Ultrafast relaxation of photoexcited superfluid He nanodroplets
M. Mudrich, A. LaForge, F. Stienkemeier, A. Ciavardini, P. O'Keeffe, M. Coreno, Y. Ovcharenko, T. Moeller, M. Ziemkiewicz, M. Devetta, P. Piseri, M. Drabbels, A. Demidovich, C. Grazioli, P. Finetti, O. Plekan, M. Di Fraia, K. C. Prince, R. Richter, C. Callegari, J. Eloranta, A. Hernando, M. Pi, M. Barranco
UUltrafast relaxation of photoexcited superfluid He nanodroplets
M. Mudrich
Department of Physics and Astronomy, Aarhus University, Denmark
A. LaForge ∗ and F. Stienkemeier Institute of Physics, University of Freiburg, Germany
A. Ciavardini, † P. O’Keeffe, and M. Coreno
CNR-ISM, Area della Ricerca di Roma 1, Monterotondo Scalo, Italy
Y. Ovcharenko ‡ and T. M¨oller Institut f¨ur Optik und Atomare Physik, TU-Berlin, Germany
M. Ziemkiewicz
Ultrafast X-ray Science Laboratory, Chemical Sciences Division,Lawrence Berkeley National Laboratory, Berkeley, USA,and Department of Chemistry, University of California, USA
M. Devetta § and P. Piseri Dipartimento di Fisica, Universit`a degli Studi di Milano, Milan, Italy
M. Drabbels
Federal Institute of Technology Lausanne (EPFL), Switzerland
A. Demidovich, C. Grazioli, P. Finetti, O. Plekan, M. Di Fraia, K. C. Prince, R. Richter, and C. Callegari
Elettra-Sincrotrone Trieste S.C.p.A., Italy
J. Eloranta
Department of Chemistry and Biochemistry, California State University at Northridge, USA
A. Hernando
Kido Dynamics, EPFL Innovation Park Bat. C, CH-1015 Lausanne, Switzerland andIFISC (CSIC-UIB), Instituto de Fisica Interdisciplinar y Sistemas Complejos,Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
M. Pi
Departament FQA, Facultat de F´ısica, Universitat de Barcelona, Spain andInstitute of Nanoscience and Nanotechnology (IN2UB), Universitat de Barcelona, Spain
M. Barranco
Laboratoire des Collisions, Agr´egats, R´eactivit´e, IRSAMC, UMR 5589,CNRS et Universit´e Paul Sabatier-Toulouse 3, Toulouse Cedex 09, FranceDepartament FQA, Facultat de F´ısica, Universitat de Barcelona, Spain andInstitute of Nanoscience and Nanotechnology (IN2UB), Universitat de Barcelona, Spain (Dated: May 14, 2019)The relaxation of photoexcited nanosystems is a fundamental process of light-matter interaction.Depending on the couplings of the internal degrees of freedom, relaxation can be ultrafast, convertingelectronic energy in a few fs, or slow, if the energy is trapped in a metastable state that decouplesfrom its environment. Here, helium nanodroplets are resonantly excited by femtosecond extreme-ultraviolet (XUV) pulses from a seeded free-electron laser. Despite their superfluid nature, we findthat helium nanodroplets in the lowest electronically excited states undergo ultrafast relaxation.By comparing experimental photoelectron spectra with time-dependent density functional theorysimulations, we unravel the full relaxation pathway: Following an ultrafast interband transition, avoid nanometer-sized bubble forms around the localized excitation (He ∗ ) within 1 ps. Subsequently,the bubble collapses and releases metastable He ∗ at the droplet surface. This study highlights thehigh level of detail achievable in probing the photodynamics of nanosystems using tunable XUVpulses. a r X i v : . [ phy s i c s . a t m - c l u s ] M a y Understanding the ultrafast response of condensedphase nanosystems to photoexcitation is essential formany research areas, including atmospheric science [1],radiation damage in biological matter [2, 3], light-harvesting mechanisms in natural and artificial com-plexes [4, 5], and photocatalysis [6]. However, the com-plex couplings of electronic and translational degrees offreedom often present major theoretical challenges [7].In addition, the complexity of heterogeneous solid orliquid systems, as well as difficulties in preparing well-controlled samples and performing reproducible measure-ments, make it difficult to unravel the elementary steps inthe relaxation process. In this respect, superfluid He nan-odroplets are ideal model systems for studying the photo-dynamics in weakly-bound nanostructures, both experi-mentally and theoretically; He atoms have a simple elec-tronic structure, interatomic binding is extremely weak,and, the structure of He nanodroplets is homogeneousand nearly size-independent due to their superfluid na-ture [8, 9]. Exploring transient phenomena associatedwith superfluidity is a particularly intriguing aspect ofHe nanodroplet spectroscopy [10, 11]. By probing thedynamics of laser-excited molecular systems coupled toHe droplets, one gains insight into the fluid dynamics,dissipation, and transport properties of a superfluid onthe molecular scale [12–14].The properties of pure He droplets can be directlystudied using electron bombardment or XUV radiation.From previous theoretical [15, 16] and static photoexcita-tion studies [17–23], the following dynamical response toresonant absorption of an XUV photon has been inferred:The electronic excitation created in the droplet local-izes on an atomic or molecular center He ∗ n , n = 1 , , . . . ,within a few 100 fs [24]. Subsequently, a void cavity orbubble forms around He ∗ n due to Pauli repulsion betweenthe excited electron and the surrounding ground state Heatoms [21], which expands up to a radius of 6.4 ˚A [25]within about 350 fs [26]. Depending on how close to thedroplet surface the excitation localizes, the bubble eithercollapses before fully forming thereby ejecting He ∗ or He ∗ out of the droplet, or remains in a metastable state inthe droplet [21]. Using laser-based high-harmonic lightsources [27], various ultrafast processes initiated by ex-citing high-lying states in the autoionization continuumof He nanodroplets have been revealed, including theemission of slow electrons [22], the ejection of Rydbergatoms and excimers [28, 29], and ultrafast interband re-laxation [23]. However, the dynamics of low-lying statesbelow the autoionization threshold and in particular thebubble formation have not been probed for pure He nan-odroplets, neither at the strongest absorption band asso-ciated with the atomic He ∗ s p P state (photon energyaround hν = 21 . s s S state ( hν = 21 . b ) Potential energy (eV) a ) * P S T e H e + P P P S S D r o p l e t a b s o r p t i o n ( a r b . u . )
I n t e r a t o m i c d i s t a n c e ( Å ) A (cid:2) u ( 2 s ) C (cid:2) g ( 2 s ) B (cid:1) g ( 2 p x ,y ) F (cid:1) u ( 2 p x ,y ) D (cid:2) u ( 2 p z ) G (cid:2) g ( 2 p z ) FIG. 1. Illustration of the pump-probe scheme. a) The filledarea represents the absorption spectrum of He nanodropletstaken from Ref. [18]. He atomic levels are shown on the right-hand side. b) Potential curves of the singlet-excited He ∗ dimer correlating to the 1 s s S and 1 s p P atomic states(see Methods section). The vertical straight arrows indicatethe pump and probe laser pulses, the dotted curved arrowsindicate the droplet relaxation pathway. The double-sidedarrow in a) illustrates the electron kinetic energy T e . tral pure He nanodroplets. The experiment was carriedout using tunable XUV pulses generated by the seededfree-electron laser (FEL) FERMI [30]. The comparisonof time-resolved photoelectron spectra (PES) with time-dependent density functional theory (TD-DFT) calcula-tions reveals an ultrafast three-step relaxation process.Despite the extremely weak binding of the He atoms inthe droplets and the superfluid nature thereof, energydissipation is very efficient even for the lowest excitedstates; more than 1 eV of electron energy is dissipatedin less than 1 ps due to the coupling of electronic andnanofluid nuclear degrees of freedom.The pump-probe scheme is sketched in Fig. 1. Thegray shaded area in a) shows the absorption spectrumof He nanodroplets taken from Ref. [18]; for reference,the He ∗ atomic levels are given on the right-hand side ofFig. 1 a). The massive broadening and shifting of theatomic-like excited state is due to unfavorable Rydberg-core interaction [31]. The straight vertical arrows illus-trate the pump (purple) and probe (blue) steps, realizedby one XUV pulse and one time delayed UV pulse. Theelectron kinetic energy, T e , measured by means of elec-tron velocity-map imaging (VMI) [30, 32], is indicatedas a black double-sided arrow. The most likely relax-ation pathway for 1 s p P -excited He nanodroplets is in-dicated by the dotted curved arrows. The inset shows aschematic view of a He nanodroplet exposed to a pair oflaser pulses, containing a localized excitation marked by a ) h (cid:1) = 2 1 . 0 e V h (cid:1) + h (cid:1) ' - I P - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5 2 . 00 . 00 . 51 . 01 . 52 . 02 . 5
AD D A h (cid:1) + h (cid:1) ' - I P b ) h (cid:1) = 2 2 . 2 e V S i g n a lD e l a y t i m e ( p s )
Electron kinetic energy (eV) d e l a y ( p s ) 0 . 2 5 0 . 4 5 0 . 6 5 0 . 8 5 2 . 5 5 d e l a y ( p s ) 0 . 2 5 0 . 4 5 0 . 6 5 0 . 8 5 2 . 4 5 d )
Peak area (arb. u.)
D e l a y t i m e ( p s ) c ) p e a k D p e a k A
Peak eK (eV)
D e l a y t i m e ( p s )
FIG. 2. Time-resolved photoelectron spectra of He nan-odroplets containing on average ¯ N = 5 × He atoms excitedto their 1s2s state at the pump photon energy hν = 21 . hν = 22 . hν (cid:48) = 4 . ( ∗ ).Examples of time-dependent PES measured by excit-ing He droplets to the 1 s s S state ( hν = 21 . s p P band ( hν = 22 . T direct e = hν + hν (cid:48) − E i ,where E i = 24 . hν (cid:48) = 4 . t (cid:46) . hν (see Methods section). Peak D [solid lines in Fig. 2 c)]rises within the first 0.5 ps delay time and then slowlydecreases, accompanied by a rapid increase of peak A(dashed lines). The opposite trends of these two compo-nents indicates a redistribution of population from D toA within 0.5-2.5 ps.The energy of peak D [Fig. 2 d)] rapidly decreaseswithin t < t < T S atom e = E (1 s s S ) + hν (cid:48) − E i = 0 . E (1 s s S ) = 20 . s s S -excited He ∗ which iseither weakly bound to the droplet surface or ejectedinto vacuum. This interpretation is supported by PESmeasured for various He droplet sizes presented in thesupplementary material (SM). While for larger dropletspeak A appears slightly later and remains less intensein proportion to peak D, its position converges to thesame final value (0 . ∗ located further inside the He droplet suchthat it is energetically shifted up. When exciting the Hedroplet to its 1 s s S state [Fig. 2 a)], the initial positionof peak D (1 . T S drop e = 21 eV + hν (cid:48) − E i = 1 . hν ,where mainly the 1 s s P droplet state is excited [Fig. 2b)], feature D corresponds to a superposition of S and P states which relaxes into the S droplet state fasterthan the cross correlation of the two laser pulses (250 fsFWHM) and thus cannot be fully resolved. Note thatnot all droplets evolve into the atomic S state (peak A),but nearly the same fraction of atoms remain in featureD which converges to an energy 0.1-0.2 eV above the S atomic value.How can the extremely weakly bound, ultracold vander Waals He clusters induce ultrafast energy relaxationby up to 1.6 eV within 1 ps? To answer this question,we first consider the potential curves of the He ∗ excimercorrelated to the atomic 1 s s S and 1 s p P levels asthe simplest model system for the excited He droplet,shown in Fig. 1 b). The blue-shifted absorption pro-files with respect to the atomic levels can be related tothe steep upwards bending of the optically active A , D and F states in the range of most probable interatomicdistances (3.6 ˚A). Following excitation of the 1 s p P -correlated droplet state, ultrafast internal conversion pro-ceeds due to level crossings at short interatomic distance FIG. 3. Evolution of the simulated He density distributionand of the probability distribution of He ∗ (yellow dot) for aninitial position of the He ∗ at 0 (left column) and at 0 . according to the pathway indicated by the pink dottedarrows. Subsequently, the local environment rearrangesto accommodate the newly formed 1 s s S He ∗ atom. Onthe longer timescale of the fluorescence lifetime, part ofthe He ∗ stabilize by forming He ∗ excimers [19, 20, 33].To simulate this process for He droplets in three di-mensions, we carried out TD-DFT calculations for a He ∗ excitation in the 1 s s S state, as outlined in the Meth-ods section. Note that this transition is forbidden in freeatoms. Therefore it preferentially takes place in the sur-face region of the droplets where the radially-varying Hedensity breaks the symmetry of the free He atom andmakes the transition partly allowed (see Methods).As seen in Fig. 3, the system evolves differently de-pending on the initial position d of He ∗ with respect to Experimental b )
Simulated Te (eV) a ) FIG. 4. Comparison between simulated (a) and measured (b)electron energies for droplet excitation of the 1 s s state at hν = 21 . the droplet surface. The radius of the droplet contain-ing N = 1000 He atoms is 2 . t afterHe ∗ excitation. Animations of these simulations for var-ious d are presented in the SM. When He ∗ is initiallyplaced at the surface of the droplet ( d = 0, left column),the surrounding region is locally compressed and formsa spherical dimple, while He ∗ flies off within t (cid:46) ∗ is initially placeddeeper in the bulk of the droplet ( d = 0 . ∗ , which thenbursts at t ≈ ∗ to escape out ofthe droplet. This scenario has been studied theoreticallyfor photoexcited silver atoms [38], and experimentally forindium atoms embedded in He nanodroplets [14].Besides visualizing the dynamics ensuing excitation ofthe droplet, the TD-DFT model allows us to simulatethe time-dependent PES, see Methods section. Fig. 4 a)shows the resulting electron energies T sim e for differentvalues of d . In the case He ∗ is initialized close to thedroplet surface ( d = 0 and 0 . T sim e rapidly dropsfrom about 1 . t = 0 to the final value of 0 . t = 250-500 fs due to prompt desorption of He ∗ .When He ∗ is placed deeper inside the droplet ( d = 0 . . T sim e from 1 . . . . t = 2 ps.The weighted average of these curves is shown in Fig. 4b) as a dashed line. It nicely follows the experimentalcurve for the droplet feature D [red solid line in Fig. 4b)] up to about 2 ps delay and eventually converges tothe final value of the atomic peak A. In particular, thefast drop between 0 and 1 ps coincides with the dropof peak D energy in the experimental PES [Fig. 2 d)]and with the appearance of peak A as the bubble formsaround He ∗ . Thereafter it slowly decreases from 0 . . ∗ . Note that thesimulated curve for d = 0 . t = 0 . T e to the oscillation of the He bub-ble around He ∗ . He bubble oscillations around impurityatoms (Ag and In) have also been discussed [14, 38].From the comparison of the experimental and theoret-ical results we can now map out the full picture of therelaxation dynamics of excited He nanodroplets: Follow-ing 1 s p P excitation, ultrafast interband relaxation tothe 1 s s S droplet state occurs within <
250 fs inducedby curve crossings of the He ∗ potentials (step 1). Thisis in line with earlier photoluminescence studies whichshowed that the 1 s p P droplet state mainly decays byXUV-photon emission of He ∗ in its A state correlating tothe 1 s s S state of He ∗ [19].Further relaxation proceeds within the 1 s s S dropletband due to the local opening of a void bubble aroundHe ∗ (step 2). The relaxation time associated with thisstep (0 . ∗ within the droplet andof the droplet size ¯ N . This explains the weak variationof the experimental pump-probe PES when changing ¯ N .Subsequently, the bubble migrates to the droplet sur-face and bursts to release a free He ∗ (step 3). The factthat in our experiment, both free and bubble-bound He ∗ are measured at t = 2 . ∗ location and there-fore on ¯ N . A recent study of the excited state dynam-ics of xenon clusters revealed electronic relaxation andthe emission of free xenon atoms [39]. Thus, our find-ings appear not to be specific to He nanodroplets butof rather general relevance for weakly bound condensedphase systems. Eventually, the He ∗ that remain attachedto the droplet surface further relax by forming He ∗ asseen in time-independent measurements [19, 20]. Thelatter radiatively decay to the ground state after under-going vibrational relaxation and partly detaching fromthe droplet [33].The presented measurements show that it is now possi-ble to follow the relaxation dynamics of free nanodropletsin great detail using ultrashort tunable XUV pulses.This paves the way to probing the photodynamics ofmore complex natural or synthetic nanosystems in var-ious regimes of excitation of the valence shell and eveninner shells. METHODS
The experiments described were performed at the LowDensity Matter (LDM) end station of the seeded free-electron laser FERMI [30].
He droplet generation
The He nanodroplets were formed by expanding Hegas from a high pressure reservoir (50 bar) through apulsed, cryogenically cooled Even-Lavie nozzle at a pulserepetition rate of 10 Hz [40]. The mean size of the Hedroplets formed in this way was controlled by changingthe temperature of the nozzle in the range of 5 to 28 K.
Light sources
Linearly polarized XUV pulses in the photon energyrange 21.0-22.2 eV were provided by the FERMI freeelectron laser set to the 5 th harmonic of the seed laserwavelength [41]. The XUV pulses generated in this wayhave a bandwidth < . . filled gas cell andan aluminum filter. The pulse energy in the interactionregion was estimated to be 6 µ J.The UV probe pulses (170 fs duration, 7 µ J pulse en-ergy) were generated by frequency tripling part of the775 nm Ti:Sa laser used to generate the seed light for theFEL. The UV pulses were focused to the same focal spotsize as the XUV beam and superimposed with the XUVpulses in a quasi collinear geometry via reflection froma holey mirror. The temporal cross-correlation functionwas measured using two-photon ionization of He atoms via the He 1 s p P state. A Gaussian fit yields a FWHMof 250 fs. Electron detection, data acquisition and analysis
PES from the He nanodroplets are recorded using aVMI spectrometer, in which electrons are accelerated byelectrostatic imaged onto a position sensitive detectorconsisting of a 75 mm microchannel plate and phosphorscreen assembly. For each step of the pump-probe delayof 50 fs delay, VMI spectrometer images from 2000 shotswere saved. A background subtraction procedure wasimplemented in which the bunches of He nanodropletswere periodically desynchronized from the FEL pulsesso that spurious signals such as scattered light could besubtracted. The VMI spectrometer images for each de-lay were then summed and subsequently inverted usingthe pBasex routine to extract the photoelectron kineticenergy and angular distributions [42]. The PES for eachvalue of the pump-probe delay were fit with a constrained3 Gaussian fit. The time variation of the resulting fitparameters reveal the temporal behavior of the variousionization channels.
Ab-initio calculations of He-He ∗ and He-He + potentials and transition dipole moment The He ∗ -He interaction potentials corresponding to 2 s and 2 p He atomic asymptotes were obtained at the CC3-EOM level [43, 44] by using the Psi4 code [45]. The basisset was taken from Ref. [46]. All the calculated potentialswere corrected for basis set superposition errors by thecounterpoise method of Boys and Bernardi [47].The transition dipole (cid:126)µ s as a function of He ∗ (2 s )-He(1 s ) distance was evaluated at the multi-reference con-figuration interaction (MRCI) level using the Molprocode [48, 49]. The active space consisted of the molecularstates originating from 1 s and 2 s atomic states. Thesecalculations employed the basis set given in Refs. [50]and [51]. The transition dipole induced by the inhomo-geneous He density in the droplet surface region is cal-culated as the vector sum of dipole moments of a singleHe ∗ -He pair weighted by the radial He density distribu-tion, (cid:126)µ drop2 s = (cid:90) d r ρ ( r ) (cid:126)µ s ( | r − r X | )= (cid:90) d r ρ ( r ) | (cid:126)µ s ( | r − r X | ) | r − r X | r − r X | . (1)We find the transition dipole moment to be peaked nearlyat the He droplet radius r N / , r = 2 .
22 ˚A, where ittakes the value | (cid:126)µ drop2 s | = 0 .
17 Debye.
Time-dependent density function theory
The dynamics of the excited He droplet was simulatedusing time-dependent density functional theory (TD-DFT) for droplets consisting of 1000 He atoms [15, 16], towhich the dynamics of the He ∗ atom is self-consistentlycoupled.Due to the light mass of the He ∗ “impurity”, its dy-namics is followed by solving the Schr¨odinger equation forit, where the potential term is given by the He ∗ -dropletinteraction. The expected high velocity of the impuritymakes it advantageous to use the test-particles methodfor solving the Schr¨odinger equation [16, 34]. We ob-tain the excess energy transfered to the photoelectron as T e ( t ) = hν (cid:48) − [ U + ( t ) − U ∗ ( t )]. Here, the interaction ener-gies of He ∗ with its local environment in the He droplet in the ( t -dependent) initial state, U ∗ ( t ) is computed as U ∗ ( t ) = (cid:90) (cid:90) d r d r (cid:48) Φ ( r (cid:48) , t ) ρ ( r , t ) V He − He ∗ ( | r (cid:48) − r | ) , (2)where Φ is the probability density of He ∗ , ρ is theground-state He density, and V He − He ∗ is the He-He ∗ in-teraction pair potential, respectively. The interaction en-ergy of He + with the droplet in the final state, U + ( t ), isobtained in the same way only using the He-He + inter-action potential, V He − He + .Funding from the Deutsche Forschungsgemeinschaft(MU 2347/8-1, STI 125/19-1), Aarhus UniversitetsForskningsfond, National Science Foundation (DMR-1828019), Carl-Zeiss-Stiftung, and Grant No. FIS2017-87801-P (AEI/FEDER, UE) is gratefully acknowledged. ∗ Now at Department of Physics, University of Connecti-cut, Storrs, Connecticut, USA † Now at CERIC-ERIC Basovizza Trieste, Italy ‡ Now at European XFEL, Schenefeld, Germany § Now at CNR-IFN, Milano, Italy[1] C. George, M. Ammann, B. D’Anna, D. J. Donaldson,and S. A. Nizkorodov, Chem. Rev. , 4218 (2015).[2] M. Barbatti, A. J. A. Aquino, J. J. Szymczak, D. Nachti-gallov´a, P. Hobza, and H. Lischka, PNAS , 21453(2010).[3] K. Gokhberg, P. Kolorenˇc, A. I. Kuleff, and L. S. Ceder-baum, Nature , 661 (2014).[4] E. Collini, C. Y. Wong, K. E. Wilk, P. M. G. Curmi,P. Brumer, and G. D. Scholes, Nature , 644 (2010).[5] H.-J. Son, S. Jin, S. Patwardhan, S. J. Wezenberg, N. C.Jeong, M. So, C. E. Wilmer, A. A. Sarjeant, G. C. Schatz,R. Q. Snurr, O. K. Farha, G. P. Wiederrecht, and J. T.Hupp, J. Am. Chem. Soc. , 862 (2013).[6] J. Schneider, D. Bahnemann, J. Ye, G. L. Puma, andD. D. Dionysiou,
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