Observation of laser-assisted electron scattering in superfluid helium
Leonhard Treiber, Bernhard Thaler, Pascal Heim, Michael Stadlhofer, Markus Kitzler-Zeiler, Markus Koch
OObservation of laser-assisted electron scattering in superfluid helium
Leonhard Treiber , Bernhard Thaler , Pascal Heim , Michael Stadlhofer , Markus Kitzler-Zeiler ,and Markus Koch ∗11 Graz University of Technology, Institute of Experimental Physics, Petersgasse 16, 8010 Graz,Austria Technische Universität Wien, Photonics Institute, Gusshausstrasse 27-29, 1040 Vienna, Austria
Abstract
Laser-assisted electron scattering (LAES), a light–matter interaction process that facilitates energy transfer betweenstrong light fields and free electrons, has so far been observed only in gas phase. Here we report on the observation ofLAES at condensed phase particle densities, for which we create nano-structured systems consisting of a single atomor molecule surrounded by a superfluid He shell of variable thickness (32–340 Å). We observe that free electrons,generated by femtosecond strong-field ionization of the core particle, can gain several tens of photon energies due tomultiple LAES processes within the liquid He shell. Supported by 3D scattering simulations, these results provide thefirst insight into the interplay of LAES energy gain/loss and dissipative electron movement in a liquid. Our resultsreveal that LAES could significantly increase the temporal resolution of ultrafast electron microscopy, potentially tothe attosecond regime. ∗ corresponding author: [email protected] a r X i v : . [ phy s i c s . a t o m - ph ] J a n ntroduction The investigation of atomic-scale processes with high spatio-temporal resolution is key to the understanding and de-velopment of materials. While pulsed light sources have been developed to provide attosecond temporal resolution [1],the diffraction limit of light waves prohibits the improvement of the spatial resolution below the ten-nanometer range.Electron probes, in contrast, allow for subatomic spatial resolution due to their picometer deBroglie wavelength,and can, in principle, achieve the temporal resolution of light pulses. Time-domain shaping of electron pulses isbased on the transfer of energy between electromagnetic radiation and free electrons, which is manifested in variousphenomena, such as bremsstrahlung, Smith-Purcell radiation [2], Cerenkov radiation [3], or Compton scattering [4].Electron–photon coupling is furthermore key to the development of novel light sources like free electron lasers [5]or high–harmonic generation [6], and to ultrafast structural probing like high–harmonic spectroscopy [7] or laser-induced electron diffraction [8]. While few- and sub-femtosecond electron pulses [9, 10] and pulse trains [11, 12]could be generated through light-field manipulation, the time resolution achievable with these electron pulses suffersfrom velocity dispersion and Coulomb repulsion [10]. Consequently, spatial separation of pulse shaping and struc-tural probing in ultrafast electron microscopy (UEM) setups [13, 14, 15, 16, 17, 18] leads to broadening of electronpulses during delivery to the sample, limiting the temporal resolution currently to about fs [19].LAES is a light–matter interaction process that holds promise to increase the temporal resolution of electron probesby combining velocity modulation and structural probing within the investigated sample. In LAES, free electronsthat scatter off neutral atoms or molecules in presence of a strong laser field, can increase (inverse bremsstrahlung)or decrease (stimulated bremsstrahlung) their kinetic energy by multiples of the photon energy ( ± n ¯ hω ) [20, 21, 22].Structural information of the scattering object is encoded in the angular distribution of the accelerated/deceleratedelectrons [23, 20]. Importantly, the energy modulation only takes place during the time window in which the shortlaser pulse overlaps with part of the much longer electron pulse within the sample. LAES can thus be viewed asan optical gating technique that allows to record scattering-snapshots at precisely defined times. The capabilityof LAES to analyze structural dynamics with subparticle spatial resolution ( ∼ pm) at timescales of electrondynamics ( < fs) was recently demonstrated in the gas-phase [23, 20]. However, in contrast to other strong-fieldphenomena [24], LAES has evaded observation in the condensed phase so far, so that its potential for advancing thetime resolution of structural probing through UEM and other techniques remains unexplored.2ere, we demonstrate that LAES can be observed at condensed phase particle densities of · cm − , for which wecreate core–shell nanostructures, consisting of a single atom/molecule located inside a superfluid He droplet (He N )[25, 26]. This system provides three unique advantages: First, the droplet size and thus the LAES interaction shellthickness underlies a well defined distribution, the mean of which can can be varied with Angstrom resolution [25].Second, the high strong-field ionization threshold of He [27] enables high laser intensities to increase the LAESprobability without solvent ionization. Third, energy dissipation of electrons propagating inside He N is very low[28]. We have chosen the experimental conditions to work in the multiple scattering regime in order to characterize theinterplay of LAES acceleration/deceleration and dissipative electron movement within the He shell; as a consequence,our experiment does not provide information about the electron angular distribution. Results
Observation of multiple LAES events
To measure the energy gain of electrons through LAES within the liquid He shell, we perform strong-field photoion-ization with femtosecond laser pulses and compare two photoelectron spectra that are recorded under the same laserpulse conditions: First, the above threshold ionization (ATI) spectrum of a bare, gas-phase atom/molecule and,second, the LAES spectrum obtained with the same atom/molecule embedded inside a He N . The He droplets, whichhave a radius of a few nanometer, are created by supersonic expansion of He gas through a cryogenic nozzle andloaded with single dopant atoms or molecules through the pickup technique [25, 26], as described in the Methodssection below. Figures 1a-c show the two types of spectra for three species: Indium (In) atoms, xenon (Xe) atoms,and acetone (AC) molecules. For all three species, the LAES spectrum shows significantly higher electron energiesthan the ATI spectrum, and both types of spectra—ATI and LAES—show equidistant signal modulations with apeak distance of 1.55 eV, corresponding to the central laser wavelength of 800 nm (1.55 eV photon energy). Closerinspection of the area-normalized spectra shows that, in addition to the higher energies of the LAES spectrum,the ATI signal exceeds the LAES signal at low energies up to ∼ eV, indicating a shift of the electron energydistribution towards higher kinetic energies due to the presence of the He shell. The energy increase of the fastestelectrons exceeds 20 eV in all three cases, which is far beyond the U P energy gain limit for a single scattering eventaccording to the strong-field Kroll-Watson approximation [30] ( U P is the ponderomotive energy, see parameters3 igure 1: Comparison of electron spectra obtained by strong-field ionization with 800 nm light (1.55 eV photon energy) ofdifferent species in gas-phase (ATI spectra, black) and inside He N (LAES spectra, red): (a) In atoms, (b)
Xe atoms, (c) acetone (AC) molecules. The spectra are area-normalized in order to account for the reduced ionization energy inside aHe N [28]. Above each plot the values of the ionization energy, E I , laser intensity, I , ponderomotive potential, U P , and dropletradius, R d , are listed. (d) ATI spectra (dashed lines) and LAES spectra (solid lines) as in a-c but with 3 eV binning (leftordinate), and cross section for total elastic electron scattering of electrons and He (gray line, right ordinate) [29]. I for Xe and AC due tothe higher ionization energy E I , compared to In, which is reflected by ATI spectra that extend to higher energies.Smoothed LAES and ATI spectra are compared in Figure 1d. The similarity of the Xe and AC spectra, for whicha very similar laser intensity was used, indicates that the species from which the electrons originate has very littleinfluence. Instead, the LAES energy gain is larger for Xe and AC (e.g., at a signal level of − : 25-30 eV gain),compared to In (20 eV gain), because of the higher laser intensities used for Xe and AC. These observations indicatethat the laser intensity dictates the energy gain.In addition to the LAES energy gain, insight into the dissipative electron movement within the liquid He shell canbe obtained from the equidistant peak structure of the LAES spectra (Figures 1a-c). Kinetic energy of an electroncan be dissipated to the He droplet through binary collisions with He atoms and through a collective excitation ofthe droplet. While elastic collision with a He atom reduces the electron kinetic energy by ∼ N excitations carry < meV energy [26]. The pronounced contrastof the LAES peaks in Figure 1 thus demonstrates that energy dissipation plays a subordinate role compared toLAES energy gain for the relatively small droplets ( R d ≈ Å radius) used in these measurements. Furthermore,the absence of a kink in the yield at or above 20 eV, the energy threshold of electronic He excitations [31], showsthat inelastic interactions are insignificant, which is in agreement with the much lower cross section for inelastic ascompared to elastic interaction [29].
Droplet size effects
We now investigate the influence of the He shell thickness on the LAES spectrum in order to deepen our insightinto the interplay of light-induced energy gain/loss and dissipative energy losses. The He droplet approach allows tochange the He shell thickness around the atom/molecule to be ionized by varying the droplet source temperature.Since LAES processes require electron–He scattering in presence of laser light, information about the electron transittime through the He shell can be gained from the droplet-size dependence of the LAES spectra. Figure 2a showsLAES spectra obtained with In atoms inside He droplets with radii from R d = 32 Å to R d = 340 Å. The energy5ain continuously increases with the He shell thickness for the accessible range of droplet radii. The maximumkinetic energy doubles from 50 eV for the smallest droplets to 100 eV for the largest ones, compared to a maximumenergy of the ATI spectrum of about 15 eV. This continuous increase provides a first indication that the transit timedistribution, which is a result of stochastic electron trajectories, is comparable to the laser pulse duration, at leastup to R d ≈ Å. Figure 2: Dependence of LAES spectra on the droplet size, for droplet radii between R d = 32 Å and R d = 340 Å ( R d values are calculated from the mean values of the droplet size distributions [25]). The spectra are obtained with In atomsat I = 1 . · Wcm and show a pronounced increase of the LAES energy gain with He shell thickness. Additionally, thegas-phase ATI spectrum is shown for comparison. The abrupt increase of the droplet radius to R d = 340 Å for the lowestdroplet source temperature ( T = 10 K) is due to the changing character of the supersonic expansion from sub- to supercriticalin this temperature regime [25]. (b)
Close-up of the low-energy region of (a).
While the LAES energy gain is restricted to the time window of the laser pulse, the electron dissipates energy aslong as it propagates within the He droplet. Since the energy transfer in single collisions with He atoms is low,energy dissipation influences the modulation contrast of the LAES signal. A close-up of the LAES spectra in thelow-energy region in Figure 2b allows to evaluate the dependence of this contrast on the droplet size. We find6hat the contrast decreases steadily from the smallest droplets, where it equals the contrast of the gas-phase ATIpeaks, until it vanishes completely for the largest droplets. We ascribe this blurring to energy dissipation of theelectron within the He shell, which has increasing influence on the spectra for larger droplets. Despite the energydissipation, the thickest He shell ( R d = 340 Å) supports the highest LAES energy gain, emphasizing the dominanceof the light-driven electron energy modulation over dissipative energy loss.
3D scattering simulation
For further insight into the electron propagation through the He shell, we perform simple 3D elastic scatteringsimulations, without considering the light field. From these simulations we obtain estimations for the transit timeand the number of electron–He scattering events. Figures 3a and b show the ratios of ejected electrons over timefor E kin = 2 eV and E kin = 10 eV, each for different droplet sizes. It can be seen that the probability for electronejection within the time span of the laser pulse (25 fs) depends strongly on the droplet size, in particular for 2 eVelectrons. This droplet size dependency is also reflected by the corresponding probability distributions of scatteringevents within 25 fs (insets of Figure 3a,b): The lower maximum of the double peak structure represents electronsthat are ejected within 25 fs, while the upper maximum represents electrons that are inside the droplet after thistime. We note that the actual time span for LAES is shorter than the pulse duration since the ionization is mostlikely around the pulse maximum, which might add to the uncertainty of the values discussed here, but does notinfluence the obtained trends.The mean number of scattering events within 25 fs (Figure 3c) is predicted to increase with droplet size for all kineticenergies, eventually leveling off. Interestingly, in the biggest droplets 10 eV electrons experience more collisions than2 eV electrons, because they propagate longer distances in larger droplets and thus undergo more collisions, despitetheir lower scattering cross section (Figure 1d).Finally, we look into the dissipative electron movement and therefore consider 5 eV electrons and the scattering eventdistribution after ejection from the droplet (long interaction times, not restricted to 25 fs, Figure 3d). Comparingthese distributions to the mean number of scattering events within the pulse duration in figure 3c, it is obvious, thatfor the biggest droplets, the majority of scattering events happen after the laser pulse.7 igure 3: 3D simulation of electron trajectories inside a He droplet for different kinetic energies E kin and different dropletradii R d in similarity to Tulsky et al. [32]. An ensemble of · electrons is considered. (a) Probability that an E kin = 2 eVelectron has been ejected as function of time T for different R d . Inset: Probability density of the number of scattering eventswithin 25 fs for E kin = 2 eV. (b) Same as (a) but for E kin = 10 eV. (c) Mean number of scattering events within 25 fs [c.f.,insets in (a) and (b)] as function of the droplet radius for E kin = 2 , , , , , eV. Vertical lines indicate the R d -valuesthat are considered in (a) and (b). (d) Probability distribution of total scattering events, i.e., without temporal limit, for E kin = 5 eV. iscussion Comparison of strong-field ionization spectra of atoms/molecules in gas phase and inside He droplets reveals that thepresence of a nanometer-thick layer of superfluid He around the ionized particle leads to a significant increase of theelectron kinetic energies. The following observations, in combination with predictions from 3D scattering simulations,lead us to the conclusion that the electron acceleration is due to multiple LAES processes within the He layer: (i)The energy gain strongly increases with droplet size (Figure 2). This behavior observed for strong-field ionization isin contrast to weak-field ionization inside He droplets, where the photoelectron spectrum is droplet-size independentbecause it is influenced only by the structure of the immediate environment of the dopant, the solvation shell [33].In the current situation, the energy gain of the electron is related to the number of light-mediated binary electron–He-atom collisions at a distance from the remaining ion, which increases with growing droplet size. (ii) Comparisonfor three different species shows that the laser intensity has the strongest influence on the LAES energy gain, whilethe ionization energy plays a negligible role (Figure 1). This is explicable by an increased LAES probability dueto increased photon flux. (iii) The upper limit of the energy gain by far exceeds the maximum light-field energyof U P that can be transferred to an electron in a single scattering event [30]. Multiple scattering events are inagreement with our simulations, which predict a broad distribution ranging up to several tens of scattering eventseven within the smallest droplets (Figure 3).For the applicability of LAES in UEM, the interplay of LAES energy gain/loss and dissipative energy losses as afunction of the thickness of the material is a crucial factor. We gain insight into the electron transit time through theHe shell, as well as the number of dissipative electron–He-atom collisions, by comparing the droplet-size dependenceof the LAES spectra to the scattering simulations. In the experiment we observe that the LAES energy gainincreases continuously over the whole range of investigated droplet sizes ( R d = 32 Å to R d = 340 Å, Figure 2).This is in agreement with the simulations, which predict that the mean number of collisions within 25 fs, increasesup to the largest droplets used in the experiment ( R d = 340 Å), most dominantly for higher electron energies.Consequently, the average transit time of the observed ensemble is on the order of the laser pulse duration. TheLAES interaction time is determined by the droplet size in small droplets and by the laser pulse duration in largedroplets (Figure 3).Finally, we want to focus on the dissipative electron movement. Considering purely elastic scattering (Figure 3d), on9verage, 5 eV electrons undergo 10 collisions inside the smallest droplets ( R d = 32 Å), resulting in an energy loss of30 meV (0.06% energy loss per collision). Inside the largest droplets ( R d = 340 Å) they loose, on average, 2 eV after830 elastic collisions. Comparing these values to the 1.55 eV distance of LAES peaks, the signal contrast is expectedto be the same as that of the gas-phase ATI spectrum for the smallest droplets, while it can be expected to fully smearout for the largest droplets, in agreement with our measurements in Figure 2b. However, the simulated electronenergy loss of 130 meV (45 collisions) for R d = 76 Å, seems insufficient to explain the observed ∼ % contrastreduction (around E kin = 5 eV) in figure 2b. This discrepancy points towards shortcomings of the simulationthat are currently neglected: excitation of collective droplet modes [25, 26], transit-time increase due to Coulombinteraction between the ion core and the electron, or additional blurring of the LAES peaks due to sequential energy-gain–energy-loss processes with varying U P . Nevertheless, the most important observation is that the largest Hedroplet (thickest He layer, R d = 340 Å) yields the fastest electrons, proving that energy gain through multiple LAESprocesses effectively dominates energy dissipation for propagation distances of several tens of nanometers.In conclusion, we have demonstrated that LAES can be observed with femtosecond laser pulses in the condensedphase at particle densities of · cm − . This demonstration shows that LAES can be used in the condensedphase to merge temporal selection via velocity modulation of electrons with ultrashort laser pulses (as demonstratedhere), and structural analysis that can be extracted from the electron angular distributions [23, 20]. While it isencouraging that in superfluid He LAES energy modulation dominates energy dissipation of electrons, it will beimportant to investigate this ratio for other materials, which is enabled by the He droplet approach through thecreation of core-shell systems [34, 35]. Photoionization of the core will allow to observe LAES-acceleration andenergy dissipation within the shell material. Furthermore, extension to a pump-probe configuration with few-cyclepulses ( ∼ fs duration) should enable the tracing of electron propagation within the target material. In view ofUEM, our results suggest that LAES can increase the temporal resolution of electron probes through optical gatingwith ultrashort laser pulses. 10 ethods Helium nanodroplet generation and particle pickup
We generate superfluid helium nanodroplets (He N ) in a supersonic expansion of high-purity He gas through a coolednozzle (5 µ m diameter, 40 bar stagnation pressure) into vacuum. Variation of the nozzle temperature between and K allows us to change the mean droplet size in the range of ¯ N = 3 . · − . · He atoms perdroplet [25], corresponding to a droplet radius of R d = 32 − Å. After formation, evaporative cooling results insuperfluid droplets at a temperature of about 0.4 K. We load the droplets with single atoms or molecules by passingthem through a resistively heated pickup oven (In), or a gas pickup cell (Xe, acetone). While pickup conditionsare optimized for single atom/molecule pickup, we found that the generation of dimers and larger complexes hasnegligible effects on the LAES spectrum.
Strong-field photoionization and detection of LAES spectra
We ionize the guest atom/molecule inside a droplet with femtosecond laser pulses from an amplified Ti:sapphirelaser system (800 nm center wavelength, 25 fs pulse duration, 3 kHz repetition rate, 1 mJ maximum pulse energy),which we focus to obtain intensities of I ≤ · Wcm , as indicated on top of Figures 1a-c. The pulse durationis measured with a single-shot autocorrelator and the intensity is calibrated using the U P energy shift of electronsgenerated by ATI of H O at a pressure of · − mbar [36]. Laser-ionization of the doped droplets takes placeinside the extraction region of a magnetic-bottle time-of-flight spectrometer and electron spectra are computed fromflight-time measurements [28, 37]. We compare LAES spectra of atoms/molecules inside the droplets to ATI spectraof bare atoms/molecules, which we obtain as effusive beam from the pickup cell by blocking the He droplets. Themeasurement chamber is operated at a base pressure of − mbar.
3D scattering simulations
For the 3D scattering simulations, we assume an ensemble of electrons with a fixed kinetic energy E kin . Theensemble with an isotropic distribution of initial directions propagates from the droplet center and scatters elasticallyuntil it finally exits the droplet. We assume binary electron-He collisions of mono-energetic electrons and neglectacceleration/deceleration due to LAES, as well as momentum transfer in elastic scattering events and inelasticinteractions. The propagation distance before a scattering event, s is chosen from the exponential distribution N ( x ) = N · e − nσx (Lambert–Beer law) as s = − log ( R )( nσ ) , with R uniformly distributed within the interval [0,1].11alues for the elastic scattering cross section σ and angular distribution dσd Ω are taken from Ref. [38] for electronenergies up to 10 eV and from Ref. [39] for faster electrons. A constant He density of n = 2 . · Atoms cm [40] isassumed. Data availabilty
The data measured, simulated, and analyzed in this study are available from the corresponding author on reasonablerequest.
Acknowledgements
We acknowledge financial support by the Austrian Science Fund (FWF) under Grants P 33166 and P 28475, as wellas support from NAWI Graz.
Author contributions
M.K. conceived and designed the experiment with contributions of L.T. and M.K.-Z. ; P.H. built the experimentalsetup with contributions of B.T. and M.K.; L.T. B.T., and M.S. performed the experiment; L.T. performed thesimulations with contributions of P.H.; L.T., B.T., M.K., and M.K.-Z. analyzed the data; all authors contributed tothe interpretation of the results; L.T., and M.K. wrote the paper.
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