Dynamics of solvation and desolvation of rubidium attached to He nanodroplets
DDynamics of solvation and desolvation of rubidium attached to He nanodroplets
J. von Vangerow, ∗ O. John, ∗ F. Stienkemeier, and M. Mudrich
Physikalisches Institut, Universit¨at Freiburg, 79104 Freiburg, Germany (Dated: August 20, 2018)The real-time dynamics of photoexcited and photoionized rubidium (Rb) atoms attached to helium(He) nanodroplets is studied by femtosecond pump-probe mass spectrometry. While excited Rbatoms in the perturbed 6p-state (Rb ∗ ) desorb off the He droplets, Rb + photoions tend to sink intothe droplet interior when created near the droplet surface. The transition from Rb + solvation to fullRb ∗ desorption is found to occur at a delay time τ ∼
600 fs for Rb ∗ in the 6pΣ-state and τ ∼ + He ions are found to be created by directly exciting bound Rb ∗ He exciplexstates as well as by populating bound Rb + He-states in an photoassociative ionization process.
I. INTRODUCTION
The laser-induced dynamics of pure and doped helium(He) nanodroplets is currently attracting considerable at-tention [1–7]. While the superfluidity of He nanodropletshas been tested in numerous key experiments by prob-ing stationary properties [8–10], the impact of the quan-tum nature of the droplets on their dynamic responseto impulsive excitation or ionization is much less wellestablished. As a prominent recent example, the rota-tional dynamics of various molecules embedded in Hedroplets induced by impulsive alignment was found tobe significantly slowed down and rotational recurrenceswere completely absent [5]. This indicates that substan-tial transient system-bath interactions are present duringthe laser pulse. In contrast, the vibrational dynamics ofrubidium (Rb) molecules Rb attached to the surface ofHe nanodroplets revealed only slow relaxation and de-phasing proceeding on a nanosecond time scale [2, 11].Various recent experimental and theoretical studieshave addressed the dynamics of solvation and desolva-tion of ionized or excited metal atoms off the surface ofHe nanodroplets [7, 12–21]. So far, these studies haveconcentrated on measuring the total yield and the finalvelocity of the ejected atoms as a function of the atomicspecies and the electronic state of excitation. In this pa-per we present the first time-resolved characterization ofthe desorption process of Rb atoms off the surface of Henanodroplets upon excitation to the droplet-perturbedstates correlating to the 6p atomic orbital. The experi-mental scheme we apply is femtosecond (fs) pump-probephotoionization in combination with time-of-flight mass-spectrometry. We find that the yield of detected Rb + photoions as a function of delay time τ between the ex-citing pump and the ionizing probe pulses is determinedby the interplay of the repulsive interaction of excitedRb ∗ with respect to the He surface and the attractiveinteraction of the Rb + ion with the He surface inducedby photoionization.The Rb ∗ -He droplet repulsion initiates the desorptionof the Rb ∗ atom off the He droplet surface. Except for the ∗ O. John and J. von Vangerow contributed equally to this work lowest excited state of Rb, 5p / , all excited states up tohigh Rydberg levels experience strong repulsion from Hedroplets [22, 23]. In contrast, the Rb + -He droplet attrac-tion causes the Rb + ion to fall back into the He dropletwhen created near the He droplet surface at short delaytimes [19, 21]. Atomic cations are known to form stable“snowball” structures consisting of a cationic core whichis surrounded by a high density shell of He atoms. As aresult, free Rb + ions appear in the mass spectrum onlyafter a characteristic pump-probe delay time τ D , whichdepends on the state the Rb atom is initially excited to.In addition to neat Rb + atomic ions, the photoioniza-tion mass spectra contain Rb + He molecular ions in thefull range of laser wavelengths correlating to the droplet-perturbed Rb 6p-state. The occurrence of such molecu-lar ions has previously been interpreted by the formationof metastable ‘exciplex’ molecules [1, 7, 14, 16, 24, 25].These bound states of excited metal atoms and one orfew He atoms can be populated either by a tunnelingprocess [12, 26–28] or by direct laser-excitation of boundstates in the metal atom-He pair potential [14, 16, 17, 29].In the former case, exciplex formation times (cid:38)
50 ps areexpected [24, 27], whereas in the latter case, exciplexesare created instantaneously. Thus, previous pump-probemeasurements revealing exciplex formation times of 8 . . He and Rb He, respectively, upon ex-citation into the droplet-perturbed 5p / -state could notbe consistently interpreted [24].In the present study we observe a time-delayed increaseof the Rb + He signal as for Rb + indicating that the pump-probe dynamics is primarily determined by the competi-tion between desorption of the Rb ∗ He exciplex off the Hedroplet surface and the Rb + He cation falling back intothe He droplet interior. Moreover, a pronounced max-imum in the Rb + He signal transients indicates that anadditional Rb + He formation channel besides photoion-ization of Rb + He exciplexes is active – photoassociativeionization (PAI) of the desorbing Rb atom and a He atomout of the droplet surface. PAI is a well-known processwhere a bound cationic molecule or complex is formedby photoionization or photoexcitation into autoionizingstates of an atom or molecule of a collision complex [30].PAI is a special case of traditional associative ionizationwhere a bound molecular cation is formed in a binarycollision of an electronically excited atom [31]. In either a r X i v : . [ phy s i c s . a t m - c l u s ] J u l case the binding energy is taken away by the electronemitted in the process. II. EXPERIMENTAL SETUP
The experimental setup is similar to the previouslyused arrangement [11, 14] except for the ionization anddetection schemes. He droplets are produced by a con-tinuous supersonic expansion of He 6.0 through a 5 µ mnozzle at a pressure of 50 bar. The transversal velocityspread of the beam is reduced by placing a 400 µ m skim-mer 13 mm behind the nozzle. Unless otherwise stated,the nozzle temperature is kept at 17 K. This results ina log-normal distribution of the He droplet size with amean size of 1 . × He atoms. Subsequently, thedroplet beam passes a mechanical chopper and a Rb-filledcell of length 1 cm, stabilized at a temperature of 85 ◦ C.At the corresponding vapor pressure, most droplets pickup on average one Rb atom following poissonian statis-tics. By overlapping the droplet beam with the output ofthe fs laser, we resonantly excite and ionize the dopantatom.In contrast to previous studies, we use amplified fs laserpulses generated by a regenerative amplifier operated ata pulse repetition rate of 5 kHz. At this repetition rate,multiple excitations of Rb atoms by subsequent pulsesfrom the pulse train are safely excluded. The pulses arefrequency-doubled in a BBO crystal resulting in a pulseduration of t p = 120 fs with a variation for different lasercenter wavelengths of 20 fs. Two identical, time-delayedpump and probe pulses are generated by means of a me-chanical delay line. The laser beam is focused into thevacuum chamber using a 30 cm lens which leads to a peakintensity in the range of 5 × Wcm − .Photoions are detected by a time-of-flight (TOF) massspectrometer in Wiley-McLaren configuration mountedin-line with the He droplet beam [32]. At the end of thedrift tube a high negative potential is applied to furtheraccelerate the arriving ions which boosts the efficiencyof detecting large cluster masses in the 10 amu rangeusing a Daly-type detector [33]. The latter consists ofa Faraday cup, a scintillator with an optical bandpassinterference filter and a photomultiplier tube. In caseof electron detection, a simple electrode setup consistingof a repeller, an extractor grid and a channeltron detec-tor with positive entrance potential is used. For bothdetectors, the resulting pulses are amplified, threshold-discriminated and acquired by a fast digitizer. Whendetecting heavy masses a counting unit is used. III. Rb DESORPTION DYNAMICS
In the present paper we concentrate on the fs pump-probe dynamics of Rb atoms attached to He nanodropletswhich are excited to droplet-perturbed states correlatingto the atomic 6p-state. These states have previously been S P R b H e +2 0 0 0 S D i s t a n c e f r o m t h e d r o p l e t s u r f a c e ( Å )
R b + Wave number (1000 cm-1) e - H e N R b
FIG. 1. Potential energy diagram of the Rb-He nanodropletcomplex. Vertical arrows depict the photo-excitation and ion-ization processes. The potential curves of the neutral Rb-He complex are taken from [23], the one of the Rb + -He complex is obtained from the Rb + -He pair potential [36] onthe basis of the He density distribution of the groundstateRbHe complex [37]. The two peaks plotted vertically onthe left-hand scale show the expected excitation spectrumbased on these potentials. studied using nanosecond pulsed excitation and velocity-map imaging of photoions and electrons [14, 16]. Dueto the interaction of the excited Rb atom with the Hedroplet surface, the 6p-state splits up into the two states6pΣ and 6pΠ according to the pseudo-diatomic modelwhich treats the whole He droplet, He N , as one con-stituent atom of the RbHe N complex [23, 34, 35].Using the RbHe N pseudo-diatomic potential curves forthe 5sΣ electronic groundstate and the 6pΣ , Π excitedstates we compute the Franck-Condon profiles for theexpected vertical excitation probability using R. LeRoy’sprogram BCONT [38]. The corresponding transitionprobability profile is depicted on the left-hand side ofFig. 1. The experimental excitation spectrum is in goodagreement with the calculated one apart from the factthat the experimental peaks are somewhat broader [14].Since both 6pΣ and 6pΠ pseudo-diatomic potentials areshifted up in energy by up to 1200 cm − with respect tothe atomic 6p level energy, we expect strong repulsionand therefore fast desorption of the Rb atom off the Hedroplet surface to occur following the excitation.However, upon ionization of the excited Rb atom byabsorption of a second photon (vertical arrow on theright-hand side of Fig. 1), the interaction potential sud- Rb+signal(arb.u.)
FIG. 2. Pump-probe transient Rb + ion count rates recordedfor various wavelengths λ of the fs laser. At λ (cid:38)
409 nm,excitation occurs predominantly to the 6pΠ-state, at λ (cid:46) denly turns weakly attractive. Thus, the Rb + ion maybe expected to turn around and to fall back into the Hedroplet provided ionization occurs at short delay timesafter excitation such that the desorbing Rb ∗ picks uponly little kinetic energy E kin, Rb ∗ ( R ) < E pot, Rb + ( R ) . (1)Here, E pot, Rb + ( R ) denotes the lowering of the potentialenergy of the Rb + ion due to the attractive interactionwith the He droplet at the distance R from the dropletsurface. Eq. 1 holds for short distances R < R c fallingbelow a critical value R c . When assuming classical mo-tion, we can infer from Eq. 1 the critical distance R c forthe turn-over. From simulating the classical trajectory R ( t ) we can then obtain the delay time τ c at which theturn-over occurs. In the following we refer to τ c as ‘fall-back time’. Thus, when measuring the number of freeRb + ions emitted from the He droplets by pump-probephotoionization we may expect vanishing count rates atshort delays τ < τ c due to the Rb + ions falling back intothe droplets, followed by a steep increase and subsequentconstant level of the Rb + signal at delays τ > τ c . ( b ) R b H e +8 7 R b H e +8 5
R b H e +8 7
R b + I o n m a s s ( a m u ) 1 7 K
R b + ( a ) Ion signal (arb. u.)
N u m b e r o f H e a t o m s 2 1 K 1 9 K 1 7 K
FIG. 3. (a) Typical mass spectra recorded for Rb-doped Henanodroplets by fs photoionization taken at a center wave-length λ = 415 nm and a 5 ps pump probe delay. In additionto the atomic isotopes Rb + and Rb + the mass spectracontain Rb + He and Rb + He molecular ions. (b) An extendedview of mass spectra taken at various nozzle temperatures us-ing single fs pulses at λ = 415 nm reveals the presence of largemasses of unfragmented ion-doped He droplets Rb + He N . A. Experimental results
Fig. 2 shows the transient Rb + ion signals measuredby integrating over the Rb and Rb mass peaks inthe time-of-flight mass spectra recorded for each valueof the pump-probe delay. The shown data are obtainedby subtracting from the measured ion signals the sum ofion counts for pump and probe laser pulses only. Theerror bars stem from error propagation taking into ac-count the uncertainties associated with the different sig-nal contributions. By tuning the wavelength of the fslaser λ we can excite predominantly the 6pΠ ( λ (cid:38) λ (cid:46) N complex.As expected, we observe a step-like increase of the Rb + -yield at delays ranging from 600 fs ( λ = 401 nm) up toabout 1500 fs ( λ = 415 nm). The signal increase occursat shorter delays when exciting into the more repulsive6pΣ-state because the Rb atom moves away from theHe droplet surface faster than when it is excited into theshallower 6pΠ-state. The rising edge of the signal jump isextended over a delay period of about 400 fs, partly dueto the finite length and bandwidth of the laser pulses.Desorption along the 6pΠ-potential appears as an evensmoother signal rise, indicating that a purely classicalmodel is not suitable for reproducing the observed dy-namics. For laser wavelengths λ <
409 nm we observe aweakly pronounced double-hump structure with maximaaround 800 and 1800 fs, respectively, which we discuss insection III B.Before discussing our model calculations for these tran-sients, let us first examine the measured time-of-flightmass spectra in more detail. Fig. 3 (a) depicts a represen-tative mass spectrum in the mass range around 100 amuat a pump-probe delay of 5 ps and a center wavelength λ = 415 nm. The spectrum is averaged over 5000 lasershots. Clearly, the dominant fragments in this massrange are neat Rb + ions at 85 and 87 amu, where thedifferent peak heights reflect the natural abundances ofisotopes (72 and 28 %, respectively). Even when ion-izing with single laser pulses the mass spectra containbare Rb + ions at a low level. We attribute this to afraction of the Rb atoms desorbing off the droplets andsubsequently ionizing within the laser pulse. A contri-bution to the Rb + signal may come from free Rb atomsaccompanying the droplet beam as a consequence of thedetachment of the Rb atom from the droplet during thepick-up process. Aside from neat Rb + atomic ions, thepump-probe mass spectra feature peaks at 89, 91, and95 amu, which evidence the formation of Rb + He andRb + He molecular ions. These masses are usually at-tributed to photoionization of bound metastable Rb ∗ Heexciplexes [1, 14, 17, 24].In addition to these discrete mass peaks, we mea-sure extended mass distributions reaching up to 64,000amu using our time-of-flight mass spectrometer whichis optimized to detecting cluster ions. These distribu-tions are in good agreement with the size distributionsof pure He nanodroplets generated in a sub-critical ex-pansion [39, 40]. From comparing the peak areas of thelight masses Rb + , Rb + He n , n = 1 , + He N we deduce that by ioniz-ing with single pulses a fraction of (cid:46)
10% of the dopedHe droplets fragments into free atomic or molecular ions.The larger part of the ionized Rb-doped He droplets gen-erates unfragmented Rb + He N due to the sinking of theRb + ion into the He droplet and the formation of a sta-ble snowball complex [19]. When adding an additionaltime-delayed probe pulse we may expect to alter this ra-tio by depleting the unfragmented Rb + He N fraction infavor of creating free ions Rb + and Rb + He , ions afterdesorption.Indeed, the delay-dependent peak integrals of the mea-sured mass peaks at λ = 400 nm confirm this picture,see Fig. 4 (a) and (b). While the atomic Rb + ion sig-nal sharply increases around 600 fs and remains largelyconstant for longer delays, the Rb + He N signal displaysthe opposite behavior. The maximum signal level at zerodelay significantly drops around τ = 600 fs and remainslow for long delay times.In addition to the mass-resolved ion signals we havemeasured the total yield of photoelectrons, depicted inFig. 4 (c). From comparing the electron counts withand without blocking the He droplet beam we find thatfor pump-probe ionization >
79% of photoelectrons cor-relates with the Rb-doped He droplet beam, <
21% isattributed to ionization of Rb and other species in thebackground gas. The observation that the electron countrate remains constant within the experimental scatter inthe entire range of pump-probe delays indicates that thephotoionization efficiency (cross-section) of a Rb atom islargely independent of its position with respect to the + R b H e
N + e - Ionsignal(arb.u.) ( c )( b ) e-signal
P u m p - p r o b e d e l a y ( f s )( a )
FIG. 4. Transient ion and electron signals measured at λ =400 nm. The ion signal traces (a and b) are obtained fromintegrating over the free atomic Rb + ion peaks and over thecharged He droplet mass distribution, respectively. The totalphotoelectron signal (c) is measured using a simple electrondetector. The thin smooth lines are fits to the data. He droplet surface. These observations further supportour interpretation of the step-like increase of Rb + countsin terms of the competition between desorption of ex-cited Rb atoms and solvation of Rb + cations into the Hedroplets.Fig. 5 (b) displays a compilation of the critical delaysfor all measured laser wavelengths which we obtain byfitting the experimental data with an error function, f Rb + ( t ) = A · { erf [( t − τ c ) /σ ] + 1 } (2)of variable amplitude A , width σ and position τ c . Shownare the results for the raw Rb + and Rb + He N transientsas well as those obtained by fitting the sum of the tran-sients of Rb + atomic and Rb + He molecular ions. In par-ticular for the 6pΠ state, the latter signal more accuratelyreflects the dynamics of the fall-back process than theindividual Rb + and Rb + He transients since additionaltransient redistribution of population between Rb + andRb + He channels, which we discuss below, cancels out.Correspondingly, the fitted time constants of the summedRb + and Rb + He transients and those of Rb + He N are ingood agreement. This confirms our conception that thelight ions fall back to produce heavy cluster ions at shortdelays. Fig. 5 (c) will be discussed in section IV. B. Simulations
Further support for our interpretation of the experi-mental findings is provided by classical trajectory simula-tions of the dynamics of the pump-probe process. In thismodel, the Rb atom and the He droplet surface are takenas two point-like particles which propagate classically ac-cording to the pseudo-diatomic model potentials [23, 37].Note that these potentials were calculated based on theminimum-energy configuration of a droplet consisting of ( b )( a ) N e f f = 1 0N e f f = 1 0 0N e f f = 1 0 0 0 R b + , 6 p S R b + , 6 p P ( c ) R b + R b + H e N R b + H e + R b + Fall-backtime t c(ps) R b H e + t E(ps)
L a s e r w a v e l e n g t h l ( n m ) FIG. 5. Simulated (a) and experimental (b) fall-back timesas a function of the laser wavelength, derived from the ris-ing edges of the pump-probe transients. The curves in (a)are obtained for various effective masses m He n = N eff m He ofthe He droplet in units of the He atomic mass m He . The dif-ferent symbols in (b) denote the experimental fit results forRb + , Rb + He+Rb + and Rb + He N signals. Panel (c) showsthe exponential decay constants from fits of the Rb + He iontransients with Eq. (4). N = 2000 He atoms subjected to the external potential ofan Rb atom in the electronic ground state. The classicalequation of motion µ ¨ R = − dV ( R ) dR , (3)is solved numerically. Here, V = V Σ , Π , Rb + ( R ) denotesthe potential curves of the excited and ionic states, and R ( t ) is the distance between the Rb atom and the He dim-ple at the droplet surface. The initial value of the Rb-Hedroplet distance is the position of the minimum of thegroundstate potential well (6.4 ˚A). Eq. 3 is first solvedfor the neutral excited state potential V Σ or V Π up to thepump-probe delay time τ . Subsequently, the Rb atom isconsidered to be ionized and the particle is propagatedfurther using the ionic Rb + -He N potential V Rb + . Thereduced mass µ = m Rb m He n / ( m Rb + m He n ) is given bythe mass of the Rb atom or ion, m Rb , and the effectivemass of the He droplet, m He n . We set m He n = 40 amufor the propagation of the excited as well as for the sub-sequent propagation of the Rb + ion with respect to theHe droplet. This value is based on previous experimentalas well as theoretical findings [16].The motion of the excited and subsequently ionizedRb atom with respect to the He droplet surface is illus-trated in Fig. 6 for different initial conditions. The time- ( b ) H e N R bR bH e N Distance from droplet center (Å)
T i m e ( p s )( a )
H e N R bR bH e N T i m e ( p s )
FIG. 6. Classical trajectories of the excited and ionized Rbatom initially located in a dimple near the He droplet surface.(a) At 6pΠ-excitation ( λ = 415 nm) and long pump-probedelay τ = 500 fs the Rb atom fully desorbs off the He dropletand propagates as a free Rb + cation after ionization. (b) Atshorter τ = 400 fs the Rb + ion turns over and falls backinto the He droplet. The schemes at the bottom visualize thedynamics for increasing time from left to right. dependent positions of the Rb atom and the He surfaceare depicted as red and blue lines in the upper parts. Thelower parts are graphical visualizations of the dynamics.Fig. 6 (a) depicts the case when the excitation of the Rbatom, which is initially located in the groundstate equi-librium configuration of the RbHe N complex, occurs at t = 0 and ionization is delayed to τ = 500 fs. The laserwavelength is set to λ = 415 nm where the motion fol-lows the 6pΠ-potential. In this case the excited Rb atomfully desorbs off the He droplet and continues to moveaway from the droplet after its conversion into an ion. Inthe case of shorter delay τ = 400 fs between excitationand ionization, shown in Fig. 6 (b), the Rb atom turnsover upon ionization as a result of Rb + -He N attractionand falls back into the He droplet.For assessing the effect of an initial spread of Rb-He N droplet distances R due to the broad laser bandwidthand of the finite length of the laser pulses t p we extendthe classical trajectory calculation to a mixed quantum-classical simulation which includes an approximate de-scription of the quantum wave packet dynamics of thesystem.The initial wave packet is obtained by transforming thespectral profile of the laser into a distribution as a func-tion of R using the potential energy difference betweenthe initial 5sΣ and the final 6pΣ , Π pseudo-diatomicstates. We use a Gaussian-shaped laser profile with afull width at half maximum, ∆ ν , inferred from measuredspectra. Typically ∆ ν ≈ i and each segment is propagatedindividually according to Eq. 3 where R ( t ) is replacedby R i ( t ) representing the Rb-He N distance for the i -th P S PS Rb+signal(arb.u.)
FIG. 7. Semiclassical simulations of the yield of free Rb + ionscreated by excitation and time-delayed ionization for variouscenter wavelengths λ of the laser pulses. See text for details. segment. Convergence of the final results with respect tothe number of segments has been checked.This simplified description of the wave packet dynam-ics is justified because no quantum interference effects areexpected for this simple dissociation reaction. Compar-ison with the full quantum simulation of the desorptionprocess yields excellent agreement within the propaga-tion time range relevant to the experiment.Simulated transient yield curves as a function of thepump-probe delay τ are obtained by taking the weightedsum of the segments which have propagated outwardsup to very large distances after long propagation times.This sum we identify with the fraction of desorbed atoms.Those segments which have turned over towards shortdistances are considered to contribute to the Rb + ionsfalling back into the droplet. For those segments thecondition formulated initially (inequality (1)) is fulfilledimplicitly. The finite duration of the excitation processis taken into account by convolving the resulting yieldcurves with the autocorrelation function of the two laserpulses.The resulting simulated yields of free Rb + ions as afunction of τ are depicted in Fig. 7 for various centerwavelengths λ of the laser pulses. The obtained curvesqualitatively resemble the experimental ones in many re-spects. Excitation at long wavelengths λ >
409 nm,at which predominantly the more weakly repulsive 6pΠstate is populated, induces a smooth signal increase atabout τ = 400 fs. At λ <
409 nm, where predomi- nantly the 6pΣ-state is excited, the signal rise occursaround τ = 210 fs, considerably earlier than for 6pΠexcitation. This result qualitatively agrees with the ex-perimental finding see Fig. 5 (b). Moreover, the superpo-sition of the two rising edges at intermediate wavelengths λ ∼
409 nm may provide an explanation for the double-hump structure observed in the experimental Rb + tran-sients at λ <
409 nm. However, the simulated risingedges occur at significantly shorter delay times than inthe experiment, roughly by a factor 2 for excitations tothe 6pΣ-state and up to a factor 4 for the 6pΠ-state.The discrepancy between the experimental results andthose of the simulations, shown in Fig. 5 (b), is presenteven when assuming very large effective masses of theHe droplet m He n > N groundstate equilibrium con-figuration [23, 37]. However, transient deformations ofthe He droplet surface in the course of the dynamicsare likely to significantly modify the effective Rb ∗ -He N interactions. Recent time-dependent density functionalsimulations show a complex ultrafast response of theHe droplet to the presence of a Rb + ion near the sur-face [21]. In particular when the desorption dynamicsis slow (Π-state) a complex reorganization of the Hedroplet surface during the Rb desorption process maybe expected [16]. A clear manifestation of the break-down of the simple pseudo-diatomic model is the forma-tion of Rb ∗ He exciplexes which we discuss in the follow-ing section. Recently, M. Drabbels and coworkers sug-gested that the pseudo-diatomic potentials of the excitedNa ∗ He N complex may be transiently shifted and even in-tersect [17, 28]. Detailed three-dimensional simulationsincluding the full spectrum of properties of He dropletsare needed to provide an accurate description of this kindof dynamics [16, 20, 21, 41]. Experimentally, the timeevolution of the interaction potential energies will be vi-sualized by means of fs time-resolved photoelectron spec-troscopy in the near future. IV. RbHe + DYNAMICS
Aside from free Rb + ions, fs photoionization of Rb-doped He nanodroplets generates Rb + He n , n = 1 , λ = 415 nm corre-sponding to the 6pΠ excitation, see Fig. 3. At λ = 399nm (6pΣ-excitation), abundances are 4% and 1%, respec-tively. Free Rb + He ions are associated with bound statesin the Rb ∗ He excited states pair potentials, so called ex-ciplexes. Both the 6pΣ and the 6pΠ-states of the RbHediatom feature potential wells which sustain bound vi-brational states that can be directly populated by laserexcitation out of the groundstate of the RbHe N com-plex [14, 29]. Thus, exciplexes are directly created in RbHe+signal(arb.u.)
P u m p - p r o b e d e l a y ( f s ) 3 9 9 n m
FIG. 8. Experimental yields of Rb + He molecular ions as afunction of pump-probe delay for various center wavelengthsof the laser pulses. The thin smooth lines are fits to the data. a process akin to photoassociation, in contrast to previ-ously observed Na ∗ He and K ∗ He exciplexes which wereformed by an indirect tunneling process upon excitationof the lowest pΠ-states [27, 28].Exciplex formation is the only route to producingRb + He ions by photoionization using continuous-wave ornanosecond lasers, where ionization takes place at longdelay times when the dynamics of exciplex formation anddesorption off the droplets is long complete. In fs ex-periments, however, ionization can be triggered beforeor during the process of desorption of the excited atomor exciplex off the droplet surface. In this case, due tothe attractive Rb + -He potential a bound Rb + He molec-ular ion can be formed upon ionization, even if the ex-cited Rb ∗ -He interaction does not sustain bound statesof the neutral diatom. The process of inducing a molec-ular bond between two initially unbound neutral speciesby photoionization is known as photoassociative ioniza-tion [31]. A. Experimental results
The transient yield of Rb + He for various laser wave-lengths is displayed in Fig. 8. Similarly to the Rb + tran-sients, we measure vanishing Rb + He pump-probe signalcontrast around zero delay. For increasing laser wave-length from λ = 399 up to 418 nm, which corresponds to ( b )( a ) Distance from droplet center (Å)
R bH e N H e
T i m e ( p s )
R bH eH e N H e N H e R b R bH e N H e
T i m e ( p s )
FIG. 9. Classical trajectories of the Rb-He-He N three-bodysystem at λ = 409 nm. The schemes at the bottom visualizethe various dynamics for increasing time from left to right. (a)The excited Rb atom departing from the He droplet surfacesuddenly experiences Rb + He pair attraction upon ionizationat τ = 400 fs (a). Consequently, a He atom attaches to the Rbatom while it leaves the droplet. (b) For short delay τ = 350 fsat λ = 409 nm a Rb + He molecule forms as in (a) but theattraction towards the He droplet makes it turn over and fallback. the crossover from the 6pΣ to the 6pΠ excited pseudo-diatomic states, a step-like increase of the Rb + He ionsignal occurs at delays ranging from τ = 500 fs up toabout 2000 fs. Besides, at λ (cid:46)
415 nm we measure atransient overshoot of the Rb + He signal by up to about100% of the signal level at long delays. The transientyield of Rb + He is fitted using the model function f Rb + He ( t ) = f Rb + ( t )( Ee − t/τ E + 1) . (4)As for the Rb + case, f Rb + ( t ) models the fall-back dynam-ics by Eq. 2. Additionally, the exponential function withamplitude E and time constant τ E takes the transientovershoot into account, whereas the additive constantaccount for a τ -independent Rb + He formation channel.The exponential time constants τ E are plotted as blackcircles in Fig. 5 (c). To obtain these values, the param-eters τ c and σ are taken as constants from the fit of thesum of Rb + and Rb + He signals with Eq. 2. Here wemake the assumption that the fall-back dynamics is onlyweakly perturbed by the attachment of a He atom to theRb atom or ion, which is confirmed by our simulations.
B. Simulation of photoassociative ionization
For a more quantitative interpretation of the Rb + Hetransients we extend our classical and mixed quantum-classical models to the one-dimensional three-bodyproblem in the second stage of the calculation after ion-ization has occurred by including one individual He atomout of the surface layer. The classical trajectories are nowobtained by solving three individual coupled equationsof motion for the three individual particles Rb + , He, andHe n . The Rb ∗ -He N interaction leading to desorption isrepresented by the pseudodiatomic potentials as before. S P
RbHe+signal(arb.u.)
P u m p - p r o b e d e l a y ( f s ) 3 9 9 n m
FIG. 10. Simulations of the yield of free Rb + He-moleculescreated by excitation and time-delayed ionization for variouscenter wavelengths of the laser pulses. See text for details.
The Rb + -He dynamics is initialized by the velocity anddistance of the dissociating Rb ∗ He N complex at themoment of ionization. The Rb + -He pair interaction isgiven by the Rb + -He pair potential [36] augmented by a16.7 cm − deep potential step to account for the He-He N extraction energy as suggested by Reho et al. [14, 24, 27].Exemplary trajectories are shown in Fig. 9 for twocases at λ = 409 nm. For long pump-probe delaysthe Rb + ion leaves the He droplet without attachinga He-atom, as shown in Fig. 6. However, there is arange of delays in which the desorbing Rb atom is farenough away from the droplet so that it will not fallback upon ionization, but it is still close enough toattract a He atom out of the droplet surface so as toform a bound molecular ion by PAI (Fig. 9 (a)). Fig. 9(b) illustrates the dynamics at short delay when theattractive forces acting between the Rb + ion and thedroplet surface prevent the full desorption and Rb + -Hepairwise attraction leads to the formation of Rb + He.For simulating the transient Rb + He yields to comparewith the experimental data shown in Fig. 8 we extendthe mixed quantum-classical model for the desorption dy-namics of bare Rb described in Sec. III B. It is augmentedby computing the probability of populating bound vibra-tional states of the Rb + He molecule for each segment ofthe Rb wave packet upon ionization as the sum of spatial overlap integrals p P AIi ( τ ) = (cid:88) v (cid:12)(cid:12)(cid:12)(cid:12)(cid:90) ∞∞ φ v ( R ) · ψ i ( R, τ ) dR (cid:12)(cid:12)(cid:12)(cid:12) . (5)Here ψ i denotes the i -th wave packet segment and φ v stands for the vibrational wave functions of Rb + He cal-culated using R. J. LeRoy’s LEVEL program [42] for the6pΣ , Π pair potentials of Rb + He [29]. The identifica-tion of bound and free Rb + He ions in the simulation isbased on analyzing the final Rb + -He and Rb + He-He N distances after long delays τ >
10 ps, respectively. Thefinal probability P of detecting a Rb + He molecule is ob-tained by summing up the detection probabilities for ev-ery segment, P ( τ ) = (cid:88) i p Di ( τ ) · ( p P AIi ( τ ) + p ex ) . (6)In agreement with Eq. 4, p Di denotes the desorptionprobability and p ex is the probability of creating a boundneutral Rb ∗ He exciplex, which is assumed to occur in-stantaneously upon laser excitation and thus does notdepend on τ . Since the relative contributions of PAIand direct exciplex formation are not precisely known weresign from quantitatively modeling the relative efficien-cies of the two pathways leading to free Rb + He. Insteadwe adjust them to the experimental transients by taking p ex as a free fit parameter. The transient signal P ( τ )is finally convoluted with the intensity autocorrelationfunction of the laser pulses, as for the Rb + transients.The resulting simulated yields of free Rb + He molecu-lar ions are depicted in Fig. 10. Clearly, the same gen-eral trends as for neat Rb + ions are recovered: (i) atshort delay times τ <
200 fs the appearance of Rb + Heis suppressed due to the falling back of the ion into theHe droplet; (ii) longer laser wavelengths λ (cid:38)
409 nm(6pΠ-excitation) lead to weaker repulsion and thereforeto the delayed appearance of free ions as compared to6pΣ-excitation at λ (cid:46)
409 nm. These results again qual-itatively agree with the experimental findings but thesimulated appearance times are shorter by a factor 2-4,as shown in Fig. 5. As in the Rb + case we attributethese deviations to the use of pseudo-diatomic potentialscalculated for the frozen RbHe N groundstate complex.Moreover, the simulation reproduces a signal overshootaround τ = 300 fs at short wavelengths, which is dueto the contribution of the photoassociative ionizationchannel. Association of a bound Rb + He ion is possi-ble only at sufficiently short Rb-He distances given atdelays τ (cid:46)
600 fs for 6pΣ-excitation and τ (cid:46)
900 fs for6pΠ-excitation, respectively. At these delay times, thePAI signal adds to the signal due to ionization of Rb ∗ Heexciplexes formed directly by the pump pulse. Note thatwe have adjusted to the experimental curves the relativecontributions to the total Rb + He signal arising from PAIand from exciplex ionization. Therefore our model doesnot permit a quantitative comparison with the experi-mentally measured signal amplitudes. A more detailedthree-dimensional simulation of the dynamics is neededfor a fully quantitative interpretation [20]. Nevertheless,we take the simulation result as a clear indication thatPAI is an additional channel producing He-containingionic complexes which needs to be considered in exper-iments involving photoionization of dopants attached toHe droplets when using ultrashort pulses.We note that in the particular case of exciting into the6pΣ-state of the RbHe N complex, unusual Rb + He sig-nal transients may arise from the peculiar shape of theRbHe pair potential curve which features a local poten-tial maximum at intermediate Rb-He distance [14, 29].This potential barrier causes the highest-lying Rb ∗ He vi-brational states to be predissociative. Semi-classical es-timates yield predissociation time constants for the twohighest vibrational levels v = 5 and 6 of 3.5 ns and 2.2 ps,respectively. However, these values significantly exceedthe exponential decay times inferred from the measuredtransients (see Fig. 5 (c)). Moreover, we may expectthat not only the highest vibrational levels are populated.Note that for the case of Na ∗ He and K ∗ He formed in thelowest 3pΠ and 4pΠ states, respectively, all vibrationallevels including the lowest ones were found to be pop-ulated to varying extents depending on the laser wave-length [26]. Therefore we tend to discard predissociationof Rb ∗ He exciplexes as the origin of the peculiar shape ofthe Rb + He transients, although we cannot strictly ruleit out. More insight into the Rb + He dynamics may beprovided by further measurements using electron and ionimaging detection.
V. SUMMARY
This experimental fs pump-probe study discloses thecompeting dynamics of desolvation and solvation of ex-cited and ionized states, respectively, of Rb atoms whichare initially located at the surface of He nanodroplets.The generic feature of the pump-probe transients – thetime-delayed appearance of photoions – is shown to re-sult from the falling back of ions into the droplets whenthe ionization occurs at an early stage of the desorptionprocess. This interpretation is backed by the experimen-tal observation of the opposing trend when measuringthe yield of unfragmented He nanodroplets containing aRb + ion. Furthermore, mixed quantum-classical model calculations based on one-dimensional pseudo-diatomicpotentials confirm this picture qualitatively. The limitedquantitative agreement with the experimental results isattributed to the use of model potentials in the calcu-lations, which do not account for the transient responseof the He density upon excitation and ionization of theRb dopant atom. Much better agreement may be ex-pected from three-dimensional time-dependent densityfunctional simulations [16, 21] of the full pump-probe se-quence which are currently in preparation.Pump-probe dynamics similar to the Rb + case is ob-served when detecting Rb + He molecular ions which pri-marily result from photoionization of Rb ∗ He exciplexes.The peculiar structure of the Rb + He transients as well asextended model calculations indicate that photoassocia-tive ionization is an additional mechanism of forming He-containing ionic complexes in fs experiments. However,the dynamics resulting from the additional photoasso-ciative ionization channel cannot unambiguously be dis-tinguished from predissociation of Rb ∗ He exciplexes inhigh-lying vibrational levels of the 6pΣ-state.These results shed new light on the interpretation ofthe Rb + He pump-probe transients measured previouslyby ionizing via the lowest 5pΠ excited state [1, 24]. Thesignal increase at short delays was interpreted as themanifestation of the formation dynamics of the Rb ∗ Heexciplex by a tunnelling process. Possibly the compet-ing desorption of the excited neutral and the fall-back ofthe photoion actually more crucially determines the risetime of the Rb + He signal in those transients. This issuewill be elucidated in future experiments using two-colorpump-probe ionization via the 5p droplet states and atlow laser repetition rate so as to exclude concurrent ef-fects by subsequent laser pulses. Furthermore, we willinvestigate the photodynamics of metal atom-doped Henanodroplets in more detail by applying refined detec-tion schemes such as ion and electron imaging [14, 16]and coincidence detection [43, 44].
ACKNOWLEDGMENTS
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