD decreases from 1000 to 400 fs. Todecouple the effect of the droplet size from the FEL in-tensity, we have additionally performed MC simulations(see the SM for details) for fixed droplet sizes. The re-sults for small and large droplets are shown in Fig. 2 asblack and gray lines, respectively. For small droplets,the ICD time is nearly constant and lower than the ICDdecay times for large droplets, which show a weak depen-dence on the FEL intensity. The ICD efficiency shownin Fig. 2 b) rises from zero as a function of the excitationprobability with a higher slope for large droplets. Over-all, the MC simulations are in excellent agreement withthe experimental data.In general, the measured ICD decay times are surpris-ingly short ( τ ICD < ∗ -He ∗ distance. Γ( d ) is calculated by the Fano-CI-Stieltjesmethod [38] for all possible combinations of electronicstates populated during droplet relaxation [26, 31] (seethe SM for details). Γ, which is inversely proportional tothe decay time, τ ICD , shows a very strong dependence onthe He ∗ -He ∗ distance. On the other hand, the measured τ ICD , in Fig. 2 a), shows only a weak dependence on theHe ∗ excitation probability, which is a measurable quan-tity proportional to the mean He ∗ -He ∗ distance. The ob-served ultrafast ICD rates, in the fs regime, can only beexplained through an additional mechanism that bringsthe two He ∗ atoms into close contact. Excitation migra-tion [39, 40], excitation delocalization [41] and hole hop-ping have been discussed extensively over the years, espe-cially in the context of Penning ionization [40, 42]. Whilefast excitation transfer, akin to exciton hopping, can ex-plain the high efficiency of the Penning process [40], itcannot account for the short ICD lifetime. Delocaliza-tion of excitations over an extended region of the Hedroplet as a consequence of exciton hopping would leadto a reduced local spatial overlap and thus to low ICDrates. Besides, the large variation of the interatomic dis-tances between He atoms in the droplets due to the largezero-point motion as well as many-body quantum effectsmay also limit delocalization [41, 42]. Unfortunately, theproblem of excitation transfer in superfluid He has notyet been addressed theoretically, despite the numerousexperimental Penning ionization studies. That said, anadditional mechanism is required that brings two He ∗ in close contact such that ICD takes place at short dis-tances.Aside from the fast delay-time dependence of the ICDsignal, we observed that the e ICD yield in most casesdoes not fully rise to the level measured at negative de-lays within the full range of pump-probe delays, see Ap-pendix 2 and 3. This indicates that some of the He ∗ decay by ICD much more slowly than the experimentally observed convergence from which we deduce τ ICD . Fur-thermore, the observation that the ICD efficiency neverexceeds 35% in our experiments points at a competing re-laxation channel that prevents the majority of He ∗ fromdecaying via ICD.To better understand the response of He nanodropletsto multiple excitations and to rationalize our ex-perimental findings, time-dependent density functional(TDDFT) simulations were performed [31, 34, 43, 44]for the motion of He ∗ pairs. To keep the simulationstractable, we considered bulk superfluid He, which is cou-pled to the He ∗ pair self-consistently. Due to the lightmass of the He ∗ “impurities”, they must be treated quan-tum mechanically with the potential term given by theHe ∗ -droplet interaction. To include the interaction be-tween the two He ∗ atoms, the He ∗ -He ∗ pair potentialswere calculated using highly correlated ab initio methods(see the SM for details).Fig. 3 a) shows the time evolution of the 2D cutsof the He density distribution (yellow-red area) whenthe two excited He atoms were initially separated by d = 10 ˚A (pink-green dots). Animation of these simu-lated dynamics for various initial conditions are includedin the SM. Upon excitation, bubbles form around themdue to the repulsion between the Rydberg electrons andthe surrounding closed shell He atoms [29–31, 44, 45].As the bubbles grow and the two He ∗ atoms weaklyattract each other, the bubbles eventually overlap andmerge into one large bubble. The salient feature is thatshortly after the two bubbles coalesce, the two He ∗ arestrongly accelerated towards each other. This process isfacilitated by the merging of the bubbles where the He ∗ sreach interatomic distances d < d up to 9 ˚A, see Fig. 3 (b). As ICD isnot explicitly included in the TDDFT simulations, theHe ∗ pair continues vibrating at short distance due to theattractive He ∗ -He ∗ potential. However, within the firsthalf cycle of the vibration, the ICD decay width reachesΓ( d = 4 ˚A) = 5 . τ theo ICD = 110 fs for the He ∗ ( S)+He ∗ ( S) pair,which has the largest branching ratio in the droplet relax-ation [26, 31]. Thus, all He ∗ pairs with d (cid:46)
10 ˚A actuallydecay via ICD within t (cid:46) . d >
10 ˚A), the time be-tween He ∗ excitation and bubble merging quickly in-creases to t >
10 ps and therefore ICD becomes very slow.This explains the observed incomplete replenishment ofthe e ICD -signal at long pump-probe delays. But why donot all He ∗ decay by ICD in the absence of the probepulse? It is known that radiative decay from He clustersis not expected to play a significant role since the lifetimeis in the ns regime [29, 46]. Previous experimental and He*-He* distance d (Å) T i m e t ( p s ) d ( Å ) 1 0 9 . 0 8 . 0 6 . 7 a )b ) c ) t = 0 p s t = 0 . 4 p s t = 1 . 2 p s t = 1 . 4 p s2 n m ICD decay width (meV)
D i s t a n c e d ( Å ) H e ( S ) + H e ( S ) H e ( S ) + H e ( S ) H e ( S ) + H e ( S ) S H e ( S ) + H e ( S ) S Figure 3. a) Snapshots of the He density evolution around two He ∗ centers separated initially by d = 10 ˚A. The probabilitydistribution of He ∗ is represented as pink dots and the black areas show the void bubbles forming. b) Evolution of the He ∗ -He ∗ distance d for various values of the initial distance d . c) Calculated ICD widths for various combinations of 1s2s-excited He ∗ atomic states. theoretical studies have shown that, following the bubbleformation, some of the He ∗ remain weakly bound to theHe droplet surface where they eventually form He ∗ ex-cimers [47], whereas others are directly ejected from thedroplets [31, 45, 48]. Once a He ∗ has detached from thedroplet, it can no longer decay via ICD, but it still con-tributes to the photoionization signal. Based on our mea-surements (Fig. 2 b)), the fraction of ejected He ∗ was es-timated to be larger than 50%. The competition betweendirect ejection and ICD for initial distances d >
10 ˚A isstrongly dependent on the droplet size.The ICD dynamics in He nanodroplets are largely gov-erned by the motion of He ∗ driven by the bubble dy-namics and the interatomic He ∗ -He ∗ potential, compet-ing against the ejection of surface He ∗ s from the droplet.To account for the aforementioned effects, a simplifiedMC simulation based on Γ( d ) was developed, the re-sults are displayed in Fig. 2 b). The He droplet wastreated as homogeneously-packed He atoms representedby same-sized spheres. An initial number of He ∗ s, ac-cording to the XUV intensity and the He droplet absorp-tion cross section [33], were placed at random positionswithin the droplet. Then, for each He ∗ the following con-ditions were tested. If the distance to the droplet surface d S < . ∗ d > . ∗ is ejected. If d S > . d < . ∗ undergoes ICD; the ICD prob-ability was then calculated based on Γ( d ) according tothe trajectory d ( t ) obtained from the TDDFT simula-tions. If d S > . d > . ∗ will notdecay by ICD and only photoionization is possible. Theprobe pulse was implemented by converting the He ∗ intophotoelectrons at a rate consistent with the experimen-tal estimate. The values d = 15 . d S = 7 . ∗ ejection, respectively, were deduced from theTDDFT simulations. Additionally, when the same simu-lation was performed for fixed positions of He ∗ , the ICDtime constants were 1-2 orders of magnitude longer thanthe experimental values, thus demonstrating the impor-tance of ultrashort bubble dynamics and the attractiveHe ∗ -He ∗ potential. An in-depth discussion of these sim-ulations is given in Appendix 4. CONCLUSIONS
To summarize, we have performed time-resolved mea-surements of resonant ICD in He nanodroplets. Overa wide range of droplet sizes and laser pulse energies,we have found the decay to be as fast as 400 fs, and tohave little dependence on the density of excited states,in contrast to the strong dependence of the predictedICD decay width on the distance between excitations.Our simulations have shown that the ICD dynamics islargely determined by the pair-wise attraction of excitedatoms, as well as the peculiar response of He dropletsto multiple resonant excitations. The formation of bub-bles around the excitations and their subsequent merg-ing accelerates ICD, whereas the ejection of excited stateatoms from the droplet competes with it. While excitedstate bubble dynamics is a phenomenon unique to flu-ids, our time-resolved results nevertheless have clearlydemonstrated that ICD in the condensed phase is gov-erned by complex, ultrafast relaxation mechanisms thatcan couple translational, electronic, and spin degrees offreedom. In general, He nanodroplets are an ideal plat-form to study processes relevant to a broad range of fieldsfrom the molecular to the condensed phase.
ACKNOWLEDGEMENTS
The authors gratefully acknowledge financial supportfrom the Carl-Zeiss-Stiftung, the Deutsche Forschungsge-meinschaft (DFG) under grant MO 719/14-2 and withinthe frame of the Priority Programme 1840 ‘Quantum Dy-namics in Tailored Intense Fields (MU 2347/12-1 andSTI 125/22-2), and the Carlsberg Foundation. TDDFTwork has been performed under grant FIS2017-87801-P(AEI/FEDER, UE) (M.B., M.P.). A.C.L. and N.B. ac-knowledge the support of the Chemical Sciences, Geo-sciences and Biosciences Division, Office of Basic EnergySciences, Office of Science, US Department of Energy,grant no DE-SC0012376. J.M.E. acknowledges supportfrom Ministerio de Ciencia e Innovaci´on of Spain throughthe Unidades de Excelencia “Mar´ıa de Maeztu” grantMDM-2017-0767.
APPENDIX 1: HIGH RESOLUTION ICDELECTRON KINETIC ENERGY DISTRIBUTION
Information about the electronic states involved in theICD process is encoded in the kinetic energy distributionof ICD electrons. Fig. 4 shows a high-resolution electronspectrum measured at the photon energy hν = 23 . × He atoms. Besides the large signalcomponent at low kinetic energy resulting from CAI [15],an additional peak is observed around 16 eV with a shoul-der near 15 eV, which is due to ICD. For comparison, weadded vertical lines showing the expected ICD electronenergies, E e, ICD , for pairs of He ∗ in the lowest excited Intensity (arb. units) e l e c t r o n k i n e t i c e n e r g y ( e V )2 * H e * ( 1 s 2 s ) S2 * H e * ( 1 s 2 s ) S2 * H e * ( 1 s 2 p ) P Figure 4. Static (XUV only) electron kinetic energy distri-bution measured at hν = 23 . ∗ atoms in the three lowest excited states. states 2s2s , S and 2s2p P according to E e, ICD = 2 E He(1 s s,p ) − E i, He . (1)Here E He(1s2s,p) is the energy of the 1s2s,p states of the Heatom, and E i, He is the He ionization potential. Clearly,the 1s2s S state is the dominant state producing ICDelectrons. The 1s2s S state and He ∗ excimer states(broad feature around E e, ICD = 11 eV) also contributebut to a lesser extent. Although this electron spec-trum was measured at a different excitation energy thanthose in the main text, ICD electrons appear to originatemostly from the same He ∗ states. This is due to fast elec-tronic relaxation, as previously observed in experimentsusing high-harmonic laser radiation [49], FEL [17, 31]and synchrotron radiation [19, 26]. APPENDIX 2: FITTING OF ICD ELECTRONYIELDS
The time-dependent ICD electron intensities are fittedwith a convolution of the gaussian instrument responsefunction obtained by resonant two-photon ionization ofHe and an exponential decay leading to the followingfunction: I ( t ) = I − A erfc (cid:104) ( σ − τ ( t − t )) / ( √ στ ) (cid:105) ×× exp( − ( t − t ) /τ ) − B erfc (cid:104) ( t − t ) / ( √ σ ) (cid:105) (2)This model is the simplest analytic function that repro-duces the experimental measurements. The exponentialfunction reproduces the rise of the electron counts for - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 00 . 0 00 . 0 50 . 1 00 . 1 50 . 2 00 . 2 50 . 3 00 . 3 5 E x p e r i m e n t a l d a t a E r f E x p ( s , t ) f i t E r f ( s ) E x p o n e n t i a l d e c a y : e - t Intensity (arb. units)
U V t i m e d e l a y ( p s )
Figure 5. Fitting of experimental time-resolved ICD data(black squares) with the function from equation 2 (red curve).The components of the fit are illustrated separately: Errorfunction (blue curve) and exponential decay (orange dottedline). long delay times. Thus, the exponential decay constant, τ , represents the effective ICD time. The parameter σ represents the cross-correlation width of the two overlap-ping laser pulses and was fixed to the value measuredby resonant two-photon ionization of He gas. The time-zero value t was constrained to 0 ±
15 fs in order toaccount for possible drifts in the FEL timing. The freeparameters I , A and B control the total ICD intensityfor t → −∞ , t → ∞ and the maximum depletion I min .Fig. 5 displays a fit of a typical experimental measure-ment. In addition to the full fit curve (red), we show theseparate contributions from the error function (blue line)and exponential decay (orange dots). APPENDIX 3: ADDITIONAL EXPERIMENTALDATA
To give a better overview of the experimental resultsand systematics, we show in the upper panel of Fig. 6 ad-ditional pump-probe ICD electron yields measured underdifferent experimental conditions. The red symbols cor-respond to small droplets with high excitation density.The resulting ICD curve is characterized by a fast timevariation as the mean interatomic distance between ex-cited atoms is small, d <
10 ˚A, and thus ICD is fast. Theblack curve is for an intermediate excitation density andintermediate droplet sizes. The blue curve is for largedroplets combined with a low excitation density. Re-plenishment of the ICD electron signal after depletion isslower as ICD mostly occurs for pairs of He ∗ with larger - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 00 . 00 . 20 . 40 . 60 . 81 . 0 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 00 . 00 . 20 . 40 . 60 . 81 . 0 ICD electron intensity (arb. units)
U V t i m e d e l a y ( p s ) < N > = 1 . 7 e 2 ; p e x c = 0 . 9 % < N > = 1 . 5 e 4 ; p e x c = 0 . 5 % < N > = 7 . 0 e 4 ; p e x c = 0 . 1 % E r f E x p f i t ; t = 0 . 3 6 p s E r f E x p f i t ; t = 0 . 6 5 p s E r f E x p f i t ; t = 0 . 9 7 p s U V t i m e d e l a y ( p s ) < N > = 1 . 7 e 2 ; p e x c = 0 . 9 % < N > = 1 . 5 e 4 ; p e x c = 0 . 5 %< N > = 7 . 0 e 4 ; p e x c = 0 . 1 % E r f E x p f i t ; t = 0 . 3 8 p s E r f E x p f i t ; t = 0 . 4 5 p s E r f E x p f i t ; t = 1 . 1 0 p s ICD electron intensity (arb. units)
E x p e r i m e n tS i m u l a t i o n
Figure 6. Upper: Experimental ICD electron intensities as afunction of XUV-UV pump-probe delay with correspondingexponential fits for three different droplet sizes and excitationdensities. Lower: Simulated ICD electron intensities and fitsfor conditions similar to those of the upper panel. initial separation. The lower panel of Fig. 6 shows theresults of the MC simulation for the same parameters asin the experiment. The good agreement shows that ourmodel captures the main aspects of the pump-probe ICDdynamics.
APPENDIX 4: THE EFFECT OF ATOMICMOBILITY ON ICD TIMESCALES
Besides providing a deeper understanding of our ex-perimental findings, MC simulations additionally allowus to ask more fundamental questions about the process,which cannot be directly addressed through experiment.For instance, how important is the mobility of the He ∗ atoms in the ICD process? To benchmark our simulationsagainst the model system where the ICD rate is entirelygiven by the initial distances between He ∗ we have carriedout simulations where the He ∗ positions are held fixed.Fig. 7 a) shows the simulated ICD electron intensity forstationary He ∗ atoms as a function of the UV time de-lay for three different excitation probabilities (blue lines).For comparison, the experimental data is shown as blacksquares and the corresponding MC simulation assumingmobile He ∗ atoms is shown as a red line. As can be E x p e r i m e n t p e x c = 0 . 5 %M o b i l e H e * a t o m s : p e x c = 0 . 5 %S t a t i o n a r y H e * a t o m s : p e x c = 0 . 1 % p e x c = 0 . 5 % p e x c = 1 % ICD electron intensity (arb. units)
U V t i m e d e l a y ( p s ) relative contribution of ICD electrons (%)
E x c i t a t i o n p r o b a b i l i t y , F p * s a b s ( % ) I C D l i f e t i m e s : t < 5 p s t > 5 p s a n d t < 1 0 0 p s t > 1 0 0 p s a )b ) Figure 7. a) Simulated ICD electron intensities as a functionof the UV time delay for fixed He ∗ positions with differentexcitation densities (blue curves). For comparison, the exper-imental data is shown as black squares and the correspondingMC simulation assuming mobile He ∗ atoms is shown as a redline. b) Relative contribution of ICD electrons broken intothree different ICD lifetime intervals as a function of excita-tion probability for fixed He ∗ positions. clearly seen, the simulated dynamics for fixed He ∗ posi-tions proceed on much longer timescales compared to theexperimental data, thus showing the critical importanceof atomic mobility in the ICD process. To further illus-trate this point, Fig. 7 b) shows the relative contributionof ICD electrons broken into three different ICD lifetimeintervals as a function of excitation probability for fixedHe ∗ positions. For low excitation probability ( (cid:46) τ >
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