# Femtosecond photoexcitation dynamics inside a quantum solvent

Bernhard Thaler  Graz University of Technology, Institute of Experimental
Physics, Petersgasse 16, 8010 Graz, Austria  Sascha Ranftl  Graz University of
Technology, Institute of Experimental Physics, Petersgasse 16, 8010 Graz,
Austria  Pascal Heim  Graz University of Technology, Institute of Experimental
Physics, Petersgasse 16, 8010 Graz, Austria  Stefan Cesnik  Graz University of
Technology, Institute of Experimental Physics, Petersgasse 16, 8010 Graz,
Austria  Leonhard Treiber  Graz University of Technology, Institute of
Experimental Physics, Petersgasse 16, 8010 Graz, Austria  Ralf Meyer  Graz
University of Technology, Institute of Experimental Physics, Petersgasse 16,
8010 Graz, Austria  Andreas W. Hauser  Graz University of Technology,
Institute of Experimental Physics, Petersgasse 16, 8010 Graz, Austria
Wolfgang E. Ernst  Graz University of Technology, Institute of Experimental
Physics, Petersgasse 16, 8010 Graz, Austria  Markus Koch  Graz University of
Technology, Institute of Experimental Physics, Petersgasse 16, 8010 Graz,
Austria

## Abstract

The observation of chemical reactions on the time scale of the motion of
electrons and nuclei has been made possible by lasers with ever shortened
pulse lengths. Superfluid helium represents a special solvent that permits the
synthesis of novel classes of molecules that have eluded dynamical studies so
far. However, photoexcitation inside this quantum solvent triggers a
pronounced response of the solvation shell, which is not well understood. Here
we present a mechanistic description of the solvent response to
photoexcitation of indium (In) dopant atoms inside helium nanodroplets (HeN),
obtained from femtosecond pump-probe spectroscopy and time-dependent density
functional theory simulations. For the In-HeN system, part of the excited
state electronic energy leads to expansion of the solvation shell within 600
fs, initiating a collective shell oscillation with a period of about 30 ps.
These coupled electronic and nuclear dynamics will be superimposed on
intrinsic photoinduced processes of molecular systems inside helium droplets.

## Introduction

Since the award of the 1999 Nobel Prize for Chemistry [Zewail2001], various
fundamental molecular processes have been investigated on their natural time
scales, e.g. fragmentation via different pathways on the molecular potential
energy surface [Townsend2004], non-adiabatic electron-nuclear coupling
[Blanchet1999], or electron dynamics initiated by ultrashort laser pulses
[Calegari2014]. Superfluid helium nanodroplets (He${}_{\textrm{N}}$) have been
used as nanocryostats to isolate atoms or molecules at 0.4 K temperature, or
to form new weakly bound aggregates [Callegari2011, Toennies2004]. Their
gentle influence on guest particles is demonstrated, for example, by electron
spin resonance [Koch2009] or molecular rotation and alignment experiments
[Shepperson2017b, Chatterley2017]. He droplets are an appealing spectrosopic
tool because of their transparency for electromagnetic radiation up to the
extreme ultraviolet energy regime [Callegari2011]. However, photoexcitation
inside the droplet leads to dissipation of significant excess energy via
coupling to collective modes of the surrounding helium, which is expected to
be a fast process. Femtochemistry inside He${}_{\textrm{N}}$ will allow real
time tracking of photochemical reactions in novel systems, such as fragile
agglomerates [Nauta2000, Nauta1999a, Higgins1996], or molecules in a
microsolvation environment [Gutberlet2009]. This will, however, require a
detailed knowledge about the response of the quantum fluid to the
photoexcitation of a dopant atom or molecule. So far, only the ultrafast
dynamics in pure helium droplets have been studied [Ziemkiewicz2015], and
femtosecond measurements on doped helium droplets were restricted to the
surface bound alkali metals [Mudrich2014, Vangerow2017] that can hardly couple
to helium bubble modes. Since most foreign atoms and molecules reside inside
the droplets and couple more strongly, we have concentrated on the electronic
excitation of single atoms well inside the droplets. In this way, no other
degrees of freedom such as rotation or vibration would interact and only the
coupling of the electronic excitation with the modes of the surrounding helium
should be detected. Previous spectroscopic studies in the frequency domain
have shown blue-shifted excitation bands of dopants inside droplets compared
to gas phase indicating that an excess energy is required to create a
correspondingly larger helium bubble to accommodate the excited electron
orbital [Callegari2011]. This excess energy must be released to the helium in
form of a damped helium excitation mode.
In our work, we follow the expansion of the helium bubble after electronic
excitation of single indium (In) dopants in real time. After an expansion from
4.5 Å to 8.1 Å radius in 600 fs, we observe a contraction of the surrounding
He at $(28\pm 1)$ ps, as well as an ejection of the dopant atom from the
droplet about 60 ps after the electronic excitation. As observable in our fs
pump-probe measurements, we chose the photoelectrons released because they
have been shown to exit the droplet rather ballistically without being
significantly influenced by the helium environment [Mudrich2014,
Ziemkiewicz2015, Loginov2005]. In spite of its importance for photochemical
studies in superfluid helium droplets, this sequence of events has not
previously been observed.

## Results

Photoexcitation dynamics of the In-HeN system. We investigate photoexcitation
dynamics of the In-He${}_{\textrm{N}}$ system with a combination of time-
resolved photoelectron spectroscopy (TRPES) and time-dependent density
functional theory (TDDFT) simulation, as described in the following. A
mechanistic description of the processes deduced from experiment and theory
will be discussed in the final paragraph.

Figure 1: Temporal evolution of the In-He${}_{\textrm{N}}$ system after
photoexcitation. (a) Sketch of the In-HeN potential energy surfaces as
function of the bubble radius for In in its ground [5s25p (2P1/2), blue],
lowest excited [5s26s (2S1/2), green] and ionic ground state [5s2 (1S0), red].
The purple arrow indicates pump excitation at 376 nm, blue arrows indicate
probe ionization at 405 nm for characteristic delay times and red arrows
correspond to the PE kinetic energy, as measured by TRPES. (b) Helium density
distributions of a He4000 droplet with an In atom located in the centre for
selected times after photoexcitation, as calculated with TDDFT. Scale bars, 10
Å.

### Time-resolved photoelectron spectroscopy

The feasibility of ultrafast experiments inside He${}_{\textrm{N}}$ ultimately
depends on the availability of an experimental observable that is available
with sufficiently low distortion by the intermediate helium. Ion detection, as
used on the droplet surface, is not possible because ions are captured inside
the droplet due to their attractive potential [Mudrich2014]. Photoelectron
(PE) detection, in contrast, has been successfully used for pure and doped
He${}_{\textrm{N}}$ [Loginov2005, Mudrich2014, Ziemkiewicz2015]. TRPES is a
well established method for ultrafast gas-phase studies and is primarily
sensitive to the electronic structure of a system [Hertel2006, Stolow2004]. As
depicted in figure 1a, after photoexcitation by a pump pulse the evolution of
the excited state is probed by time-delayed photoionization and the PE kinetic
energy (red arrows) is measured. When applied inside a He${}_{\textrm{N}}$,
photoexcitation induces an abrupt disturbance of the quantum fluid solvation
shell due to expansion of the valence electron wave function. Because the
energies of the electronic states depend on the structure of the He
environment, the transient response of the quantum solvent can be sensed with
TRPES (see figure 1a).

Figure 2: Time-resolved photoelectron (PE) spectra of single In atoms solvated
inside He${}_{\textrm{N}}$. The average droplet size is 4000 He atoms. (a) PE
kinetic energy spectrum as function of the pump-probe time delay $\Delta t$,
together with the simulated dynamics (dashed line) and the gas-phase PE energy
(solid line). Around time-zero the PE signal is increased due to temporal
overlap of the pump and probe pulses. Additionally, the total PE signal
decreases during the expansion, which might be due to a decreased ionization
probability for larger bubbles and/or lower escape probability of slow
electrons from larger bubbles at long delays compared to fast electrons from
small bubbles at short delays [Wang2008, Loginov2005]. (b) Selected spectra
for different pump-probe time delays, which resemble horizontal cuts through
the 2D plot in (a).

Figure 2 shows the time-dependent evolution of the PE signal within the first
picosecond after photoexcitation (a), together with PE spectra at selected
pump-probe times (b). Within about 600 fs the PE peak energy is shifted from
0.61 eV to 0.34 eV, followed by a slower decrease to 0.32 eV at 1000 fs, which
is about 0.02 eV above the gas-phase peak that appears at around 0.30 eV
(solid line in figure 2). The remaining shift represents the reduced
ionization potential of In atoms in the He environment due to polarization
effects [Loginov2005]. The linewidth of the PE spectra is significantly
increased and changes within the first picosecond (figure 2b), which we
ascribe to the following four reasons: First, during pump-probe cross
correlation of 150 fs, saturation effects and the spectral width of the pump
pulse are expected to contribute to the PE linewidth. Second, within the first
500 fs, a peak shift with a maximum slope of about 1 meV/fs in combination
with the 150 fs pump-probe cross correlation leads to an expected contribution
of about 150 meV. Third, ionization inside the droplet increases the
linewidth, given by the Franck-Condon overlap of the excited and the ionic
state (c.f., figure 1), which seems to be the dominant contribution to the
linewidth after 500 fs. Fourth, relaxation of the photoelectrons due to binary
collisions with individual He atoms on the way out of the droplet leads to an
asymmetric shape of the PE peaks [Loginov2005]. These decelerated electrons
can be seen as wing extending to PE energies below the gas phase value (red
line in figure 2b and Supplementary Fig. 7b).
In figure 3 the PE kinetic energy up to 100 ps is shown (blue dots). After a
steep decrease representing the tail of the initial peak shift shown in figure
2, the peak position slowly decreases to reach a constant value at about 60 ps
with a temporary increase at $(28\pm 1)$ ps. The PE peak width shows a very
similar trend (figure 3, red diamonds) with a steady decrease over time to
about 35 meV at long time delays and a temporary increase. Detailed scans of
PE peaks at short and long time delays are shown in Supplementary Fig. 7b. We
note that except for very short time delays right after the pump-probe overlap
(cross-correlation), the total PE yield stays constant over the whole
investigated temporal region.

Figure 3:  Photoelectron (PE) peak position and linewidth as function of time
delay $\Delta t$. The transient peak position (blue dots) and full width at
half maximum (FWHM, red diamonds) are shown within 100 ps after
photoexcitation, as measured with TRPES and simulated with TDDFT (orange
line). The experimental peak position and FWHM are obtained by Gaussian fits
to the corresponding PE energy spectra. The start position for the TDDFT
simulation was 20 $\mathrm{\AA}$ from the droplet center in order to obtain a
similar ejection behavior as the experiment.

### Time-dependent helium density functional theory

To obtain further insight into the ultrafast dynamics, photoexcitation of the
In-He${}_{\textrm{N}}$ system is simulated with TDDFT using the BCN-TLS-He-DFT
computing package [BCN-TLS-codes], which has been successfully applied to
reproduce the dynamics of He${}_{\textmd{N}}$ loaded with various different
atomic species [Ancilotto2017a]. In the present case, an extraordinary amount
of excess energy of several hundred meV is coupled into the system in the
photoexcitation process. We therefore carefully tested the simulations for
convergence by variation of the simulation parameters (see Supplementary Note
3 and Supplementary Figs. 4 and 5).
figure 1b shows He density distributions for selected times after
photoexcitation and the corresponding bubble expansion over time is plotted in
figure 4a. Inside the droplet the energies of the In excited state (5s26s) and
its ionic state (5s2) deviate from the bare atom values by the interaction
energies $E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$ and
$E_{\textrm{He}_{\textrm{N}}\textrm{-In${}^{+}$}}$, respectively. These
interaction energies, plotted in figure 4b, are calculated by integrating the
respective In-He pair potentials over the He density. While
$E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$ (cyan curve) is positive and
decreases with time (for larger bubbles),
$E_{\textrm{He}_{\textrm{N}}\textrm{-In${}^{+}$}}$ (red curve) is negative and
increases. This behavior can be expected from the repulsive and attractive
character of the excited and ionic state pair potentials, respectively
(Supplementary Fig. 3). The simulated PE peak shift with respect to the free
atom, as plotted in figure 4c, is calculated as the difference of the two
interaction energies ($E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$ \-
$E_{\textrm{He}_{\textrm{N}}\textrm{-In${}^{+}$}}$) and compared to the
measured transient peak shift in figures 2a and 4c, revealing good agreement.
Note that within 1000 fs $E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$ decreases
to zero, whereas $E_{\textrm{He}_{\textrm{N}}\textrm{-In${}^{+}$}}$ is
negative and reaches zero only at higher time delays. This results in a
further peak shift between 1000 fs and 60 ps (see figure 3), as the dopant is
ejected from the droplet. As can be seen in figure 4c, below 200 fs the
experimental peak shifts are slightly lower than the simulated ones, which we
ascribe to a distortion of the PE peaks due to a cross correlation signal
caused by overlap of pump and probe pulses in this temporal region (c.f.,
figure 2b).

Figure 4: Photoexcitation (PE) dynamics of the In-He4000 system simulated with
TDDFT. (a) Bubble radius as a function of time delay $\Delta t$, determined as
position of the corresponding He distribution at which the density has dropped
to 50% of the bulk value. Times for which the calculated He density is shown
in figure 1b are indicated. (b) Interaction energy
$E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$ of the 5s26s excited state (cyan
curve) and interaction energy
$E_{\textrm{He}_{\textrm{N}}\textrm{-In${}^{+}$}}$ of the 5s2 ionic state (red
curve). Additionally, the kinetic energy of the He atoms, $E_{\textrm{kin,
He}}$, is plotted as dashed line. (c) Simulated PE peak shift induced by the
He environment (orange line), obtained as
$E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$ \-
$E_{\textrm{He}_{\textrm{N}}\textrm{-In${}^{+}$}}$ (indicated by the shaded
area in (b)), which is also shown in figure 2a. For comparison to the measured
shift of the PE peak position over time, the recorded electron spectra at all
time delays (c.f., figure 2b) are fitted with Gaussian functions and the line
positions are indicated here by blue dots.

Next, we compare the steady decrease of the excited state electronic energy
(cyan curve in figure 4b) to the kinetic energy of the helium atoms (dashed
line in figure 4b), and find that the two curves show almost exactly
complementary trends.
Finally, the simulated PE peak position for an In atom, that is photoexcited
at a distance of 20 $\mathrm{\AA}$ from the droplet center, is shown in figure
3 (orange line). The choice of this position is justified by comparing
simulated PE peak transients with different starting positions (see
Supplementary Note 4 and Supplementary Fig. 6). The simulated curve shows the
same overall decrease as the experimental values (blue dots), although with a
more pronounced temporal increase at 22 ps.

## Discussion

The transient shift in the pump-probe PE spectrum of the In-
He${}_{\textrm{N}}$ system within the first ps (figure 2) has to be related to
solvation shell dynamics, as no internal degrees of freedom are available for
relaxation of the In atom in its lowest electronically excited state. The
energy of the excited valence electron in the In*-He${}_{\textrm{N}}$ system
is a very sensitive probe for the temporal evolution of the He environment
because of strong Pauli repulsion with the surrounding helium [Haeften2002].
TRPES measures the transient PE kinetic energy, which additionally depends on
a temporal shift of the ionic state energy
($E_{\textrm{He}_{\textrm{N}}\textrm{-In${}^{+}$}}$, figure 4b). Therefore, we
use TDDFT modeling of the photoexcitation process in order to distinguish
these two contributions. Previously, TDDFT simulations could only be compared
to time-dependent experiments at the weakly-interacting droplet surface
[Vangerow2017]. In the interior, the dopant-He interaction is much stronger,
with the consequence that significantly more excess energy (270 meV $\approx$
2200 cm-1 in our case) is coupled into the system during photoexcitation,
challenging the accuracy of the TDDFT approach. The reproduction of the
observed transient PE peakshift by TDDFT (figures 2a and 4c), without using
any experimental input for the simulation, demonstrates that a simulation of
photoexcitation dynamics is possible even in the case of significant excess
energy.
By combining experiment and theory we obtain the following mechanistic picture
of the coupled, ultrafast electronic and nuclear relaxation process:
Photoexcitation increases the radial expansion of the valence electron wave
function, as is suggested by the strong repulsive part of the In-He pair
potential at short distances in the excited state (Supplementary Fig. 3).
Pauli repulsion between the extended electron density and the closed-shell He
thereby pushes the surrounding solvation shell away (see Supplementary Movie
1). The spherical He bubble containing the excited In atom almost doubles its
radius from 4.5 $\mathrm{\AA}$ to 8.0 $\mathrm{\AA}$ within 600 fs after
excitation (figures 1b and 4a). This process can also be explained with the
corresponding potential energy surfaces (figure 1a): Because the equilibrium
bubble radius of the excited electronic state is larger than that of the
ground state, photoexcitation causes enlargement of the solvation shell. This
nuclear relaxation can be followed as transient PE peak shift because the
potential energies of the excited state and the ionic state depend on the
distance of neighboring He atoms to the In dopant. From an energetic
viewpoint, the bubble expansion is accompanied by the conversion of electronic
energy into kinetic energy of the He atoms, as illustrated by the mirror-
imaged progression of the two corresponding curves (excited state interaction
energy $E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$ and kinetic energy of the
He atoms $E_{\textrm{kin, He}}$) in figure 4b. The minute decrease of the sum
of $E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$ and $E_{\textrm{kin, He}}$ over
time represents energy transferred to He-He interactions (correlation
energies).
The impulsive stimulation of the He solvation layer initiates a collective
oscillation of the He bubble, the first contraction of which is observed as
increase of the PE kinetic energy and linewidth in figure 3 at $(28\pm 1)$ ps,
induced by the temporally increased He density in the vicinity of the In atom.
The repulsive character of the excited state In-He pair potential (see
Supplementary Note 2 and Supplementary Fig. 3) leads to ejection of the In
atom from the droplet on a time scale of about 60 ps (see Supplementary Movie
2). Consequently, the PE kinetic energy decreases to the free-atom value
within this time span (see figure 3) and only one bubble oscillation can be
observed. Dopant ejection is further confirmed by observing a rise in photoion
yield on the same time scale (Supplementary Fig. 7a) and a transient change of
the linewidth of the PE peak (see figure 3 and Supplementary Fig. 7b). While
the TDDFT simulation assumes a fixed starting location of the In atom, the
experimentally observed ensemble comprises a distribution of In atoms within
the droplet. As a consequence, the timing of the first bubble contraction will
appear smeared out in the experimental data, because the PE energy peak shift
due to dopant ejection is superimposed on the pure bubble oscillation.
Photoexcitation of the In dopant in the centre of the droplet induces multiple
oscillations and no ejection within the simulated time span (see Supplementary
Movie 3 and Supplementary Note 4). We therefore conclude, that the collective
solvation shell oscillation has a period of about 30 ps, the observation of
which provides insight into the hydrodynamics of the bubble in real time
[Moroshkin2008].
In conclusion, our experiments prove that ultrafast, coupled electronic and
nuclear dynamics of particles located inside superfluid He nanodroplets can be
observed and simulated. The expansion of the dopant solvation shell will be
superimposed on any molecular relaxation dynamics on femtosecond time scales
inside the droplet. When applying photoelectron detection, which seems to be a
promising observable for intrinsic molecular dynamics inside helium droplets,
the photoelectron transients induced by solvation shell dynamics have to be
known. The duration of dopant ejection, on the other hand, limits the time
frame for which ultrafast reactions inside the quantum fluid can be observed.
As a proof of concept, our results pave the way to use helium droplets as a
novel sample preparation technique for ultrafast studies on previously
inaccessible tailor-made or fragile molecular systems.

## Methods

### Helium droplet generation and In atom pickup

Helium droplets with an average size of about 4000 atoms are generated by
supersonic expansion of high purity (99.9999 %) helium gas through a cooled
nozzle (5 $\mu$m diameter, 18 K temperature, 40 bar stagnation pressure) into
high vacuum. The expansion in combination with evaporative cooling results in
droplet temperatures of about 0.4 K, which is well below the superfluid phase
transition of helium. The He${}_{\textrm{N}}$ are doped with In atoms inside a
pickup region, where indium is resistively heated. Pickup conditions are
optimized for single atom pickup and for an acceptable signal-to-noise ratio.
Indium was chosen as dopant because of its simple electronic structure with
one valence electron and because its excited state is symmetric, simplifying
the TDDFT simulations, as well as the interpretation. After passing a
differential pumping stage to increase the vacuum quality, the doped droplets
enter the measurement chamber, where the He${}_{\textrm{N}}$ beam is crossed
at right angle by the femtosecond laser pulses inside the extraction region of
a time-of-flight spectrometer.

### Time-resolved photoelectron spectroscopy

A commercial Ti:sapphire femtosecond laser system (Coherent Vitara oscillator,
Legend Elite Duo amplifier) delivers 25 fs laser pulses with 800 nm central
wavelength and 4 mJ pulse energy at a repetition rate of 3 kHz. The pulses are
split into a pump and a probe path with variable time delay. Pump pulses are
frequency up-converted by an optical parametric amplifier (Coherent OPerA
Solo) that tunes the wavelength to 376 nm (3.30 eV, 6 nm $\approx$ 60 meV full
width at half maximum, FWHM). Probe pulses are frequency doubled to 405 nm
(3.06 eV) with a 1 mm thick BBO crystal (3 nm $\approx$ 25 meV, FWHM) for
short delays and with a 5 mm thick LBO crystal (1.5 nm $\approx$ 10 meV, FWHM)
for long delays and guided over a delay stage. Dichroic mirrors are used in
both beam paths to remove undesired wavelengths from the upconversion process.
Pump and probe pulses are focused into the extraction region of the linear
time-of-flight spectrometer, where they overlap in space and time at the
intersection region with the He${}_{\textrm{N}}$ beam. A magnetic bottle
configuration [Kruit1983] ensures high electron detection efficiency and a
small positive repeller voltage of a few hundred mV increases the electron
kinetic energy resolution. At these parameters we estimate the relative energy
resolution of the spectrometer to be about 10%, based on reference
measurements. PE energies are calibrated with the free atom line, which
position is retrieved by subtraction of the excited state binding energy
[NIST_ASD] from the probe photon energy. The measurement chamber is operated
at a base pressure of $10^{-10}$ mbar.
The intensities of the pump and probe pulses are optimized to obtain a maximum
pump-probe signal with respect to pump-only and probe-only backgrounds. The
pump wavelength for In excitation to the lowest excited state (5s26s) is
chosen to be 376 nm in order to optimize the monomer to dimer ratio (see
Supplementary Note 1 and Supplementary Fig. 2), which is blue-shifted by 270
meV with respect to the gas-phase excitation wavelength at 410 nm [NIST_ASD].
This amount of excess energy is coupled into the In-He${}_{\textrm{N}}$ system
at photoexcitation. The pump-probe cross correlation is estimated with 150 fs.

### Time-dependent helium density functional theory

In the last years the approach of TDDFT for the bosonic system of helium has
been successfully applied to describe the dynamical interaction of surface-
and centre-located species with the helium quantum fluid, providing important
insight into effects like superfluidity on the microscopic level [Brauer2013],
desorption dynamics [Vangerow2017], or collision processes [Leal2014,
Coppens2017].
Details on the application and formalism of static and dynamic HeDFT are given
elsewhere [Ancilotto2017a] and the computing package of the BCN-TLS group is
available to the public as open source [BCN-TLS-codes]. Here only the basic
concepts and the terms that affect the presented results are given: Both
static and dynamic computations are based on the Orsay-Trento functional
[Dalfovo1995], which attributes for He-He interactions, and the diatomic In-He
potential energy surfaces. These pair potentials were calculated with high
level ab initio methods for the ground, excited and ionic state (see
Supplementary Note 2 and Supplementary Fig. 3). The simulations are performed
for a He4000 droplet with the In impurity located in the centre by using a He-
functional that includes the solid term [Ancilotto2005]. We use a three
dimensional Cartesian box of 96 Å length with a discrete grid size of 320 pt
(0.3 Å spacing) and time steps of 0.1 fs to simulate the bubble expansion
dynamics within the first ps and a grid size of 256 pt (0.375 Å spacing) and
time steps of 1 fs for the bubble oscillation dynamics up to 100 ps. For the
bubble oscillation dynamics the starting position was chosen to be at 20 Å
distance to the centre, which leads to a similar ejection behavior as in the
experiment. Both the bubble expansion and the oscillation period are local
effects and are found to be very similar for dopant locations in the droplet
centre. With the statically optimized ground state He density, a dynamical
evolution is triggered by replacing the ground state pair potential with the
excited state pair potential. This instantaneous perturbation drives the
system and TDDFT allows to follow the resulting dynamics in real time
[Ancilotto2017a], by solving the TDDFT equations for the helium and Newton’s
equations of motion for the impurity. Photoelectron spectra are simulated by
integrating the pair potential energies $E_{\textrm{{He-In}}}$ over the whole
droplet density $\rho_{\mathrm{He}}$ for both the excited and the ionic state
for various timesteps in the simulation. The difference between the
interaction energies directly compares to the difference in ionization energy
of the immersed impurity and therefore to the shift in PE energy:

$\mathrm{PE~{}shift~{}(t)}=\int{\rho_{\mathrm{He}}\mathrm{(\mathbf{r},t)}E_{\mathrm{In^{*}-He}}\mathrm{(\mathbf{r}-\mathbf{r}_{In^{*}}(t))}~{}\mathrm{d}\mathbf{r}}-\int{\rho_{\mathrm{He}}\mathrm{(\mathbf{r},t)}E_{\mathrm{In^{+}-He}}\mathrm{(\mathbf{r}-\mathbf{r}_{In^{+}}(t))}~{}\mathrm{d}\mathbf{r}}$

Since a huge amount of energy is deposited into the system in the excitation
process, the simulations were tested for numerical uncertainties by variation
of different parameters (grid size, time step and cutoff energy), as presented
in Supplementary Note 3 and Supplementary Figs. 4-5.

### Data availability

The data measured, simulated and analysed in this study are available from the
corresponding author on reasonable request.

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## Acknowledgements

We thank Manuel Barranco, Martí Pi and the whole BCN-TLS-HeDFT-code team for
their support with technical details of the simulations and fruitful
discussions. We appreciate the experimental support by Miriam Meyer and
acknowledge financial support by the Austrian Science Fund (FWF) under Grant
P29369-N36, as well as support from NAWI Graz.

Supplementary information for
Femtosecond photoexcitation dynamics inside a quantum solvent
Thaler et al.

Figure 5: Snapshots from Supplementary Movie 2. Helium density distributions
of a He4000 droplet with an indium atom, originally located at 20 Å distance
to the center, as obtained with TDDFT for characteristic time delays. The
dopant is ejected from the droplet after 60 ps, accompanied by a contraction
of the solvation shell (bubble) around 22 ps.

### Supplementary Note 1: The In-He${}_{\textrm{N}}$ excitation spectrum

The In-He${}_{\textrm{N}}$ excitation spectrum in the region of the In
5s26s$\leftarrow$5s25p transition was previously recorded and is shown in
Supplementary Fig. 6. In addition to the monomer signal (blue line) an In
dimer band (red line) appears with strong overlap to the monomer. The monomer
signal shows a maximum at 368 nm, which is blue-shifted by 2800 cm-1 with
respect to the free atom line (green, solid line) [NIST_ASD]. The excitation
wavelength was chosen at 376 nm (black, dashed line) to obtain a good monomer-
to-dimer ratio. Additionally, a reduced pickup temperature was used to
minimize the dimer influence.

Figure 6: Excitation spectrum of the indium monomer (In) and the indium dimer
(In2), both solvated inside He${}_{\textrm{N}}$. The spectra are measured in a
pump-probe experiment with 200 ps time delay and photoion detection at the In
monomer mass (115 amu) and the In dimer mass (230 amu), respectively. The
pump-probe delay time is sufficiently long that both monomers and dimers are
ejected from the droplet and ionized in the gas phase. The spectra were
recorded at a higher In pickup temperature as the presented experiments in
order to obtain a stronger dimer signal. Additionally, the gas phase In
transition (green, solid line) and the applied excitation wavelength (black,
dashed line) are indicated.

### Supplementary Note 2: The In-He pair potentials

The most important inputs for both the static and time-dependent DFT
simulations are the dopant-helium diatomic potential energy surfaces for all
electronic states that are populated in the experiment. The spin-orbit
coupling corrected energy curve of the ground state (X${}^{2}\Pi_{1/2}$), the
first excited state ($2^{2}\Sigma_{1/2}$) and the ionic state of the In-He
molecule are shown in Supplementary Fig. 7. All three states are spherically
symmetric and the spin-orbit splitting of the ground state to the 2P3/2
($1^{2}\Pi_{3/2}$ and $1^{2}\Sigma_{1/2}$, not shown in Supplementary Fig. 7)
has a value of about 2000 cm-1, for which reason the latter is not taken into
account in the simulation.

Figure 7: Indium-Helium interaction pair potentials used for the DFT and TDDFT
simulations. Ground state (blue), first excited state (green) and ionic state
(red).

For completeness, we give a short summary of the ab initio strategy: In the
calculation, the aug-cc-pV5Z family of basis sets [Woon1994, Kirk2003] in
combination with the ECP28MDF effective core potential of the Stuttgart/Köln
group [Metz2000] is used. The ab initio calculations are performed with the
MOLPRO software package [MOLPRO]. To account for the weak van der Waals-type
binding between the He and In, a combination of multiconfigurational self
consistent field calculations (MCSCF) [Knowles1985, WK88] and multireference
configuration interaction (MRCI) [KW92, boys70] is applied. The active space
of the MRCI approach consists of three valence electrons, the core orbitals
are optimized in the MCSCF calculation and kept doubly occupied. The curves
are basis set-extrapolated by applying additional calculations with the aug-
cc-pVQZ and aug-cc-pVTZ basis set families and the three-point extrapolation
formula by Wilson and Dunning [Wilson1997]. By using the Breit-Pauli operator,
the spin-orbit splitting is calculated.

### Supplementary Note 3: Numerical error tests for the simulation

The large amount of 270 meV excess energy coupled to the system in the
photoexcitation process, which is represented as high blueshift of the in-
droplet excitation wavelength with respect to the free atom line (see
Supplementary Fig. 6), is connected to an equally high amount of excited state
interaction energy $E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$ (Fig. 3b in the
main manuscript). This situation requires a careful choice of the simulation
parameters in order to avoid numerical errors. For example, the He repulsion
by the excited state electronic wave function of the In atom causes a strong
increase in the kinetic energy of the He. A correct description of the He
movement requires a fine grid size and small time steps, especially within the
first few fs, where the acceleration is high. We test for numerical errors by
calculating the transient change of
$E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$ for different grid sizes and
different time steps, as shown in Supplementary Figs. 8 and 9.

Figure 8: Dependence of the excited state interaction energy $E_{\textrm{He-
In*}}$ on the grid size parameters. (a)
$E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$ as function of time within the
first picosecond for three different grid sizes of 256, 320 and 384 pts,
calculated with 0.10 fs time steps. (b)
$E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$ for higher time delays for grid
sizes of 192, 256 and 320 pt, calculated with 1 fs time steps. (c) Difference
of interaction energy obtained with 320 pt grid size to that obtained with 256
and 384 pt, respectively. (d) Difference of interaction energy obtained with
256 pt grid size to that obtained with 192 and 320 pt, respectively.

The grid sizes used for the simulations presented in the paper are 320 pt for
simulation of the bubble expansion dynamics (0 to 1 ps) and 256 pt to simulate
the bubble oscillation (0 to 100 ps). Supplementary Fig. 8c shows that for the
short dynamics an increase to 384 pt does not change the interaction energy
significantly, while a decrease to 256 pt would introduce errors on the order
of about 1%. A similar behavior is observed for the higher timescales (see
Supplementary Fig. 8d), where a grid size of 192 pt introduces numerical
errors that are on the order of the simulated energies, whereas nearly no
deviation to the grid size of 320 pt is found.

Figure 9: Dependence of the excited state interaction energy $E_{\textrm{He-
In*}}$ on the time step parameter. (a)
$E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$ within the first picosecond as
function of time for three different time steps of 0.50, 0.10 and 0.05 fs,
calculated with a grid size of 320 pt. (b)
$E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$ for higher timedelays for the time
steps of 1.5, 1.0 and 0.5 fs, calculated with a grid size of 256 pt. (c)
Difference of interaction energy obtained with 0.10 fs to that obtained with
0.50 fs and 0.05 fs, respectively. (d) Difference of interaction energy
obtained with 1.0 fs to that obtained with 1.5 fs and 0.5 fs, respectively.

The influence of the time step parameter turned out to be less pronounced, as
shown in Supplementary Fig. 9c. An increase from 0.10 fs, as used for the
shorter bubble expansion simulations, to 0.50 fs gives a slightly stronger
change of $E_{\textrm{He}_{\textrm{N}}\textrm{-In*}}$, as compared to a
decrease to 0.05 fs, both of which are, however, in the $10^{-10}$ eV range.
The influence on the simulation for the longer bubble oscillation (simulated
with 1 fs steps) is an order of magnitude higher (see Supplementary Fig. 9d),
but still remains in the $10^{-9}$ eV range.

Another important parameter is the cutoff-energy for the different pair
potentials, that has to be chosen high enough in order to avoid unphysical He
density cumulations and energetic instabilities. The cutoff-energies for the
ground state, the excited state and the ionic state potential are chosen with
2150 cm-1, 1008 cm-1 and 5560 cm-1, respectively. As the excited state cutoff-
energy has the lowest value, different energies around 1008 cm-1 were tested
with the result that the influence on the excited state interaction energy was
below 10-10 eV (not shown).

### Supplementary Note 4: Bubble dynamics for different locations inside the
droplet

Whereas the simulated bubble expansion dynamics at short time delays ($<$1 ps)
show no dependence on the position within the droplet where the dopant is
photoexcited, the ejection process and the accompanied bubble oscillation
observed at longer time delays are strongly dependent on the photoexcitation
position. In Supplementary Fig. 10a the bubble radius over time for a starting
location in the center of the droplet is shown, revealing a continued
oscillation of the solvation shell with a period of about 30 ps and no
ejection. This is in contrast to the 20 Å off-center excitation position,
which shows only one contraction, superimposed to an overall increase of the
radius due to the ejection. Supplementary Fig. 10b shows calculated PE peak
energies as function of delay time for photoexcitation at various distances to
the droplet center. The counter-propagating trends of bubble radius and PE
energy for both the center and the 20 Å position clearly show that a
contracted bubble coincides with an increased PE energy, which is a
consequence of the increased In-He interaction energy of smaller bubbles (see
Fig. 1 in the main manuscript). Different appearance times of the first
contraction for different starting locations can be explained with the
superimposed PE energy decrease due to ejection, as well as effects caused by
helium shock-waves that propagate through the droplet following the initial
bubble expansion (see Supplementary Movies 2 and 3).
We choose the simulation of the 20 Å starting position for comparison with the
measured transient PE peak shift (Fig. 3 of the main text) because for other
locations either multiple or no bubble oscillations are predicted.

Figure 10: Comparison of the simulated In-HeN dynamics for photoexcitation at
different positions. The bubble radius as function of time is shown in (a) and
the corresponding transient change in photoelectron energy is shown in (b).

### Supplementary Note 5: Transient ion yield and PE spectra at long time-
delays

Ejection of the indium atoms can further be confirmed by a transient rise of
ion yield. Because the ionic In+-He potential is strongly attractive, the
atoms deeply solvate into the droplets when being ionized within or even in
the vicinity of the droplets, in which case they are not detected. Only when
escaped from the long-range, attractive potential of the droplet they are
truly free and are measured [Vangerow2017]. This is seen in the transient ion
yield (Supplementary Fig. 11a), where there is absent signal for the first 40
ps, followed by a signal rise within about 30 ps (to 67% of the maximum). The
steady rise is connected to a position (and velocity) distribution of dopants
inside the droplets before photoexcitation, resulting in an ensemble that gets
ejected, which blurs the ion and electron transients. The same timescale of PE
peak shift (Fig. 3 in main manuscript) and photoion yield rise confirms the
correct interpretation of dopant ejection.
Further insight into the ejection process can be obtained from the line shapes
of the PE lines. Supplementary Fig. 11b shows PE spectra obtained from
In–He${}_{\textrm{N}}$ at time delays of 0.8 ps (blue line) and 200 ps (red
line), as well as for bare In atoms (yellow line). Ionization inside the
droplet at 0.8 ps leads to a shift of the PE peak to higher energies with
respect to the bare atom due to the reduced ionization potential inside the
droplet [Loginov2005]. The PE spectrum is significantly broader [$(62\pm 2)$
meV, FWHM] compared to that of the bare atom [$(35\pm 1)$ meV, FWHM] (see also
Fig. 3 of the main text), which we ascribe to the Franck–Condon overlap of the
excited and ionic potential energy surface inside the droplet. Additionally,
the 0.8 ps spectrum shows a wing extending below the bare atom line,
representing decelerated electrons [Loginov2005], as discussed in the results
section of the main text. Ionization of the In–He${}_{\textrm{N}}$ system at
200 ps gives exactly the same line shape as the bare atoms, proving that all
In atoms are ejected from the droplets.

Figure 11: Transient photoion yield (a) and comparison of PE spectra at short
and long time delays, as well as a PE spectrum of bare In atoms (b). The bare
atom spectrum was recorded by deactivating the droplet source and exploiting
the effusive In atom beam from the pickup source. The excitation wavelength
for the bare indium spectrum was chosen with 410 nm (see Supplementary Fig.
6).

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