Desorption Dynamics of Rb_2 Molecules off the Surface of Helium Nanodroplets
A. Sieg, J. von Vangerow, F. Stienkemeier, O. Dulieu, M. Mudrich
DDesorption Dynamics of Rb Molecules off theSurface of Helium Nanodroplets
A. Sieg, † J. von Vangerow, † F. Stienkemeier, † O. Dulieu, ‡ and M. Mudrich ∗ , † Physikalisches Institut, Universität Freiburg, 79104 Freiburg, Germany, and Laboratoire AimÂt’eCotton, CNRS, UniversitÂt’e Paris-Sud, ENS Cachan, UniversitÂt’e Paris-Saclay, 91405 OrsayCedex, France
E-mail: [email protected]
Phone: +49 (0)761 2038405. Fax: +49 (0)761 2037611
Abstract
The desorption dynamics of rubidium dimers (Rb ) off the surface of helium nanodropletsinduced by laser excitation is studied employing both nanosecond and femtosecond ion imag-ing spectroscopy. Similarly to alkali metal atoms, we find that the Rb desorption processresembles the dissociation of a diatomic molecule. However, both angular and energy distribu-tions of detected Rb + ions appear to be most crucially determined by the Rb intramoleculardegrees of freedom rather than by those of the Rb He N complex. The pump-probe dynamics ofRb + is found to be slower than that of Rb + pointing at a weaker effective guest-host repulsionfor excited molecules than for single atoms. ∗ To whom correspondence should be addressed † Physikalisches Institut, Universität Freiburg, 79104 Freiburg, Germany ‡ Laboratoire AimÂt’e Cotton, CNRS, UniversitÂt’e Paris-Sud, ENS Cachan, UniversitÂt’e Paris-Saclay, 91405Orsay Cedex, France a r X i v : . [ phy s i c s . a t m - c l u s ] A ug ntroduction The dynamics of pure and doped helium (He) nanodroplets induced by laser excitation is cur-rently being studied both experimentally and theoretically by various groups.
The goal is tobetter understand the dynamic response of a microscopic superfluid to an impulsive perturba-tion. Furthermore, dopant atoms and molecules embedded in He nanodroplets exhibit variouspeculiar dynamical phenomena upon electronic excitation or ionization such as solvation into ordesolvation out of the droplets, complex formation of dopants with He atoms, or thelight-induced collapse of metastable structures formed by aggregation in droplets.
Recently,the time-resolved study of rotational wave packet motion of molecules embedded in He dropletsrevealed that molecular rotation is significantly slowed down compared to isolated molecules andthat rotational recurrences were completely absent. This is in contrast to our previous observa-tion of long-lasting coherent vibrational motion of Na , K , Rb , and Rb molecules formed onthe surface of He droplets which we interpreted in terms of weak system-bath couplings. However, no clear signature of the desorption process of Rb off the droplet surface was seen sothat some uncertainty has remained with regard to the location of the molecule after excitation –on the droplet surface or in the vacuum.In the present work we report on an ion imaging study of the desorption dynamics of Rb molecules formed on the surface of He nanodroplets. This work extends previous experimentalstudies of the desorption process of alkali (Ak) metal atoms on the one hand, and onof the vibrational wavepacket dynamics of Ak dimers and trimers formed on He droplets on theother. Ak metals are particularly well-suited for these studies due to their location in shallowdimple states at the droplet surface.
Upon electronic excitation, Ak metal atoms and moleculestend to desorb off the He droplet as a consequence of repulsive interaction caused by the overlapof their extended valence orbitals with the surrounding He.
The only known exceptions areRb and Cs atoms excited to their lowest excited states.
Ions of Ak metals, in contrast, tend tobe submerged in the He droplet interior where they form stable AkHe n ‘snowball’ complexes dueto strong attractive polarization forces. Thus, in femtosecond (fs) pump-probe experiments,2here a first pump pulse excites the Ak atom and a second probe pulse ionizes it, the competingdynamics of desorption of the excited Ak atom versus the fall-back of the atom into the dropletupon ionization can be followed in real-time. For low-lying excited states, the dynamics of the desorption process is well described by thepseudo-diatomic model which treats the whole He droplet, He N , as one constituent atom of theAkHe N pseudodiatomic molecule. This approach provides a reasonably precise assign-ment of the spectral features in absorption spectra of the AkHe N complex, rationalizes ki-netic energies of desorbed Ak atoms, and explains the angular distributions of desorbed Ak atomsin terms of the symmetries of ground and excited pseudo-diatomic molecular states. Moreover, fs pump-probe transients revealing the desorption dynamics of Ak atoms are reasonablywell interpreted using the pseudo-diatomic model. For Ak dimers, trimers and larger Ak n oligomers attached to He droplets the dynamics inducedby electronic excitation is not as well established as for single atoms. On the one hand, Paulirepulsion resulting from the overlapping of a diffuse excited state-electron distribution with thesurrounding He tends to be weaker for large molecules and clusters because the relative changeof orbital radius upon electronic excitation generally is smaller than for single atoms excited ina similar energy range. Besides, larger clusters are more stably bound to the He droplet withincreasing cluster size as a result of attractive dispersion forces. Note that polyatomic moleculesgenerally remain attached to He nanodroplets upon electronic excitation into low-lying excitedstates.
Thus, the desorption probability tends to be reduced for larger Ak metal clusters. On theother hand, the increasing density of internal states may enhance slow evaporation of Ak n followingexcitation due to energy redistribution from intra-cluster (Ak n ) to inter-cluster (Ak n -He N ) degreesof freedom. The present work clearly shows that Rb molecules desorb off the surface of Henanodroplets when excited into intermediate electronic states. However, the desorption dynamicsis more intricate than in the case of Ak atoms and appears to be most crucially determined bythe Rb molecular states rather than by coupled states of the Rb He N complex as for He dropletsdoped with single Ak atoms. 3 xperiment The experiments presented here are performed using the same setup as described previously.
In short, a continuous beam of He nanodroplets with a mean size of about 20,000 He atoms perdroplet is produced by a continuous expansion of He out of a cryogenic nozzle ( T =
15 K) witha diameter of 5 µ m. The resulting average droplet size is about 20,000 He atoms per droplet.An adjacent vacuum chamber contains a vapor cell filled with bulk metallic Rb heated to around100 ◦ C to achieve the maximum signal of Rb + dimer ions while keeping larger oligomer massesbelow the detection limit. Under these conditions He droplets are doped with two Rb atoms whichsubsequently form Rb molecules on He droplets. The released binding energy of the moleculesis dissipated by evaporation of He atoms from the droplets. In this formation process by trendAk molecules in the more loosely bound triplet metastable state remain attached to the droplets.However, for larger He droplets as we use in this study, substantial amounts of Ak molecules intheir singlet groundstate and even small clusters in low-spin states are also being formed on thedroplets. In the detector chamber further downstream, the doped He droplet beam intersects at rightangles the beam of either a tunable dye laser (Sirah Cobra, pulse length 10 ns, pulse energy 1 µ J,repetition rate 1 kHz, focal length of the focusing lens f =
12 cm) using Coumarine 102 and Exalite411 or that of a fs laser (Coherent Legend, pulse length 120 fs, pulse energy 20 µ J, repetition rate5 kHz, f =
30 cm for both pump and probe). Photoions are detected using a standard velocitymap imaging (VMI) spectrometer. Ion images are recorded selectively for Rb + -ions by gatingthe imaging detector at the corresponding ion time-of-flight. The laser is linearly polarized alongthe direction of the He droplet beam, which is perpendicular to the symmetry axis of the VMIspectrometer. We record single events per image frame and determine the coordinates using thecentroid method. Typically 10 events are summed up in the images recorded with the ns laser. Forthe fs experiment, the delay between pump and probe pulse is adjusted by a movable delay stagefrom 0 up to 10 ps with 50 fs increments. Images with 10 events are recorded for each delay step.VMIs are transformed into kinetic energy distributions using the Abel inversion routine pBasex. S u - P u ( 0 -u ) S u - P u ( 1 u ) P u - S u ( 1 u ) S u - P u ( 0 +u ) P u - S u - P u ( 1 u ) P u - S u ( 0 +u ) S g ( 0 +g ) L u (W u ) FCF a )
Rb+ 2-counts [per laser shot]
W a v e n u m b e r ( c m - 1 )b ) P u - D u - S u ( 1 u ) Figure 1: a) Franck-Condon-factors of allowed g → u -transitions between the singlet groundstateand excited spin-orbit coupled states of Rb . The red ( Σ ) and blue ( Π ) colors indicate the main(non-spin-orbit) character of the relevant potential energy curves in the range of laser excitation.b) Measured yield of Rb + -ions. 5 esults and discussion Nanosecond spectroscopy
In the present article we study He nanodroplets doped with Rb molecules excited into electronicstates at the laser wavelengths in the range 465-495 nm and 412-427 nm (20200-21500 and 23400-24300 cm − ). At these wavelengths, the Rb molecules are photoionized by resonant 1+1 one-color two-photon ionization. The measured yield of Rb + molecular ions created by the nanosecond(ns) laser is shown in Fig. 1 b). Two maxima are clearly visible at 20500 cm − and at 21170 cm − ,and a third less pronounced peak appears at 23750 cm − .To assign these spectral features to molecular excitations we first inspect the Rb spin-orbitcoupled potential energy curves neglecting the influence of the droplet environment. The poten-tial curves of Ω = + / − u , g and 1 u , g symmetry accessible by optical transition from the lowest singletor triplet states in the relevant wavelength range are depicted in Fig. 2. For the excitation from the Σ + g (cid:0) + g (cid:1) groundstate only ungerade states and from the lowest triplet state Σ + u ( − u , u ) only ger-ade states are accessible. States of 2 u , g symmetry cannot be excited out of the 0 + / − g , u groundstates. The vertical arrows and rectangles indicate the energy range covered by our experiments. In thisintermediate range of excitation the energy levels are quite dense. This holds even when takinginto account that vibronic lines of Ak molecules attached to He droplets are typically blue-shiftedby up to about 100 cm − with respect to the gasphase values due to the interaction with the dropletenvironment. When spin-orbit-coupling is negligible (Hund’s coupling case a), only singlet (triplet) statescan be reached by (optical) excitation from a singlet (triplet) state. In the presence of strong spin-orbit coupling (Hund’s case c) which is the case for heavy Ak dimers like Rb , this selection ruleis relaxed. We note that the mixing of singlet and triplet states of Rb due to spin-orbit couplinghas previously been observed in several spectroscopic studies. We therefore calculate the transition probabilities (Franck-Condon factors, FCF) for the al-lowed transitions from the lowest (Hund’s case c) electronic levels Σ + g ( + g ) and Σ + u ( − u ) into6 Potential energy [103 cm-1]
I n t e r n u c l e a r d i s t a n c e [ Å ] 0 +u +u u u +g -g -u g Figure 2: Potential energy curves of spin-orbit coupled Rb states. The vertical arrows andrectangles indicate the range of laser excitation from the Σ + g (cid:0) + g (cid:1) and the Σ + u ( − u ) groundstatesinto the excited state manifold. For the excitation from 0 + g ( − u ) all relevant u ( g )-states are shown.The thick lines indicate the relevant curves for the present experiments. To distinguish states of thesame Ω g , u -symmetry at avoided crossings some curves are drawn as dashed and some as solid. Thethick gray horizontal lines on the right hand side show the calculated asymptotic energies inferredfrom the experimental KER spectra. 7xcited spin-orbit states Ω = u , u using R. LeRoy’s program LEVEL. In the following, weneglect excitations out of the lowest triplet state Σ + u because of the lacking correspondence of therespective FCF contours with the measured spectrum. The calculated FCF for transitions out of the Σ + g groundstate are shown in Fig. 1 a) to compare with the measured photoionization spectrum inb). Each of the Ω = u , u -states is composed of different non-spin-orbit states in various rangesof the interatomic distance, as indicated. Crossings of coupled potential curves become avoidedwhen taking spin-orbit-coupling into account. However, in wide regions of internuclear distanceand energy the coupled potential curves still retain a dominant character of non-spin-orbit states.The dominant Σ and Π -characters in the region of excitation are highlighted by the red and bluecolors of symbols in Fig. 1 a), respectively.The first broad peak around 20500 cm − matches the absorption profile of the 1 u -state. Withoutspin-orbit coupling this state would have Σ + u -symmetry and dissociate towards the 5 s + p atomicasymptote. Due to the SO-coupling with a Π u and a Π u state, the latter state becomes bindingwith 1 u (or 0 + u )-symmetry asymptotically correlating to 5 s + d .The maximum around 21170 cm − has overlap with the computed absorption profiles of abinding Σ + u (0 + u ) and a Π u (1 u ) state, both correlating to 5 s + d . However, the measured peak isslightly red-shifted by 170 and 300 cm − , respectively, compared to the computed profiles. Notethat absorption features of intermediate excited states of other Ak atoms attached to He dropletshave also been found to be shifted in the same range of wavenumbers with respect to simplemodel calculations. Most likely reasons for this deviation which are hard to quantify areinhomogeneous broadenings due to droplet size-dependent line shifts in combination with a broaddroplet size distribution as well as due to local fluctuations of the He density around the dopant. Besides, the accuracy of potential curves of such intermediate levels of excitation may be an issue.The left wing of the feature around 23800 cm − overlaps with the right wing of the FCF contourof the Π u ( u ) -state. At higher photon energies the feature reaches out to the FCF contours of the Σ + u ( u , − u ) -states.Another possible source of distortions of the spectra is the fragmentation of Rb and larger8lusters into Rb which might add signal to the Rb spectrum. However, given the low Rb vaporpressure in the doping cell as well as the lack of any signals of unfragmented Rb + up to the noiselevel of 0.03% of the Rb + -signal in the entire tuning range of our lasers, we dismiss fragmenta-tion of heavier masses as highly unlikely for the conditions set in our experiment. While the Heenvironment is likely to induce blue-shifting and additional broadening of the measured spectralfeatures of the order of tens to a few hundreds of cm − , we refrain from attempting to includesuch effects due to the poor characterization of the droplet effect on Ak metal molecules excited tointermediate states. Rb + ion imaging More detailed information about the nature of the excited Rb -states is obtained from the velocitydistributions of the desorbed Rb + ions measured by means of VMI using the dye laser. TypicalVMIs recorded at the laser wavelength 488 nm (20500 cm − ) and 424 nm (23600 cm − ) aredisplayed in Fig. 3 a) and b), respectively. The figures are made up of one half of the raw image[upper in a), left in b)] and one half of the Abel inverted image [bottom in a), right in b)]. Clearly,the images display angular distributions with pronounced opposite anisotropies, where in a) thepreferred direction of Rb emission is along the polarization of the laser (yellow arrow), whereasin b) it is perpendicular to the laser polarization.Aside from angular distributions, from these VMIs we can infer the final velocity of desorbedRb by integrating the Abel inverted images over angles. The resulting velocity distributions forvarious laser wavelengths are shown in Fig. 4. In contrast to the velocity distributions of desorbedRb + atomic ions measured at similar laser wavelengths, the Rb + velocity distributions featuremore complex structures. They are best modeled by a sum of two to four Gaussian functions,depicted as smooth colored lines in Fig. 4. The presence of several velocity components indicatesthat either a superposition of initial states is excited, where each state evolves along a distinctpotential energy curve with respect to the interaction of the excited Rb with the He droplet, or thatrelaxation occurs due to the coupling of the initial to some final states, probably induced by the He9 v x [ m / s ] vy [m/s] a ) 2 0 5 0 0 c m - 1 e - - ---- e b ) 2 3 6 0 0 c m - 1 v x [ m / s ] vy [m/s] --- - - - Figure 3: Typical raw and inverted Rb + ion images recorded at two different wavenumbers of thedye laser. The vertical arrow indicates the laser polarization.10 - 1 - 1 Probability (arb. u.) - 1
V e l o c i t y [ m / s ] 2 1 3 0 0 c m - 1
Figure 4: Rb + velocity distributions inferred from VMIs recorded at various wavenumbers of thedye laser. The dashed colored lines indicate the results of a fitting procedure using the sum of 2 to4 Gaussian functions. 11roplet environment. Such behavior was recently observed for Na atoms excited into high-lyinglevels which were subjected to massive droplet-induced configuration interaction. The angular anisotropy of velocity distributions resulting from the dissociation of a diatomicmolecule by one-photon absorption is quantified by the parameter β . Here, β = parallel transitions with no change of angular momentum projection, such as Σ → Σ . The resulting angulardistribution of fragments is peaked along the polarization direction, similar to that of Fig. 3 a). Incontrast, for perpendicular transitions of the type Σ → Π fragmentation occurs preferentially inthe plane perpendicular to the polarization as the transition dipole moment points perpendicular tothe molecular axis and therefore β = −
1. In that case, VMIs resemble the one shown in Fig. 3 b).The mean values of Rb + kinetic energies and anisotropies obtained from the fits of the velocitydistributions are graphically summarized in Fig. 5 for various investigated laser wavelengths. Thesymbol colors match the fit curves of the velocity distributions shown in Fig. 4. The error barsreflect the velocity ranges used to calculate the weighted mean values and approximately matchthe full widths at half maxima (FWHM) of the gaussian fit curves. Thus, overlapping error barsindicate that the corresponding peaks partly or even fully overlap. The sizes of the circles visualizethe relative peak integrals of the fit curves.The velocity distributions in the range 20300 cm − to 20700 cm − are nearly constant featuringone large (black) and one small peak (red). By increasing the photon energy to 20800 cm − additional components at higher velocities appear (blue and dark yellow). New components atlower velocities (green and orange) grow in at 21000 cm − , while others (dark yellow and blue)disappear. These four peaks subsequently shift towards higher velocities as the laser is tunedto 21700 cm − . At higher wavenumbers 23500-24400 cm − the distributions have two featureswhich shift to higher velocities with increasing wavenumber.For every gaussian fit curve we calculate the weighted average of the β -parameter, which isdepicted with the same color-coding in Fig. 5 b). The error bars illustrate the variation of β within the FWHM. Since in the studied regions of excitation the excited states are predominantly12 b ) Anisotropy b P /S
Rb2 kinetic energy [meV] p e a k 1 2 3 4 5 6 7 8
S P a )
W a v e n u m b e r [ c m - 1 ] p e a k 1 2 3 4 5 6 7 8
Figure 5: a) Graphical compilation of Rb + kinetic energies resulting from fits of the velocity distri-butions. The sizes of the circles indicate the relative weights of the respective velocity components.b) Anisotropy parameter β associated with the individual velocity components.13etermined in their character by one single non-SO-coupled state we discuss the recorded angulardistributions in terms of these uncoupled states.The lower part of the tuning range (20300-20800 cm − ) shows an anisotropy parameter β > β = . ( ) -1 . ( ) for peak 1 and β = . ( ) -0 . ( ) for peak 2) which means that predominantlya parallel transition is driven. The accessible 1 u -state correlating to the 5 s + p -atomic asymptotehas predominantly Σ + u -symmetry in the region of excitation. Thus, a Σ − Σ transition is excitedwhich leads to the observed anisotropy of the velocity distribution in the direction of the laserpolarization. The fact that the Rb kinetic energy is constant in this range of photon energiesis at odds with previous measurements using Ak metal atoms where linearly increasing kineticenergies with increasing photon energy were found. Those experiments were interpreted interms of the pseudo-diatomic model in which the repulsive dopant-He droplet interaction energyis converted into kinetic energy released in the course of the desorption process. Accordingly, theobserved constant and rather small kinetic energy of desorbed Rb points at weak Rb -He dropletrepulsion in that excited state and at inefficient conversion of internal vibrational energy of the Rb into kinetic energy.In the range from 20900 to 21700 cm − peak 2 gives the largest contribution. The meananisotropy of β = − . ( ) points at an excited Π -state contribution. This agrees with the FCFcalculation according to which the 2 Π u -state carries a larger transition strength than the 2 Σ + u -state. The linear dependence of Rb + kinetic energy as a function of wavenumber in this range ofphoton energies indicates that now potential energy, either stored in internal Rb excitations or inthe Rb -He N inter-cluster degree of freedom, induces repulsion of Rb with respect to the dropletsurface and therefore partly converts to kinetic energy of the desorbing Rb . The extrapolation of alinear fit function to the data down to zero kinetic energy then yields the internal energy of the freeRb molecule in that excited state. The found value of about 20360 cm − , which is displayedas the bottom thick gray line on the right hand side of Fig. 2, roughly matches the bottom of thepotential well of the lowest 0 + u (2 Σ + u )-state. Thus, we assume that in the course of desorption boththe Rb -He droplet interaction energy as well as Rb vibrational energy are converted into kinetic14nergy.From the slope of the linear fit we deduce an effective mass of the He droplet m e f f = . . in the desorption process. This isabout twice the value previously found for Rb atoms ( ∼ which appears plausible as the Rb dimer has roughly twice the size of the Rb atom. Linear regressions of peaks 5 and 6 extrapolateto a potential energy at vanishing Rb kinetic energy in the range 20710-20825 cm − , which ismarked by the upper thick gray line on the right hand side of Fig. 2. This energy matches thepotential well at the internuclear distance R ≈ u -state correlating to the 5 s + p atomic asymptote (dashed red line). In the range of R where this state is excited it is dominated bythe Π u -contribution which is consistent with the measured negative anisotropy of β = − . ( ) (peak 5) and β = − . ( ) (peak 6).In the laser wavenumber range 23600-24200 cm − the Rb kinetic energy distributions arebest fitted by a sum of two gaussian functions, peaks 7 and 8 in Fig. 5. The anisotropy of bothcomponents evolves from β = − .
38 (peak 7) and β = − .
19 (peak 8) to β = .
58 and β = . Σ − Π to Σ − Σ transitions. This conclusion is supported by the FCF spectrumin Fig. 1 which features the 4 Π u -state at the lower and the 3 Σ + u -state at the upper end of this rangeof wavenumbers.From linear regressions we extrapolate to the minimum potential energy of the state associatedwith peak 8 of about 22800 cm − which matches the potential well depth of the upper 4 Π u ( u ) -state (see Fig. 2). Peak 7 extrapolates to a minimum energy of about 23360 cm − which can beassigned to the outer plateau of the 3 Σ + u -state potential curve correlating to the 5 s + p -atomicasymptote. Thus, again it appears that the Rb internal energy is efficiently converted into kineticenergy release by droplet-induced relaxation, where a fraction of about 58% of molecules stabilizesin the plateau of the 3 Σ + u -potential and the remainder relaxes down into the wells of the 4 Π u or3 Σ + u -potentials. The slopes of the linear fits yield effective numbers of He atoms interacting withthe desorbing excited Rb molecules of 17 and 18 for peaks 7 and 8, respectively.15 Ion signal normalized [arb.u.]
P u m p - p r o b e d e l a y [ f s ] R b + R b H e R b Figure 6: Femtosecond pump-probe measurements of the yields of Rb + and RbHe + ions in a), andRb + in b), recorded at a laser wavelength 413 nm (24210 cm − ). The smooth black line is a fit ofan error function. Femtosecond desorption dynamics
In addition to measuring the yields and final velocity distributions of Rb + ions generated by nslaser ionization, we have investigated the time-evolution of the Rb + signals in the course of thedesorption process using fs pump-probe spectroscopy. Fig. 6 shows the transient yield of Rb + ions recorded at a laser wavelength of 413 nm (242100 cm − ), which we compare to the sum ofthe yields of Rb + and RbHe + ions recorded at the same wavelength. In these measurements, afirst pump pulse resonantly excites the dopant atom or molecule while ionization is induced by asecond time-delayed probe pulse.At this wavelength, the Rb atomic dopant is excited into the 6 p -state which is perturbed bythe He droplet to form pseudo-diatomic 6 p Σ and 6 p Π states. Rb dimers are excited in betweenthe Π u (1 u ) and Σ + u (1 u ,0 − u ) states correlating to the 5 s + p atomic asymptote. The observedtime-delayed rise of the ion signals reflects the competing dynamics of desorption of the exciteddopant off the He droplet surface and the solvation of the ionized dopant into the He droplet16nterior induced by attractive He-ion interactions. Thus, at short pump-probe delay ionization ofthe dopant occurs in close vicinity of the He droplet such that all ions turn over and fall-back intothe He droplet to form stably bound snowball complexes. Only at larger delays the exciteddopants have gained enough kinetic energy so as to overcome the attraction they experience afterionization by the probe pulse.In Fig. 6 we plot the sum of Rb + and RbHe + ions as the characteristic signal for the desorptiondynamics of the atomic dopants. Upon excitation of a Rb atom on the He droplet surface stableRbHe excited molecules, so-called exciplexes, can form and decay in the course of desorption offthe droplet. This may lead to transient redistribution of Rb + and RbHe + signals irrelevant for thepresent study. By fitting the transient yield curves with an error function we obtain the fall-backtimes t Rbc = . ( ) ps and t Rb c = . ( ) ps as those delay times at which the signal has increasedto half the final value reached at long delays. The significantly longer fall-back time for Rb + pointsat weaker repulsion as compared to the excited Rb atom, in line with our expectation based on thetrend that Ak clusters are more strongly bound to He droplets than atoms and that Pauli repulsiondue to electronic excitation tends to be weaker for large molecules (see Sec. ). Thus, we predictthat larger Rb oligomers will feature even longer fall-back times than Rb and may not desorb atall for dopant clusters exceeding a certain size. Besides this, molecules and larger oligomers havelarger masses and are likely to induce larger effective masses of the He droplet they interact withdue to their larger spatial extension, which additionally slows down the desorption process.Apart from transient ion yields, velocity map images of Rb + fragments have been recordedfor different pump-probe delays. Fig. 7 a) shows the speed distributions obtained by inverse Abeltransformation of the raw images. For each pump-probe delay step, the maximum of the spectrumis normalized to the corresponding ion yield. In addition to the pump-probe correlated signal, adelay independent background contribution of about 15% of the signal at long delays is measured.In order to extract the pump-probe correlated data, this contribution is subtracted. The measuredvelocity distributions are rather broad and show a slight asymmetry. Nevertheless, a shift of thepeak position towards higher velocities with increasing delay is clearly visible. To analyze this in17ore detail, each spectrum is fitted by a epsilon skew gaussian distribution, which was found toyield the best fit result. From the fit result at every delay step the mean velocity and the anisotropyparameter are inferred and plotted in Fig. 7 b). The anisotropy parameter is calculated by weightingthe angular distribution with the velocity probability distribution within one standard deviation.
01 0 02 0 03 0 0
Velocity [m/s] a ) b )
P u m p - p r o b e d e l a y [ f s ]
Mean velocity [m/s] b Figure 7: a) Time evolution of Rb + ion speed distributions inferred from velocity-map imagesrecorded as a function of pump-probe delay. Each distribution is background subtracted andweighted with the corresponding ion yield (see text). b) Transient mean velocities (black sym-bols, left vertical scale) and anisotropy parameters β (red symbols, right vertical scale). The blueline is a fit of an exponential function to the velocity data.When significant Rb + ion signal starts to appear in the ion images at a pump-probe delay ofabout 600 fs we measure velocities with a mean value of 54(3) m/s. This time marks the onsetof the pump probe-correlated signal within the experimental uncertainty. It is identified with thetime when a first fraction of the created wavepacket has gained enough kinetic energy to overcomethe potential barrier provided by the ionic potential curve. The origin of the leveling out of the18on velocity at short delay to a finite value around 55 m/s is unresolved at this point. Note thatexperimental artifacts such as a limited resolution of the imaging setup can be excluded. Wemention that similar finite velocity values at short delay are also observed in for Rb + and RbHe + ion in experiments where the He droplets are doped with single Rb atoms. This will be discussedin a forthcoming paper.With increasing delay the velocity shifts to higher values till it reaches 90% of the asymptoticvalue of 179.6(5) m/s at a delay of 5 . ( ) ps. This monotonous increase in velocity directlyreflects the dynamics of desorption of excited Rb molecules off the He surface. As expected, atlong delay times the velocity map ion images converge towards those measured using the ns laserwithin the experimental uncertainty.From fitting an exponential function v ( t ) = v rise (cid:0) − exp (cid:0) − t τ (cid:1)(cid:1) to the data we obtain a char-acteristic time constant for the desorption process τ = . ( ) ps. Note that this value exceeds theRb fall-back time derived from the ion yield measurement. The difference between ion yield andvelocity transients is attributed to the more extended range of repulsive interaction of the excitedRb molecule as compared to the range of attraction of the Rb + ion towards the He droplet. Asa consequence, the excited Rb continues to be accelerated away from the droplet surface evenbeyond the fall-back time.The time evolution of the anisotropy parameter β is shown as red symbols in Fig. 7. It onlyslightly varies between β = . ( ) at short delays and β = . ( ) at long delays. The lattervalue falls slightly below the value measured with the ns laser ( β = . ( ) ). This is likely due tothe excitation of a superposition of states of opposing symmetry by the broad-band fs laser wherethe Σ -component dominates. Desorption model
First of all we point out that our time- and velocity-resolved measurements confirm our conceptionof prompt, pseudo-diatomic dissociation of the Rb He N complex as discussed above in the con-text of our ns experiments. The observed pump-probe delay-dependent dynamics clearly shows19 ε Σ Π Singlet μ Σ Σ Triplet ε Σ Π μ Σ Σ μ εε Figure 8: Schematic representation of the configuration of Rb molecules in the singlet (left) andtriplet (right) groundstates attached to He droplets and the corresponding angular distributionsupon desorption. Vector (cid:126) ε indicates the direction of laser polarization and (cid:126) µ is the transition dipolemoment. See text for details.that in the studied energy range one-photon vibronic excitation of neutral Rb dimers induces anaccelerated, directed motion of the Rb away from the droplet surface during a few ps.Based on these experimental findings we suggest the following general scheme for the desorp-tion process of Rb diatomic molecules from the surface of He droplets. The argumentation mostlikely holds for other Ak metal dimers as well. The central assumption is that the quantizationaxis which determines the symmetry of the molecular state and thus the direction of the transitiondipole moment is determined by the molecular axis of the Rb dopant. This is justified by thefact that the excitation is mostly centered on the Rb due to droplet excitations falling into verydifferent ranges of energy as compared to those of the Rb molecules. Furthermore, the excitedstates are governed by the generally much stronger intramolecular interactions ( ∼ − )as compared to the interaction of the Rb dimer with the He droplet ( ∼ − ).Thus, for the singlet groundstate where the Rb stands perpendicular on the He droplet sur-face, the angular distribution of Rb “fragments” coincides with that of Rb atomic fragmentsfor the hypothetical case that free Rb molecules were excited into dissociative states of the samesymmetry. This situation is schematically sketched on the left hand side of Fig. 8. In contrast,the lowest triplet state of Rb would result in an angular distribution of desorbed Rb molecules20f the opposite anisotropy as compared to the singlet groundstate. That is, counter-intuitively, β = perpendicular transition Σ → Π , as shown on the right hand sideof Fig. 8. Unfortunately this conjecture cannot be directly assessed with the data measured inthis work. However, in future experiments we will check this situation by exciting better isolated,low-lying triplet states of Ak dimers as we have done before. In addition to the angular distri-butions, the internal states of the Rb molecule appear to govern the kinetic energy released intothe translational degree of freedom of the desorbing Rb off the droplet surface through efficientcoupling between intramolecular vibration and Rb -He N relative motion. The observed desorptiontimescale of a few picoseconds being in the same range as the vibrational periods of the Rb dimerstates is in agreement with this conclusion. In contrast, previous experiments indicated that Rb dimers remain attached to the droplet after excitation to the lowest lying triplet state even for highvibrational states. Thus, we argue that the desorption probability most strongly depends on theelectronic state. The analysis of time-resolved imaging experiments with Rb atoms attached to Hedroplets excited to different electronic states will further clarify this issue.
Summary and conclusions
The present study clearly demonstrates that Rb dimers formed on the surface of He nanodropletspromptly desorb off the surface upon electronic excitation into intermediate states, similarly to Rband other alkali metal dopant atoms. However, in contrast to Rb atoms, the angular distributionof detected molecular ions is not determined by the symmetry of the dopant-droplet complex, butrather by the symmetry of the internal molecular states of the Rb dopant. The latter remainsweakly perturbed due to the relatively weak Ak-He coupling. We conclude that this leads to op-posite anisotropies of the angular distributions of desorbed Rb formed in the singlet and tripletgroundstates when driving transitions of the same symmetry.Likewise, the kinetic energy distributions of desorbed Rb appear to be mostly determined bythe internal energy of Rb which is converted into kinetic energy released into the translational mo-21ion of the desorbing Rb . This is enabled by efficient He droplet-induced vibrational relaxationand coupling of intra and inter-molecular degrees of freedom of the Rb He N complex. Thereforethe resulting multi-peaked structures of kinetic energy distributions elude from a simple interpre-tation in terms of pseudo-diatomic dissociation as in the case of Ak metal atoms on He droplets.Femtosecond time-resolved measurements of Rb + ion yields and velocities reveal qualitativelythe same transient dynamics as Rb atoms, which is determined by the competition of repulsion ofthe excited dopant away from the droplet surface and attraction of the dopant towards the dropletonce ionized. However, this desorption dynamics proceeds more slowly for Rb dimers as forRb atoms at the probed laser wavelength pointing at a weaker repulsion of excited Rb than ofexcited Rb. In future experiments we will refine this study by probing Ak metal dimers in betterdefined singlet as well as triplet states. Moreover, time-resolved imaging spectroscopy of Ak metaltrimers and larger clusters will shed new light on both the dynamics of intra-cluster degreesof freedom as well as the complex cluster-He droplet couplings. Acknowledgement
The authors gratefully acknowledge support by the Deutsche Forschungsgemeinschaft in the frameof project MU 2347/6-1 as well as IRTG 2079. J. v. V. is supported by the Landesgraduierten-förderungsgesetz of Baden-Württemberg.
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