# Near-unity indistinguishability of single photons emitted from
dissimilar and independent atomic quantum nodes

Félix Hoffet<EMAIL_ADDRESS>ICFO – Institut de Ciencies Fotoniques, The
Barcelona Institute of Science and Technology, Spain  Jan Lowinski  ICFO –
Institut de Ciencies Fotoniques, The Barcelona Institute of Science and
Technology, Spain  Lukas Heller  ICFO – Institut de Ciencies Fotoniques, The
Barcelona Institute of Science and Technology, Spain  Auxiliadora Padrón-Brito
ICFO – Institut de Ciencies Fotoniques, The Barcelona Institute of Science and
Technology, Spain  Hugues de Riedmatten<EMAIL_ADDRESS>ICFO –
Institut de Ciencies Fotoniques, The Barcelona Institute of Science and
Technology, Spain  ICREA – Institució Catalana de Recerca i Estudis Avançats,
08015 Barcelona, Spain

###### Abstract

Generating indistinguishable photons from independent nodes is an important
challenge for the development of quantum networks. In this work, we
demonstrate the generation of highly indistinguishable single photons from two
dissimilar atomic quantum nodes. One node is based on a fully blockaded cold
Rydberg ensemble and generates on-demand single photons. The other node is a
quantum repeater node based on a DLCZ quantum memory and emits heralded single
photons after a controllable memory time that is used to synchronize the two
sources. We demonstrate an indistinguishability of $94.6\pm
5.2\text{\,}\mathrm{\char 37\relax}$ for a temporal window including
$90\text{\,}\mathrm{\char 37\relax}$ of the photons. This advancement opens
new possibilities for interconnecting quantum repeater and processing nodes
with high fidelity Bell-state measurement without sacrificing its efficiency.

Single photons play a crucial role in quantum technologies. Since their
quantum state is little affected by the transmission, they are well-suited as
information carriers to connect and entangle distant quantum nodes [1]. In a
quantum network, these quantum nodes serve specific roles, dedicated either to
information processing, communication, or sensing [2]. Consequently, they
utilize various physical systems, often employing photons with differing
frequencies, bandwidths, and waveforms. A major challenge is to interface
these different nodes and distribute entanglement between them, despite their
inherent differences. This can be achieved by interfering single photons
emitted from these nodes, but a high degree of indistinguishability between
the photons is required [3].

The indistinguishability $\eta$ between two photons can be inferred by
measuring the visibility $V$ of a Hong-Ou-Mandel interference [4]. When two
photons impinge on a beamsplitter, the Hong-Ou-Mandel effect states that if
they are indistinguishible, they will bunch at the output, leading to a
suppression of coincidence events relative to the distinguishable scenario.
This two-photon interference is also at the heart of photonic Bell state
measurements, which enable quantum teleportation and the generation of
entanglement between remote systems [5].

High indistinguishabilities have been demonstrated for consecutive photons
emitted from a single source, including quantum dots [6, 7, 8, 9], single
rare-earth ions [10], Rydberg ensembles [11, 12], spontaneous parametric down
conversion [13, 14] and single atoms in cavities [15]. However, it is
important to note that these results do not guarantee that independent photons
from two of these sources would be indistinguishable. Recently, a handful of
experiments have demonstrated two-photon interference from independent sources
[16, 17, 18, 19, 20, 21, 22, 23, 24, 25], sometimes allowing the generation of
remote entanglement between nodes based on the same platform [26, 27, 28, 29,
30].

$\ket{r}$
---

$\ket{e_{2}}$
---

$\ket{g_{2}}$
---

$\ket{s}$
---

$\ket{g_{1}}$
---

$\ket{e_{1}}$
---

Quantum Node 1
---
Based on DLCZ protocol
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Quantum Node 2
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Based on Rydberg Blockade
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Quantum interference
---
Ensemble 1
---
photon
---
Read
---
pulses
---
Write
---
photon
---
Write
---
pulse
---
Read
---
Ensemble 2
---
QWP
---
HWP
---
DM
---
BS
---
SPAD 2a
---
SPAD 2b
---
photon
---
Rydberg
---
photon
---
Rydberg
---
beam
---
Coupling
---
beam
---
Coupling
---
beam
---
Coupling
---
blockade
---
Rydberg
---
blockade
---
Rydberg
---
probe
---
Input
---
probe
---
Input
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DM
---
FPC 2
---
FPC 1
---
APD 1
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PBS
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AOM
---
photon
---
Read
---
pulse
---
Read
---
photon
---
Write
---
pulses
---
Write
---
$\left(+\omega_{aom}\right)$
---

Figure 1: Schematic view of the experiment. Two quantum nodes generate
independent single photons that are sent to a measurement setup, where they
interfere. Quantum node 1 is based on the DLCZ protocol, where the detection
of a write photon in APD1 heralds a collective excitation. This excitation is
later mapped to a waveshape-tunable single photon by applying a read pulse. At
the same time, Node 2 generates a single photon by means of dynamical Rydberg-
EIT in a Rydberg-blockaded ensemble. The photon generated in Node 1 is
frequency shifted by a single-pass acousto-optic modulator (AOM) to match the
one generated in Node 2. Both photons are then sent to a Hong-Ou-Mandel setup
consisting of two detectors (SPAD2a(b)) and a beam-splitter (BS). Coincidences
are recorded in the case when both photons are set to be overlapping
(indistinguishable case), and temporally separated (distinguishable case). DM:
Dichroic mirror; PBS: Polarizing beam-splitter; FPC: Fabry-Perot cavity;
HWP(QWP): Half-(quarter-)wave plate

However, most of these realizations had to discard a large amount of their
photon detections to keep the two-photon indistinguishability sufficiently
high. This is done by selecting a temporal detection window much shorter than
the photon duration. In quantum communication, this selection is detrimental
as it reduces the entanglement distribution rate between the two nodes. Up to
now, it is still a challenge to interface independant nodes with high
indistinguishability, without discarding any photon detections.

Additionally, interfacing hybrid systems adds another layer of complexity
since their generated photons usually have different properties (e.g.
frequencies, bandwidths, temporal modes), making them distinguishable. Hong-
Ou-Mandel interferences between a single-photon source and a classical source
such as a laser [31], or the Sun [32], have been demonstrated before, albeit
with an overall visibility below the classical limit of 50%. To our knowledge,
only one experiment measured the indistinguishability of photons emitted from
dissimilar and independent matter quantum nodes [33], but again the overall
interference visibility couldn’t surpass the classical limit due to temporal-
mode mismatch.

Platforms currently investigated as quantum network nodes include laser cooled
atoms and ions, as well as solid-state systems. Cold atomic-ensembles provide
a versatile platform that enables several functionalities. Ground state
collective excitations (spin waves) allow for the realization of long-lived
and efficient quantum memories that can be used as quantum repeater nodes,
using the Duan-Lukin-Cirac-Zoller (DLCZ) scheme [34, 3, 30, 16]. Additionally,
atomic ensembles enable quantum processing nodes [35, 36, 37, 38, 39, 40] and
deterministic quantum light sources [11, 12, 41] using the Rydberg blockade
effect.

In this work, we demonstrate the generation of highly indistinguishable
photons from two dissimilar cold atomic quantum nodes. Node 1 relies on the
probabilistic and heralded generation of spin waves following the DLCZ
protocol, later converted into a single photon after a controllable storage
time used to synchronize the nodes. Triggered by Node 1, Node 2 then generates
single photons in a deterministic fashion using Rydberg electromagnetically-
induced transparency [42, 43], and the two photons are combined at a beam
splitter. We achieve a Hong-Ou-Mandel visibility of $V$=$80.2\pm
3.6\text{\,}\mathrm{\char 37\relax}$ leading to an indistinguishability of
$\eta$=$89\pm 4.9\text{\,}\mathrm{\char 37\relax}$ between the independent
photons, without discarding any detection. By considering a temporal window
containing $75\text{\,}\mathrm{\char 37\relax}$ of the photons, the visibility
increases to ${V=$93.2\pm 2.3\text{\,}\mathrm{\char 37\relax}$}$. This
experiment opens up new possibilities for connecting remote dissimilar quantum
nodes.

Our two quantum nodes are based on ensembles of cold 87Rb atoms. They are
located in the same laboratory on two optical tables separated by
$3\text{\,}\mathrm{m}$ (see Fig. 1). We first start with the individual
description of each node before we turn to the quantum interference involving
their respective photons.

The first node is based on the DLCZ protocol, producing heralded photons. It
has the capability to generate entangled photon pairs with an in-built quantum
memory that can be used for synchronization of the network. The DLCZ protocol
starts by sending a train of write pulses to ensemble 1, detuned by
${\Delta=$-40\text{\,}\mathrm{MHz}$}$ from the
${\ket{g_{1}}=\ket{5S_{1/2},F=2,m_{F}=+2}}$ to
${\ket{e_{1}}=\ket{5P_{3/2},F=2,m_{F}=+1}}$ transition. With a low
probability, this generates a write photon (Stokes photon) in the heralding
mode which, upon detection at detector SPAD1, heralds a collective spin
excitation in the spin state $\ket{s}=\ket{5S_{1/2},F=1,m_{F}=0}$. After a
programmable time that is set to synchronize the photon generation from two
nodes ($2.8\text{\,}\mathrm{\SIUnitSymbolMicro s}$), we then send a read pulse
resonant with the $\ket{s}\rightarrow\ket{e_{1}}$ transition that maps the
collective excitation into a read photon (anti-Stokes photon). This photon is
resonant with the $\ket{g}\rightarrow\ket{e_{1}}$ transition and is emitted
into a well-defined mode that depends on the phase matching conditions of the
process. For the DLCZ source to generate photons efficiently, the optical
depth ($\mathrm{OD}$) of the ensemble must be large [44]111Nevertheless, OD
shouldn’t be too large since it can lead to incoherent absorption and
reduction of efficiency. and the lifetime of the collective excitation must be
longer than the synchronization time between the write and the read pulse. To
fulfill both requirements, we employ conventional methods of magneto-optical
trapping (MOT) aided by a single retro-reflected beam dipole trap at
$797\text{\,}\mathrm{nm}$. This dipole trap is useful to increase the duty-
cycle of the experiment 222However, the increase in duty cycle is partial,
since the writing process of the DLCZ protocol heats the atoms and is
associated with rapid loss of optical depth. Still, when producing photons
with low $g^{(2)}_{n1}(0)$, we were able to keep a sufficient optical depth
during the $4\text{\,}\mathrm{ms}$ of interrogation time.. We obtain a cloud
with $\mathrm{OD}=6$ and an initial temperature of
$\sim$80\text{\,}\mathrm{\SIUnitSymbolMicro K}$$. Furthermore, we use Fabry-
Perot cavities (FPC) to filter out unwanted background noise that comes from
the write and read pulses, increasing both the efficiency of the heralding and
the purity of the generated photons. The probability to generate a read photon
conditionned on the detection of a write photon is around 25% with these
experimental parameters. Finally, an acousto-optical modulator is employed to
adjust the frequency of the read photons and to adjust the photon flux,
aligning it with that of the other node.

Figure 2: Quantum nodes properties. (a): Temporal modes of the photons emitted
from Node 1 and Node 2. The gray straight lines represent the temporal windows
in which the coincidences of the two-photon interference experiment are
counted. (b) and (c): Single-photon autocorrelation of the photons emitted
from Node 1 an Node 2. We measure ${g^{(2)}_{n1}(0)=$0.13\pm 0.04$}$ for the
photon issued of Node 1 and ${g^{(2)}_{n2}(0)=$0.09\pm 0.03$}$ for the photon
coming out of Node 2.

The second node is based on a blockaded Rydberg ensemble generating single
photons in a deterministic fashion. Thanks to a two-beam crossed dipole trap
at $852\text{\,}\mathrm{nm}$, we create a small spherical atomic cloud with
size of $13.5\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (FWHM), $\mathrm{OD}=12$
and temperature of $\sim$40\text{\,}\mathrm{\SIUnitSymbolMicro K}$$. We send a
laser pulse resonant with the
${\ket{g_{2}}=\ket{5S_{1/2},F=2}\rightarrow\ket{e_{2}}=\ket{5P_{3/2},F=3}}$
transition together with a counter-propagating coupling beam resonant with the
${\ket{e_{2}}\rightarrow\ket{r}=\ket{103S_{1/2}}}$ transition, effectively
establishing Rydberg electromagnetically-induced transparency that creates a
propagating Rydberg polariton in the cloud [42, 43]. The Rydberg blockade
radius is $r_{b}\approx$16\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ at the
$n=103$ Rydberg state [47]. Since it is larger than the cloud size, the strong
dipole-dipole interactions prevents the existence of multiple Rydberg
excitations in the cloud [48], allowing us to retrieve a single photon at the
output of the cloud with a generation probability of 14%. During the Rydberg
polariton’s propagation, we switch off-and-on the coupling field (a process
known as Dynamical EIT), that effectively freezes the propagation and stores
the polariton in the Rydberg state, what is known to enhance the non-linearity
and the single photon’s quality [49, 50].

Due to the different nature of the two quantum nodes, their respective
experimental cycles differ from one another. During the
$200\text{\,}\mathrm{ms}$ of interrogation time of Node 2, Node 1 performs 17
full cycles, each one containing $4\text{\,}\mathrm{ms}$ of interrogation
time. During each cycle, Node 1 tries to herald a spin wave each
$4\text{\,}\mathrm{\SIUnitSymbolMicro s}$. Once a write photon is detected on
SPAD1, an electronic signal is sent to Node 2 which then generates a photon
that either temporally overlaps with Node 1 photon (indistinguishable case),
or is separated in time (distinguishable case) 333A detailed description of
our experimental cycle and the communication between the two nodes is given in
the supplementary material.. Every half an hour, the experiment is
automatically put in calibration mode for around ten minutes in order to
compensate for any possible slow drift. In the distinguishable case, the final
triple-coincidence rate is around $0.02$ events per second.

Both photons are sent to a measurement platform consisting of a fiber beam-
splitter (BS) and two single-photon detectors SPAD2a(b). If the two photons
are completely indistinguishable, they bunch together at the output of the
beam-splitter and no coincidence between SPAD2a and SPAD2b is recorded. Truly
indistinguishable photons can be obtained only if all their degrees of freedom
(spatial, polarization, frequency, time) are mode-matched with one another.
The spatial mode matching can be ensured by using a single-mode fiber beam-
splitter. Since the polarization of the incoming photons needs to be well
controlled at the position of the BS, we use polarization-maintaining fibers
and a set of half-wave and quarter-wave plates before the fiber incoupling.
Injecting classical light at slightly different frequencies into the setup and
adjusting the beating fringes, we then measure a polarization-matching greater
than $99.9\text{\,}\mathrm{\char 37\relax}$. The frequency offset
($266\text{\,}\mathrm{MHz}$) determined by the atomic levels used to generate
the photons in each quantum node is compensated by sending the heralded
photons from the DLCZ node to a single-pass acousto-optical modulator (AOM).
The temporal offset can be controlled by changing the synchronizing time (or
storage time) of each quantum node. Finally, assuming that both photons are
Fourier limited, their frequency-mode is completely determined by their
temporal mode. We match the temporal mode of the DLCZ produced photon to that
of the Rydberg-produced photon by modulating the intensity of the read pulse
in the DLCZ protocol [52], allowing us to maintain a temporal mode-matching
higher than $98\%$ as represented in Fig. 2(a). In both cases, we produce a
photon with a steep leading edge of $60\text{\,}\mathrm{ns}$ and resembling an
exponential decay trailing edge with $1/e$ time of around
$180\text{\,}\mathrm{ns}$. The photon flux is also adjusted by changing the
driving amplitude of the AOM, such that the probability to have a photon at
the beamsplitter is similar for each source (around 2.8% per trial).

To evaluate the quality of each photon, we measure the autocorrelation
function $g^{(2)}_{n1}(\tau=0)$ and $g^{(2)}_{n2}(\tau=0)$. The results are
displayed in Fig. 2(b), where the counts are integrated over a temporal window
of length $t_{\mathrm{w}}=$800\text{\,}\mathrm{ns}$$ in each
$5.4\text{\,}\mathrm{\SIUnitSymbolMicro s}$-long bin, representing one
experimental trial. We measure $g^{(2)}_{n1}(0)=$0.13\pm 0.04$$ for the photon
generated by node 1 and $g^{(2)}_{n2}(0)=$0.09\pm 0.03$$ for the photon coming
from node 2.

Figure 3: Two-photon interference. (a), (b), (c): Normalized coincidence rate
$g^{(2)}(\tau)$ between SPAD2a and SPAD2b in the distinguishable case (blue)
and indistinguishable case for the whole pulse (red), and for a proportion
$\mathcal{P}=75\%$ of counts (yellow). (d): Measured visibility ($V$),
indistinguishability ($\eta$) and photon counts share ($\mathcal{P}$), for
various lengths of the temporal window.

We now move to the two-photon interference between the two quantum nodes. In
both indistinguishable case and distinguishable case, we record coincidences
to measure the visibility of the two-photon interference which is given by

$V=1-\frac{g^{(2)}_{i}(0)}{g^{(2)}_{d}(0)}\text{,}$ (1)

where $g^{(2)}_{d}(0)(g^{(2)}_{i}(0))$ is the normalized coincidence rate
between SPAD2a and SPAD2b in the distinguishable (indistinguishable) case.
Coincidences are recorded in a specific temporal window as illustrated on Fig.
2 where a window of length ${t_{\mathrm{w}}=$800\text{\,}\mathrm{ns}$}$
contains ${\mathcal{P}=$100\text{\,}\mathrm{\char 37\relax}$}$ of photon
counts and another window of length
${t_{\mathrm{w}}=$200\text{\,}\mathrm{ns}$}$ contains a proportion of
${\mathcal{P}=$75\text{\,}\mathrm{\char 37\relax}$}$.

For counts integrated over the full window
(${t_{\mathrm{w}}=$800\text{\,}\mathrm{ns}$}$), we measure a visibility of
${V=$80.2\pm 3.6\text{\,}\mathrm{\char 37\relax}$}$ with
${g^{(2)}_{d}(0)=$0.57\pm 0.05$}$ and ${g^{(2)}_{i}(0)=$0.11\pm 0.02$}$, as
shown in Fig. 3(top). This result is, to our knowledge, the highest reported
visibility of a two-photon interference in hybrid systems, and it is higher
than most realizations with nodes made of the same platform without discarding
photon counts. If we take ${\mathcal{P}=$75\text{\,}\mathrm{\char 37\relax}$}$
of all photon counts (${t_{\mathrm{w}}=$200\text{\,}\mathrm{ns}$}$), we
measure a visibility as high as ${V=$93.2\pm 2.3\text{\,}\mathrm{\char
37\relax}$}$, with ${g^{(2)}_{i}(0)=$0.04\pm 0.01$}$. We further confirm the
strong suppression of the coincidence rate for overlapping pulses by looking
at the time-resolved HOM interference, as shown in Fig. 4(left). When the
photons are set to be distinguishable, we observe a peak of coincidences (blue
data) around zero delay that is linked to the convolution of the photons’
temporal mode. One can appreciate a strong suppression of the coincidence
number (red data) over the whole temporal window. We emphasize here that the
results presented in this paragraph were measured with raw coincidences and
without correction of any kind.

Figure 4: (a): Number of detected coincidences separated by a time delay
$\Delta t$, within the analysis window
$t_{\mathrm{w}}=$800\text{\,}\mathrm{ns}$$. (b): Measured two-photon
visibilities for different values of DLCZ photons autocorrelation
$g^{(2)}_{n1}$, for the temporal window containing
$\mathcal{P}=$100\text{\,}\mathrm{\char 37\relax}$$ and
$75\text{\,}\mathrm{\char 37\relax}$ of the counts. The solid lines are the
expected values estimated from eq. 2 for an indistinguishability of
$\eta=$86\text{\,}\mathrm{\char 37\relax}$$ (red) and
$\eta=$100\text{\,}\mathrm{\char 37\relax}$$ (yellow).

To estimate the indistinguishability $\eta$ between the two photons, we take
into account the fact that the non-zero value of the single-photon
autocorrelation $g^{(2)}(0)$ (see Fig. 2) reduces the visibility of the
interference. For a 50/50 beamsplitter, assuming that each node emits at most
two photons, the indistinguishability $\eta$ can then be evaluated using the
following formula [33]:

$V=\frac{2\eta}{g^{(2)}_{n1}(0)x+g^{(2)}_{n2}(0)/x+2}$ (2)

where $g^{(2)}_{n1}(0)(g^{(2)}_{n2}(0))$ is the autocorrelation of the photon
incoming from Node 1(2) and $x=p_{n1}/p_{n2}$ is the ratio between the
probabilities to detect a photon from Node 1 and 2. We infer an
indistinguishability ${\eta=$89.2\pm 4.9\text{\,}\mathrm{\char 37\relax}$}$
for ${\mathcal{P}=$100\text{\,}\mathrm{\char 37\relax}$}$. The
indistinguishability increases to $94.6\pm 5.2\text{\,}\mathrm{\char
37\relax}$ for ${\mathcal{P}=$90\text{\,}\mathrm{\char 37\relax}$}$ and
becomes compatible with unity within error bars for
$\mathcal{P}=$75\text{\,}\mathrm{\char 37\relax}$$, showing that both photons
exhibit a near-perfect indistinguishability between one another. To further
study this interference, we repeat this measurement for different values of
$g^{(2)}_{n1}(0)$ to see if the scaling of the visibility in eq. 2 is well
respected. $g^{(2)}_{n1}(0)$ can be changed by varying the write pulse power
in the writing stage of the DLCZ protocol, which changes the probability to
generate more than one atomic excitation. These measurements are plotted in
Fig. 4 alongside the predictions of eq. 2 (solid lines) with parameters
${x=1.3,\ g^{(2)}_{n2}(0)=0.1}$ and where the indistinguishability is
$\eta=\\{86,100\\}\%$ for $\mathcal{P}=\\{100,75\\}\%$. We observe a good
agreement of our data with the formula, indicating that our visibility is
indeed reduced due to non-zero two-photon suppression of each photon.

For completeness, we plot in Fig. 3(bottom) the visibility $V$,
indistinguishability $\eta$ and proportion $\mathcal{P}$ of photon detections
as a function of the length of the temporal window $t_{\text{w}}$. In the
limit of large temporal window, we observe a saturation of
indistinguishability $\eta$ around $90\%$, meaning that the photons’ mode-
matching is not perfect. We attribute this to small spectral impurity, meaning
that our photons might not be completely Fourier limited. By decreasing
$t_{\text{w}}$, we effectively broaden our frequency mode, allowing for a
better overlap in frequency space, and thus higher indistinguishabilities.

Throughout the experiment, the input probe mean photon number of Node 2 was
kept low to maintain low $g^{(2)}_{n2}(0)$. However, it is important to note
that a high mean input photon number would not just degrade the
$g^{(2)}_{n2}(0)$, but it could also diminish the purity of the single photons
generated by Node 2, as predicted by Gorshkov et al. [50]. This decrease in
purity would consequently lead to a reduction in the indistinguishability of
the photons. We report on the observation of this effect and analyse our
results in the supplementary material of this manuscript.

In summary, our work demonstrates high-visibility interference of two photons
produced in dissimilar and independent quantum nodes. We achieve high
indistinguishability by carefully mode-matching the two photons in all degrees
of freedom, without the need of discarding photon detections. If this setup
was used for a quantum communication protocol, such as generating remote
entanglement between Node 1 and Node 2, the maximum achievable fidelity of the
entanglement with respect to the ideal Bell-state would be equal to
$F=(1-\eta)/2$ [33] for ideal single photons. Based on the data presented in
Fig 4.(b), it means that without discarding any photon detection, we would be
limited to $F=93\%$. By keeping a proportion $\mathcal{P}=75\%$ of the counts,
thus reducing the efficiency of the protocol by only $25\%$, a fidelity close
to $F=100\%$ would be theoretically achievable. For such an experiment, one
would need to generate entangled photon pairs in Node 2, as done for example
in [53], and perform a Bell-state measurement [3]. Our setup in Node 2 would
need to be upgraded to gain the ability of addressing different Rydberg states
at the same time and coherently control these single Rydberg excitations with
high fidelity [53]. In this context, this experiment opens the path towards
remote entanglement of hybrid systems, and connection of quantum processors
through quantum repeater links.

###### Acknowledgements.

This project received funding from the Government of Spain
(PID2019-106850RB-I00 project funded by MCIN/ AEI /10.13039/501100011033;
Severo Ochoa CEX2019-000910-S), from MCIN with funding from European Union
NextGenerationEU (PRTR-C17.I1), from the European Union Horizon 2020 research
and innovation program under Grant Agreement No. 899275 (DAALI), from the
Gordon and Betty Moore Foundation through Grant No. GBMF7446 to H. d. R, from
Fundació Cellex, Fundació Mir-Puig and from Generalitat de Catalunya (CERCA,
AGAUR). L.H. and J.L. acknowledge funding from the European Union Horizon 2020
research and innovation program under the Marie Skłodowska-Curie grant
agreement No. 713729.

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