Diffraction imaging of light induced dynamics in xenon-doped helium nanodroplets [original]

New J. Phys. 24 (2022) 113043 https://doi.org/10.1088/1367-2630/aca176

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PAPER

Diffraction imaging of light induced dynamics in xenon-doped

helium nanodroplets

BLangbehn

1,∗,YOvcharenko

1,2,AClark

3,MCoreno

4,RCucini

A Demidovich6, M Drabbels3, P Finetti6,MDiFraia

4,6, L Giannessi6, C Grazioli5,

DIablonskyi

7,ACLaForge

8, T Nishiyama9, V Oliver ´

Alvarez de Lara3,CPeltz

10,

PPiseri

11,OPlekan

6,KSander

10,KUeda

7, T Fennel10,12 ,KCPrince

6,13 ,

FStienkemeier

8, C Callegari4,6,TM¨

oller1and D Rupp12,14

1Technische Universit¨

at Berlin, Institut f¨

ur Optik und Atomare Physik, 10623 Berlin, Germany

2European XFEL GmbH, 22607 Hamburg, Germany

3Laboratory of Molecular Nanodynamics, Ecole Polytechnique F´

ed´

erale de Lausanne (EPFL), 1015 Lausanne, Switzerland

4ISM-CNR, Istituto di Struttura della Materia, LD2 Unit, 34149 Trieste, Italy

5IOM-CNR, Istituto Ofﬁcina dei Materiali, 34149 Trieste, Italy

6Elettra–Sincrotrone Trieste, S.C.p.A., 34149 Trieste, Italy

7Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan

8Institute of Physics, University of Freiburg, 79104 Freiburg, Germany

9Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan

10 Institut f¨

ur Physik, Universit¨

at Rostock, 18059 Rostock, Germany

11 CIMAINA and Dipartimento di Fisica, Universit`

a degli Studi di Milano, 20133 Milano, Italy

12 Max-Born-Institut f¨

ur Nichtlineare Optik und Kurzzeitspektroskopie, 12489 Berlin, Germany

13 Department of Chemistry and Biotechnology, Swinburne University of Technology, Victoria 3122, Australia

14 Laboratorium f¨

ur Festk¨

orperphysik, ETH Z¨

urich, 8093 Z¨

urich, Switzerland

∗Author to whom any correspondence should be addressed.

E-mail: bruno.langbehn@physik.tu-berlin.de,thomas.moeller@physik.tu-berlin.de and

[email protected]

Keywords: coherent diffraction imaging, helium nanodroplets, superﬂuid, dynamics

Abstract

We explore the light induced dynamics in superﬂuid helium nanodroplets with wide-angle

scattering in a pump–probe measurement scheme. The droplets are doped with xenon atoms to

facilitate the ignition of a nanoplasma through irradiation with near-infrared laser pulses. After a

variable time delay of up to 800 ps, we image the subsequent dynamics using intense extreme

ultraviolet pulses from the FERMI free-electron laser. The recorded scattering images exhibit

complex intensity ﬂuctuations that are categorized based on their characteristic features.

Systematic simulations of wide-angle diffraction patterns are performed, which can qualitatively

explain the observed features by employing model shapes with both randomly distributed as well

as structured, symmetric distortions. This points to a connection between the dynamics and the

positions of the dopants in the droplets. In particular, the structured ﬂuctuations might be

governed by an underlying array of quantized vortices in the superﬂuid droplet as has been

observed in previous small-angle diffraction experiments. Our results provide a basis for further

investigations of dopant–droplet interactions and associated heating mechanisms.

1. Introduction

The interaction of intense laser pulses with matter plays an important role in many ﬁelds, from modern

high-tech applications such as laser machining [1]andmicrosurgery[2], extreme ultraviolet (XUV)

lithography [3], or propulsion of small satellites [4,5] to fundamental and applied science. For example, in

structure analysis of biological specimen using x-ray diffraction, radiation damage poses a substantial

problem, thus fueling a considerable research interest, in the processes accompanying and following the

irradiation with intense x-ray bursts [6].

New J. Phys. 24 (2022) 113043 BLangbehnet al

In particular, atomic clusters can serve as isolated model systems of simple geometrical structure.

Time-resolved studies, where an initial pump light pulse excites the system and a subsequent probe light

pulse measures the state of the system after a deﬁned temporal delay, enable observation of the light

induced dynamics. In the extreme case, the free cluster will eventually fully disintegrate, as the energy

deposited by the pump pulse cannot dissipate otherwise. A detailed investigation of the fragments and the

dynamics can give an insight into the processes and their inherent time scale, which, in comparison with

theoretical models of the interaction, enable development of a fundamental understanding [7–12]. A basic

picture divides the interaction of an intense light pulse with an atomic cluster into three steps [13,14]:

(i) the ionization of cluster atoms and emission of electrons until the increasing positive charge prevents

further electrons from leaving the cluster, (ii) the formation and evolution of a nanoplasma of ions and

quasi-free electrons on a short timescale, often only a few femtoseconds, and (iii) an expansion leading to

complete destruction of the cluster, accompanied by relaxation and recombination processes.

Helium clusters, often referred to as helium nanodroplets, are model systems particularly suited to such

studies due to their very simple electronic structure and smooth behavior: they remain liquid down to

absolute zero forming mostly spherical shapes [15,16], and they are transparent from the far-infrared to the

vacuum ultraviolet because of the large ionization potential of helium (24.6 eV). Using a near infrared

(NIR) laser pulse, helium nanodroplets can be ionized only when the power density is sufﬁciently high that

multiphoton ionization or ﬁeld driven processes like tunneling ionization become signiﬁcant

(∼1015 Wcm

−2)[17,18]. Another option is to dope the droplets using atoms with a low ionization

potential: in this case, ionization becomes possible already at lower laser intensity [19,20], starting an

avalanche-like process at the dopant positions [21,22]. Depending on the interaction of the impurity with

the helium solvent, the dopants remain at the surface of the droplet or get immersed, as is the case for, e.g.,

xenon atoms [23]. When xenon-doped droplets are irradiated by an NIR pulse, theory predicts a very

efﬁcient complete ionization even with only a few xenon atoms embedded [19]. For the simple model of a

compact dopant cluster in the center of the helium droplet, an anisotropic growth of the nanoplasma along

the laser polarization axis has been predicted upon ignition [19]. On the other hand, dopant cluster

formation has been observed at multiple centers in larger droplets [24]. Further, the superﬂuid nature of the

helium nanodroplets leads to the occurrence of quantized vortices in large droplets [15], and the dopants

agglomerate along the vortex lines [25,26]. Nanoplasma ignition can therefore be expected in large droplets

at multiple sites, randomly distributed or structured by the vortex positions, which might lead to complex

dynamics. In addition to nanoplasma dynamics governed by Coulombic forces between charged

constituents, geometric changes beyond homogeneous Coulombic explosion or hydrodynamic expansion

might have to be considered in helium nanodroplets. For example, the formation of voids around free

electrons, so-called electron bubbles, has been described in liquid helium [27]. Further, the formation of gas

bubbles has been observed on a macroscopic scale around copper nanoparticles in bulk liquid helium [28]

and has also been reported on a microscopic scale around silver clusters in helium nanodroplets [29], in

both cases induced by resonant heating of the metal particles with an optical laser. Although superﬂuid

helium is known for its very large heat conductivity, the ﬂow of thermal energy from a solid particle to

liquid helium is hindered by a discrepancy in velocity of sound, an effect called Kapitza resistance [29,30],

that leads to a sudden evaporation of the surrounding helium, eventually forming a gas bubble. A third

process that could be taken into account is the ejection of dopant ions from a helium nanodroplet, leaving

the droplet with several helium atoms attached to them [31,32]. These considerations show that the study

of light induced dynamics in doped helium droplets may have particularly interesting aspects. So far, most

theoretical work has been carried out for relatively small helium droplets (N⩽106atoms per droplet).

While imaging experiments inherently address larger droplets [15,16], their outcome has already stimulated

theoretical studies, e.g., on the droplet shapes [33,34]. It has been the close interplay between theory and

experiment that established a more profound knowledge of the underlying physics of rotating superﬂuid

droplets [35]. Therefore, it would be particularly interesting to experimentally visualize the droplet

dynamics after laser excitation, giving a basis for comparison with theoretical models. Eventually, if droplet

ignition at multiple sites or geometric changes in the droplets are observed, such experiments might lead to

an extension of the models or even to a new approach to gain further insight into the processes, e.g., by

employing molecular dynamics simulations.

In this work, we report on a study of the dynamics triggered by intense NIR laser pulses in large,

xenon-doped helium nanodroplets. In this context, the advent of short-wavelength free-electron lasers

(FELs) has opened up a new route to determine the structure of individual nanoparticles via coherent

diffraction imaging (CDI) [36], which is based on recording the light scattered off a particle. In general,

such a diffraction pattern reﬂects the scattering behavior of the particle, i.e., it depends on the distribution of

atoms and their response to the wavelength of the incident light. Therefore, a change in scattering strength,

e.g., because of a modiﬁcation of the particle’s density or its electron distribution, leads to a change of the

New J. Phys. 24 (2022) 113043 BLangbehnet al

intensity distribution in the diffraction pattern, which is the basis for our method. The intense femtosecond

FEL light pulses enable the taking of a snapshot of the particle in time, thus allowing tracking of the

evolution of the particle in a pump–probe measurement scheme. This technique has been recently used to

study light induced dynamics in a variety of systems, e.g., structural changes in rare gas clusters [37–40],

surface melting of metal clusters [41], plasma dynamics in SiO2nanospheres [42], and anisotropic

evaporation of helium nanodroplets [18]. Here, we present a scenario where the energy is coupled into the

system via the dopants at localized positions. The agreement between outstanding features in our recorded

diffraction patterns and our qualitative model of randomly distributed and ordered voids in the droplets

gives a strong indication that the dynamics is not homogeneous but starts at several distinct sites in the

droplets.

2. Methods

The investigation is based on the analysis of wide-angle scattering images recorded at the FERMI FEL in a

similar conﬁguration to that previously described [16]. The experimental setup is described in section 2.1.

In section 2.2, the procedure to simulate wide-angle diffraction patterns in order to retrieve information on

the droplet dynamics from the recorded scattering images is presented.

2.1. Pump–probe imaging setup

The experiment was carried out in a pump–probe measurement scheme at the low density matter

end-station [43] of the FERMI FEL. The helium nanodroplets are ﬁrst irradiated with an NIR pulse

(wavelength λNIR =780 nm, duration 90 fs) to trigger dynamics (pump) and subsequently, after a variable

time delay of up to 800 ps, imaged using a 90 fs long XUV pulse (probe). The NIR laser is focused to a

100 μmspot(1/e2diameter) resulting in a power density of INIR =9×1013 Wcm

−2.TheFEListunedto

either non-resonant or resonant photon energies (Eph =19.4eVor21.5 eV, respectively) delivering power

densities exceeding IFEL =3×1014 Wcm

−2at spot sizes of 9 ×13 μm2(FWHM) and smaller. Please note

that the focus size of the NIR laser is chosen to be larger than that of the FEL to ensure that each droplet is

hit by the NIR laser before being imaged with the FEL. The XUV light scattered off a helium droplet is

collected up to a maximum scattering angle θmax =30◦by a detector consisting of a circular microchannel

plate (MCP) stacked onto a phosphor screen [7] located 65 mm downstream of the interaction region.

Pictures of the ampliﬁed scattering images on the phosphor screen are taken via a 45◦mirror using a

sCMOS Andor Neo 5.5 camera. The MCP, phosphor screen, and mirror have centered holes to let the FEL

and NIR beams pass through.

The helium droplets are produced by supersonic expansion into vacuum of helium through a 100 μm

trumpet-shaped nozzle with half opening angle of 20◦at a stagnation pressure p0=80 bar and temperature

T0=5.4 K, yielding a measured droplet velocity of 320 m s−1[44] and a mean droplet radius of

R=400 nm (corresponding to a mean droplet size of N=6×109atoms per droplet) as determined

from scattering images of approximately spherical droplets [44]. The droplets get doped with xenon by

traversing a 35.3 mm long gas cell, successively capturing ∼1.6×106xenon atoms per droplet (0.3 %)

[23,45]. The kinetic energy deposited in the droplet by each captured atom leads to the evaporation of

roughly 500 helium atoms [45,46]. Hence, the average droplet radius can be calculated to shrink to about

R=380 nm [47], which matches well the measured average radius of doped droplets. Overall, the

dopant atoms constitute only a small fraction of the total count of droplet atoms. Thus, for the wavelengths

used in this experiment we can assume the recorded diffraction patterns are dominated by light scattered off

the helium atoms.

In the analysis presented here, 26 390 images exhibiting meaningful scattering signal have been included.

The visibility of the scattering signal has been improved in post processing of the data by subtracting the

straylight background. In addition, the images have been corrected for the uneven detector sensitivity (that

is, e.g., due to the 8◦bias angle of the MCP [48]) and an angle-dependent intensity correction (∝cos−3θ)

has been applied that accounts for the ﬂat shape of the detection locus [49]. The thus corrected patterns are

made available via the CXI data bank [50] under the identiﬁer (ID) 208 [51].

2.2. Wide-angle scattering simulations

In order to retrieve information on the droplet density distribution, the diffraction patterns of individual

droplets are analyzed. In the case of small-angle scattering (θ5◦) the droplet’s electron density projection

can be reconstructed from the diffraction pattern using a phase retrieval algorithm which is commonly

utilized in CDI experiments and has already been successfully applied to doped helium nanodroplets

[25,26].Inthecaseofwide-angle scattering, however, multiple projection planes contribute to the

diffraction pattern rendering the reconstruction of a single projected density using algorithms based on

New J. Phys. 24 (2022) 113043 BLangbehnet al

inverse 2D Fourier transform impossible. For the same reason, wide-angle scattering images contain

valuable information on the three-dimensional droplet shape and orientation, that can be retrieved by

matching simulated diffraction patterns to the experimental data, as has been shown for faceted silver

clusters [52]. This forward-ﬁtting technique has further been employed to investigate the shapes of spinning

helium nanodroplets [16,53,54] and is adapted here to address density ﬂuctuations inside the droplets via

systematic simulations. The choice of employing systematic simulations instead of directly deriving the

shape information from the diffraction patterns was enforced by the ﬁrm constraints of the data set. These

are (i) the large number of strongly varying complex patterns, impossible to manually analyze in an

appropriate manner to generate reliable statistics of the abundances, (ii) the nonlinear detector response

together with the wide-angle detection which prevent object reconstruction by iterative phase retrieval, and

(iii) the large range of complicated features from inhomogeneous densities in the evolved droplets that

could not be captured by generalized model shapes, which are needed for direct forward ﬁtting.

For calculating the wide-angle scattering patterns, a fast algorithm based on the multi slice Fourier

transform (MSFT) [55] approach was used. While its approximations neglect multiple scattering events,

e.g., backscattering of the propagating electromagnetic ﬁeld, material properties can be approximated via

effective optical parameters even for photon energies close to the resonance [44]. These parameters have

been determined by matching scattering simulations to diffraction patterns of spherical helium

nanodroplets and comparing the radial intensity distribution to simulations based on Mie theory [56]fora

variety of droplet sizes and photon energies ranging from 19.0eVto23.7eV[44].

3. Results

In the following, the measured scattering images are described and discussed. First, the emergence of

dynamic features in the patterns is exempliﬁed, i.e., of features that are not observed in static (XUV only)

data. In section 3.1, the temporal evolution of the patterns is investigated, while in section 3.2 different

classes of patterns are identiﬁed based on their salient features.

Figure 1shows a small selection of scattering images of xenon-doped helium nanodroplets at short time

delay Δtbetween pump and probe pulse. It should be noted that much more pronounced changes of the

scattering occur at longer delays which will be discussed later (cf ﬁgures 3and 4). In the early stages of the

dynamics, i.e., Δt⩽3 ps, see ﬁgures 1(a)–(c), the images exhibit no visible difference from those of pristine

droplets [16]: in contrast to data taken with hard x-rays [26] the dopants do not lead to a change of the

intensity distribution. Presumably, the nanometer-sized structures of dopant aggregates are not resolvable at

the wavelength of the incoming XUV pulse. However, as shown in ﬁgures 1(d)–(f), intensity ﬂuctuations

along the diffraction rings become apparent for longer delays Δt>3 ps. We assume these ﬂuctuations are

linked to the dynamics in the droplets and consequently refer to these data as images exhibiting dynamic

features. Details of the determination of the images showing dynamic features and an overview of the whole

data set are given in appendix A. Overall, for short time delays and only slight intensity ﬂuctuations, the

droplet shapes can still be inferred from the known characteristic patterns [16] and classiﬁed as spherical

(ﬁgures 1(a) and (d)), ellipsoidal (ﬁgures 1(b) and (e)), and pill-shaped (ﬁgures 1(c) and (f)). Nonetheless,

the longer the delay the more complicated it is to identify droplet shapes, as the diffraction patterns become

increasingly distorted (cf ﬁgures 3and 4).

3.1. Temporal evolution of the patterns

In ﬁgure 2, the manually determined fraction of images exhibiting dynamic features is shown versus the

time delay Δtfor the non-resonant (Eph =19.4 eV) and resonant (Eph =21.5 eV) photon energy of the

XUV pulse. The reproducibility of the manually performed assignment of the dynamic fraction was tested

(see appendix A)andfoundtobebetterthan90%.Asaguidetotheeye,limitedgrowthfunctionsare

shown as dashed lines. Three main observations can be made: (i) there is a steep increase of the dynamic

fraction, that is faster for the non-resonant wavelength, (ii) the dynamic fraction saturates to less than 100%

at long delays (Δt>200 ps) indicating that not all images exhibit dynamic features, and (iii) the saturation

percentage is higher for the resonant wavelength.

We attribute the ﬁrst point to the wavelength-dependent inﬂuence of the refractive index on the

scattering. In the resonant case (Eph =21.5 eV) the absorption is high, hence, mostly the front surface of

the droplet contributes to the scattering and density changes inside the droplet are not visible in the

diffraction pattern. When the dynamics initiated by the NIR pulse starts inside the droplet (which we expect

to be the case for xenon dopants) and propagates toward the surface, it can be observed earlier in the

diffraction patterns recorded at the non-resonant photon energy (Eph =19.4 eV). The second and third

observations, however, are most probably related to an experimental artifact: we assume that an imperfect

overlap of the pulses leads to a situation where the dynamics is obviously not initiated in every droplet, even

New J. Phys. 24 (2022) 113043 BLangbehnet al

Figure 1. Emergence of dynamic features in diffraction patterns of xenon-doped helium nanodroplets. (a)–(c) For a time delay

Δt⩽3 ps the scattering images resemble those of pristine droplets described before [16], i.e., the dopants do not lead per se to

visible changes in the patterns. (d)–(f) For longer delays, intensity ﬂuctuations become apparent in the images that are linked to

the dynamics in the droplets and therefore referred to as dynamic features.

Figure 2. Temporal evolution of the fraction of scattering images exhibiting dynamic features. After a steep increase within

100 ps to 150 ps after NIR irradiation the dynamic fraction saturates at about 60% to 80%, i.e., the dynamics is not ignited in

every droplet. From the inset it can be seen that for short delays (Δt<3 ps) no dynamics are observed in the patterns. Further,

the rise of the dynamic fraction is slower for the resonant photon energy (Eph =21.5 eV), cf the data points at 20 ps. The dashed

lines are limited growth functions as a guide to the eye.

though a larger focal spot was chosen for the pump (NIR) than for the probe (XUV) pulse. Further, we

identify the third observation—a slightly lower asymptotic value for the non-resonant photon energy—as a

decreasing overlap between the two pulses over time, as even lower values were observed for subsequent

delay scans that were taken several hours apart (not shown).

The dynamic features in the patterns become, as expected, more pronounced with longer time delay. As

well, the intensity not only ﬂuctuates along the diffraction rings, but the complexity of the intensity

distribution increases. It should be noted that many patterns exhibit strong directionality, which is

completely different from what was observed in earlier pump–probe experiments on pure rare gas clusters

[37,38], thus indicating multiple scattering centers at speciﬁc sites rather than surface smoothing or

homogeneous fragmentation of the particle. The development toward long time scales is exempliﬁed in

ﬁgure 3, where the four brightest scattering images are shown for short (∼10 ps) and long (∼800 ps) delays

at non-resonant (ﬁgure 3(a)) and resonant (ﬁgure 3(b)) photon energy. It can be seen that the intensity

ﬂuctuations at short delays are more pronounced for non-resonant scattering (Eph =19.4eV),wherethe

droplets are almost transparent and information on density ﬂuctuations inside the droplets is encoded in

the diffraction pattern. For the resonant case (Eph =21.5 eV), less pronounced ﬂuctuations presumably

reﬂect changes on the droplet surface that occur later in time. Note that this observation is in line with the

slower rise of the respective curve in ﬁgure 2.

The images shown in ﬁgure 3already exhibit complex features, especially at long delays. However, this

situation becomes even more complicated when not only the brightest images are examined but the whole

data set is analyzed. While the overall trend—the longer the delay, the more distorted the diffraction

pattern—remains the same, the degree of complexity in the images at a given delay varies considerably. In

particular, no deﬁnite evolution in time is discernible when individual patterns are compared. Two facts can

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