# Transient fluorescence with a single trapped ion

Nicolás A. Nuñez Barreto  1,2,* Lucas T. Giardino  1 Carla J. Crucianelli  1
Muriel Bonetto  1,2 Martín Drechsler  1,2 and Christian T. Schmiegelow1,2  1
Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales,
Departamento de Física, Laboratorio de Iones y Átomos Fríos, Pabellón 1,
Ciudad Universitaria, 1428 Buenos Aires, Argentina
2 CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires
(IFIBA), Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina
<EMAIL_ADDRESS>
###### Abstract

In this paper we present a method to measure transient fluorescent dynamics
with single trapped ions in a Paul trap. We use 40Ca+ ions which exhibit a
$\Lambda$-type three-level system and measure the characteristic optical
pumping times between the ground $S_{1/2}$ and the meta-stable $D_{3/2}$
levels. We prepare one of these states, then pump it to the opposite via the
excited $P_{1/2}$ state. By measuring the scattered photons of the ion, we
retrieve transient curves of the atomic fluorescence. These curves provide
fundamental information about the atomic system, such as branching fractions
and excited-state lifetimes, as well as experimental parameters like the
efficiency of the detection system and the saturation parameter of one of the
transitions. Finally, we study the time dependent fluorescence as a function
of optical power and detuning of the lasers and find a very good agreement
with simulating the dynamics via a three-level open quantum system through a
set of optical Bloch equations. Being able to record time dependent
fluorescence is of particular interest as it contains information about the
temperature, cooling and heating dynamics of the ion.

††journal: opticajournal††articletype: Research Article

##  1 Introduction

Spurred by the invention of the laser, the interaction of atomic systems with
light sources has allowed for significant advances in the last decades,
leading to the coherent control of single quantum systems [1]. Due to its high
coherence times and, therefore, narrow bandwidths, laser spectroscopy has not
only become one of the most reliable methods to study atomic structures and
dynamics, but also a platform to explore fundamental physics using optical
clocks [2] as well as applications of quantum mechanics including quantum
computing [3, 4], quantum simulation and quantum thermodynamics [5, 6].

The absorption probability of photons by a single atom can exhibit varying
time dynamics of the atomic populations, particularly when optical pumping
plays an important role [7]. Typically, for dipole allowed transitions, these
dynamics have time scales in the order of a few ns to $10~{}\mu$s. These
specific time dynamics can be used as a tool to measure atomic properties such
as the precise determination of the branching ratio of an excited state [8, 9,
10], performing direct atomic spectroscopy [11], measuring dipole matrix
elements[12], estimating of the temperature of a single atom [13], detecting
trapped-ion states using the motion of the ion [14] or even performing direct
measurements of the motion near the quantum level [15].

In this work we use a single trapped calcium ion to study the time dependent
atomic dynamics of a $\Lambda$-type system formed by the fundamental
$4^{2}S_{1/2}$ state and the meta-stable $3^{2}D_{3/2}$ state which connect to
the $4^{2}P_{1/2}$ excited state via dipolar transitions. We use a commercial
FPGA-based ARTIQ control system [16, 17] to produce nanosecond timed digital
sequences which control the laser power and detunings via acousto-optic
modulators, while recording fluorescence by time stamping events detected on a
photomultiplier tube. This allows us to measure and determine laser switching
times and collection efficiencies as well as branching fractions and
saturation parameters of the atomic transitions. We also observe the
dependence of the time dynamics on the power and detuning of the respective
lasers and find a very good agreement with a three-level optical Bloch
equations model. In the future we expect to use this system to study thermal
and coherent motional dynamics of ionic crystals, as well as a tool to
optimize atomic spectroscopy [18].

##  2 Theory

We describe the dynamics of the atomic populations by a set of differential
equations for the elements of the density matrix $\rho$ of the system, namely,
the optical Bloch equations (OBE). We consider a three-level system consisting
of two fundamental states $\ket{S}$ and $\ket{D}$ connected with the excited
state $\ket{P}$ by two different lasers, one near 397 nm named Doppler and one
near 866 nm named repump due to their physical roles in observing resonance
fluorescence, as depicted in Fig. 1(a). Here we do not take into account the
magnetic degeneracy nor Zeeman splittings as the dynamics of interest are well
described by a three-level system.

Writing the Hamiltonian of the system in a rotating frame of reference with
the frequencies of the lasers, and using the rotating-wave approximation, one
obtains

$H/\hbar=\Delta_{\textrm{dop}}\outerproduct{S}{S}+\Delta_{\textrm{rep}}\outerproduct{D}{D}+\frac{\Omega_{\textrm{dop}}}{2}(\outerproduct{S}{P}+\outerproduct{P}{S})+\frac{\Omega_{\textrm{rep}}}{2}(\outerproduct{D}{P}+\outerproduct{P}{D}),$
(1)

where $\Omega_{\textrm{dop}}$, $\Omega_{\textrm{rep}}$ are the Rabi
frequencies of both transitions (assumed real for simplicity), and
$\Delta_{\textrm{dop}}$, $\Delta_{\textrm{rep}}$ are the detunings of the
lasers, i.e., the difference between the frequency of the transition and that
of the laser. The OBE arise from a master equation for $\rho$ which considers
non-unitary dynamics as spontaneous emission and finite laser linewidths. This
is done by adding a Linbladian superoperator to the unitary dynamics such that
the final master equation is

$\frac{d\rho}{dt}=-\frac{i}{\hbar}\left[H,\rho\right]+\sum_{m}\left[\mathcal{C}_{m}\rho\mathcal{C}_{m}^{\dagger}-\frac{1}{2}\left(\mathcal{C}_{m}^{\dagger}\mathcal{C}_{m}\rho+\rho\mathcal{C}_{m}^{\dagger}\mathcal{C}_{m}\right)\right].$
(2)

The transition operators $\mathcal{C}_{m}$ model two non-unitary processes.
First, the two spontaneous emission channels from the upper level to the lower
levels. These have the form
$\mathcal{C}_{\mathrm{SP}}=\sqrt{\Gamma_{\mathrm{SP}}}\outerproduct{S}{P}$ and
$\mathcal{C}_{\mathrm{DP}}=\sqrt{\Gamma_{\mathrm{DP}}}\outerproduct{D}{P}$,
where $\Gamma_{\mathrm{SP}}$ and $\Gamma_{\mathrm{DP}}$ are the linewidths of
the respective transitions. Second, we consider finite laser-linewidths by
adding broadenings to the $S$ and $D$ states through the operators
$\mathcal{C}_{\textrm{dop}}=\sqrt{\Gamma_{\textrm{dop}}}\outerproduct{S}{S}$
and
$\mathcal{C}_{\textrm{rep}}=\sqrt{\Gamma_{\textrm{rep}}}\outerproduct{D}{D}$,
where $\Gamma_{\textrm{dop}}$ and $\Gamma_{\textrm{rep}}$ are the linewidths
of the Doppler and the repump laser respectively.

We numerically integrate the OBE and compare the simulations with the
experimental results. In the next section, we present the results of measured
transitory dynamics and show how we can apply these methods to perform
estimations of atomic parameters like optical pumping characteristic times and
branching fractions, and experimental parameters such as detection
efficiencies and saturation parameters.

##  3 Experimental results

###  3.1 Experimental setup

We performed experiments with single 40Ca+ ions. These are trapped in an
electrodynamical Paul trap which consists of an array of electrodes that
provide a dynamical 3D confinement of the ions in its center. The trapping is
accomplished by a radial confinement given by a ring-shaped electrode of $\sim
1.2$ mm in diameter carrying $\sim 600~{}$Vpp at 22.1 MHz, and an axial
confinement generated by two endcaps located $\sim 0.6$ mm from the center of
the trap pointing in opposite directions, both with a DC voltage of $\sim
1~{}$V. Also, there are additional DC electrodes near the trap to compensate
for stray electrical fields and to position both the DC and the AC potential
minima in the same location, thus avoiding excess micromotion and therefore,
inefficient cooling. The trap design, discussed in [18], was inspired by the
PTB Trap design discussed in [19].

In Fig. 1(a) we show the relevant $\Lambda$-type three-level scheme for the
system. The $4^{2}S_{1/2}$ ground state is dipole-connected with the excited
$4^{2}P_{1/2}$ state by an ultraviolet (UV) 397 nm-laser. This excited state
has a probability $p$ of decaying to the $S$ state, and a probability $1-p$ of
decaying to the meta-stable long-lived $3^{2}D_{3/2}$ state. To avoid
population to be pumped to the $D$ state, we use an infrared (IR) 866 nm-laser
to repump the atomic population to the $P$ state, hence describing a closed
fluorescence cycle. Other nearby-lying atomic levels do not play a role in
these experiments as they are either far detuned or transitions to them are
prohibited by selection rules.

Both lasers are frequency locked to two independent mid-finesse ($\sim 200$)
Fabry-Perot cavities through Pound-Drevel-Hall method [20] using Red Pitaya
boards [21] adapted for this purpose [22]. This also reduces the linewidth of
the lasers to $\sim 100~{}$kHz. The beams go through two independent acousto-
optic modulators (AOMs) in double-pass configuration which serve as fast
optical switches, providing a high level of control in turning on and off the
lasers, as well as a mechanism to change or sweep their frequencies a few tens
of MHz.

In Fig 1(b) we show a sketch of the experimental setup. The ion is trapped in
the center of the ring-trap and illuminated with the two lasers from one side.
As it scatters part of the incoming light, UV and IR photons are emitted in
all directions by spontaneous emission, a fraction of which are collected by
an objective lens with a 50 mm focal length. The light is then filtered by a
397 nm-interference filter to detect only photons from the $S$-$P$ transition
and is then split with a non-polarizing beamsplitter which transmits $\sim
90$% of the light to a photomultiplier tube (PMT) for fast time-tagged
measurements, and reflects the remaining $\sim 10$% to a CMOS Andor camera for
ion visualization and monitoring.

To perform the experiments we use an ARTIQ control system [16, 17]. It has two
radio-frequency (RF) outputs which control the AOMs and one TTL input which is
used to read the PMT. The system allows one to program and synchronize the
tuning and switching of the AOMs and to time-tag the incoming photons.

Figure 1: (a) Relevant level scheme for 40Ca+ ions. A $4^{2}S_{1/2}$ level is
connected to a $4^{2}P_{1/2}$ level with a UV 397 nm (Doppler) laser, from
which it has a probability $p$ to decay to the same level and a probability
$1-p$ to decay to a long-lived metastable $3^{2}D_{3/2}$ state. An IR 866 nm
(Repump) laser depopulates the D state in order to have a closed fluorescence
cycle. (b) Scheme of the experimental setup. The ion (light-blue) is trapped
in the center of a ring-shaped Paul trap (gray), and illuminated with a pair
of lasers in a collinear configuration. The ion scatters light and a part of
it is collected with an objective lens, filtered with a 397 nm-interference UV
filter and focused onto a photomultiplier tube (PMT) and a CMOS camera. (c)
Time dependent collected light of a single fluorescent ion (aquamarine), the
UV stray light (blue) and the background light (purple). We performed 50 M
$1~{}\mu$s-long measurements to gain contrast in the transient part of the
curves. (d) Histograms of detected counts in the stationary regime, with the
respective Poisson distributions, for the same three cases, taken from a total
of 3 M, $10~{}\mu$s-long measurements.

###  3.2 Steady-state fluorescence and laser switching timing

Here we describe a basic characterization of the detection system, where we
measure the background counts with the lasers off and compare it with the
transitory of stray light from the UV laser and the fluorescence light of a
single ion.

In Fig. 1(c) we show the transient curves of the three cases. In all cases at
$t=0$ we turn on different lasers and begin acquisition with the PMT for up to
1 $\mu$s. This sequence is repeated 50 M times to reduce statistical
uncertainties and gain contrast in the transient zone. In purple, we show the
background counts acquired by leaving all the lasers off. We obtain a
measurement with a constant mean value as expected, which is due to spurious
light and dark counts. In blue, we show the measurement of the UV stray light.
At $t=0$, the RF output of the AOM is turned on. We see that there is an
initial dead time of $\sim 0.2$ $\mu$s and a rise time of $\sim 70$ ns. The
dead time is mainly composed of an initial delay response time of the RF
source ($\sim 50$ ns), plus delays due to propagation in coaxial cables ($\leq
10$ ns) and finally the propagation time it takes the acoustic wave to reach
the beam in the crystal ($\sim 140$ ns). The rise time is mainly due to turn
on behaviour of the RF source ($\sim 50$ ns) with a smaller contribution from
the time that it takes the acoustic wave to go through the whole laser beam
($\sim 20$ ns). The two times associated with the AOM depend on the speed of
sound in the material, the location of the beam within the crystal and the
diameter of the beam. Finally, in aquamarine, we show a transient curve of a
fluorescent single ion. This is achieved by, first, turning on a 5 $\mu$s long
IR pulse to prepare the S state, and, at $t=0$, turning on both the UV and IR
lasers thereby creating a closed fluorescence cycle. We observe a transient
time of $\sim$100 ns, which is a combination of the AOM rise time and the
transient time of the atomic populations to reach a steady state according to
the previously described optical Bloch equations. After that, the detected
fluorescence, due mostly to the ion, has a constant mean value

Taking into account only the stationary values one can study the photon number
statistics. In Fig. 1(d) we show count frequency histograms obtained with 3 M
measurements, each 10 $\mu$s long for the three light conditions. We use a
binning window of 10 ns and plot the measurements along with theoretical
Poisson distributions. We find the mean value of the measurements for each
case, which match the expectation values of the distributions, to be
{19.54(1),69.76(2),226.24(1)} counts per 10 ns for the background, stray and
fluorescence lighting conditions respectively. As predicted by the nature of
the uncorrelated events, the measurements are in good agreement with a Poisson
distribution.

Figure 2: Measurement of one $S$-$P$ and one $D$-$P$ transition. (a) Scheme to
measure the $S$-$P$ transition. The ion is initialized in the $S$ state after
scattering some UV photons. After that, the UV laser is turned on, and we
start recording the scattered UV photons. Finally, the population ends in the
$D$ state. (b) Scheme to measure the $D$-$P$ transition. The ion is instead
initialized in the $D$ state and after that, the IR laser is turned on. At the
same time, we begin recording the scattered UV photons. The ion scatters only
one UV photon and the atom goes to the $S$ state. (c) Fluorescence as a
function of time for the two optical pumping transitions. We repeat both
measurements 50 M times and record the arrival of photons by time-tagging
events. The measurements of the $S$-$P$ transition curve (green) and the
$D$-$P$ transition curve (purple) are binned with a window of 10 ns. The areas
are visibly different and this gives information on the value of $p$, i.e.,
the branching fraction of the atom. (d,e) Simulations of the atomic
populations for the $S$-$P$ and $D$-$P$ optical pumping processes
respectively. The fluorescence curves observed in (c) are proportional to the
atomic populations of the excited state $\rho_{{}_{PP}}$ in each case. We also
show the population of the other two levels, where one can appreciate optical
pumping occurring.

###  3.3 Detection efficiency and branching ratio measurement via transient
fluorescence

To perform transitory experiments where optical pumping takes place, we
initialize the ion either in the $S$ or the $D$ state with a strong 5
$\mu$s-long pulse of the 866 nm or the 397 nm laser respectively (pump laser),
as seen in Fig. 2(a) and Fig. 2(b). This way, the atomic population is
optically pumped to the desired initial state. After this, we proceed to turn
on the other laser (probe laser) and at the same time, enable the detection of
the PMT. The ion absorbs photons and the atomic population gets optically
pumped to the opposite state. In both measurements we detect and timestamp
only the UV scattered photons of the $S$-$P$ decay, and bin the data with a
window of 10 ns. We call the first one "$S$-$P$ transition" and the second one
"$D$-$P$ transition" since those are the transitions driven by the probe laser
in each one.

To extract useful physical data from the transient phenomena, a background
subtraction needs to be done. We split the background into two main
contributions: the general background given by dark counts and light sources
at the laboratory, and the scattered spurious UV light. The main difference
between them is that the first one is constant through all the experiments and
the second one can have a time-dependent behaviour, as seen previously, given
by the slew in the AOM turn on.

For the $S$-$P$ experiments, we need to measure the AOM transient curves
without the ion and use them to subtract it from the measurements. On the
other hand, for the $D$-$P$, since the detection system filtrates the IR
light, the background curve for this case will only be the general background,
so it will be sufficient to subtract a constant value from the measurements.

In Fig. 2(c) we see one $D$-$P$ curve in green and one $S$-$P$ curve in
purple, both with the respective backgrounds subtracted. The measurement
algorithm used is the following: first we turn on a strong 5 $\mu$s-long pump
UV (for the $D$-$P$ curve) or IR (for the $S$-$P$ curve) pulse; then, we turn
off the pump laser and wait for 2 $\mu$s to account for the transient turn-off
response. Finally, we turn on the probe laser (IR for the $D$-$P$ curve and UV
for the $S$-$P$ curve) and acquire the photon count on the PMT for 5 $\mu$s.
We repeat this 50 M times to reduce statistical uncertainties. Also, once
every 50 repetitions we turn on both lasers for 1 ms to avoid excess heating
of the ion. The whole measurement for each curve takes approximately 1 hour
and 20 minutes. In this time, the drift in frequency is below 1 MHz due to the
Pound-Drever-Hall stabilization to vacuum-sealed cavities built from ultra low
expansion glass. On the other hand, the drift in optical power is below 1%, so
both effects are ignored for the present analysis.

As seen in Fig. 2(c), the area of both the $S$-$P$ and $D$-$P$ curves are
noticeably different. This is well modeled by the simulations of the OBE shown
in Fig. 2(d) and 2(e), where optical pumping manifests in the behavior of the
population of the states. Following Ramm et.al. [9] we obtain the branching
fraction of the $P$ state, which represents the probability of the ion to
decay to the $S$ level, by comparing the total counts detected in each
transition, named $N_{\mathrm{SP}}$ and $N_{\mathrm{DP}}$ respectively. This
way, one can calculate $p=N_{\mathrm{SP}}/(N_{\mathrm{SP}}+N_{\mathrm{DP}})$
which in our experiment yields $p=0.9357(14)$, in good agreement with previous
measurements by Ramm et al. Here we only considered the uncertainty given by
the shot noise of the measured counts, since, due to the short duration of the
experiment, this is much greater than other sources of uncertainty like
frequency or power drifts, electronics dead times, etc.

Furthermore, with the measurement of the $D$-$P$ transition alone we can
estimate the efficiency of the detection system. This is a magnitude that is
determined by the solid angle of the collection lens as well as the optical
transparencies of the vacuum chamber windows, the beam-splitter and the PMT
quantum efficiency. We directly measure this integrated efficiency by making
use that if the ion is initially in the $D$ state, and the repump laser is
turned on, it will only emit one UV photon before it is pumped to the $S$
state and goes dark. This way, by performing $N$ cycles, the ratio of photons
detected over the number of cycles will represent the detection efficiency of
our system. A measurement of 50 M cycles reveals a detection efficiency of
0.140(1)%.

Figure 3: Characteristic decay time of the fluorescence of a single ion
varying the optical intensity (i.e. the Rabi frequency) of the UV laser
driving the $S$-$P$ transition. We perform measurements for two different
detunings, $\sim-20$ MHz and $\sim-50$ MHz. We also plot theoretical level
curves for nine different detunings (black solid lines) obtained with
simulations of the OBE. We find the measurements in good agreement with the
simulations. In an inset we show curves for three different UV optical powers,
displaced a certain amount in the $y$ axis for better appreciation as noted in
each curve. The $x$ axis was also displaced such that $t=0$ corresponds to the
beginning of the curve. The respective characteristic times retrieved from the
curves are marked in the plot with the same colors.

###  3.4 Power and detuning behavior of transient fluorescence

We now analyze the effect of laser power and detuning to the transient
fluorescence behavior during optical pumping. We focus particularly on the
$S$-$P$ transition.

The total number of scattered photons in each transition is independent of the
power of the lasers, since the branching fraction depends only on the atom.
However, if we vary the power of the laser, the characteristic time of the
optical pumping varies. This is reflected in the characteristic time of the
exponential decay of the atomic fluorescence. Using the $S$-$P$ optical
pumping transition, we varied the optical power of the UV laser, and measured
different curves. We fitted the last part of each curve with an exponential
function $N(t)=N_{0}e^{-t/\tau}+C$, where $\tau$ represents the characteristic
time of the optical pumping process and $N_{0}$ and $C$ are free fitting
parameters. In the inset of Fig. 3 we show three different transitory curves
of the $S$-$P$ transitions for three different optical powers of the UV laser.
As can be seen, the characteristic time shortens with higher powers. In Fig. 3
we plot $\tau$ vs. the optical intensity of the laser, obtained by dividing
the power with the beam area, and compare it to simulations to the optical
Bloch equations. We measure the intensity dependence for two different
detunings, finding the measurements in good agreement with the simulations
corresponding to detunings of $\sim-20$ MHz and $\sim-50$ MHz.

Now, we show how one can use these transitory curves to measure laser
parameters. We can get a comparison of the branching fraction from the $P$
level to the two lower levels by comparing the areas of the $S$-$P$ and
$D$-$P$ curves of Fig. 2(c). We determine the branching fraction from the $P$
level to the $S$ level to be $\sim 14$ times greater than the one from the $P$
to the $D$. Therefore, we can approximate the dynamics of the $S$-$P$
transition as a fast two-level system dynamics between the $S$ and the $P$
state reaching a steady-state, with a slow decay channel to the $D$ state.
This means that after one prepares the $S$ state and turns on the UV laser,
one can approximate a stationary value for the atomic populations using the
usual two-level system results. Measuring the characteristic decay time to the
$D$ state, one can then directly measure the saturation parameter of the
transition $S$-$P$, defined as $s={2\Omega^{2}}/({4\Delta^{2}+\Gamma^{2}})$,
where $\Omega$ is the Rabi frequency of the transition of interest
(proportional to the square root of the optical power), $\Delta$ is the
detuning and $\Gamma$ is the corresponding linewidth. Then, the stationary
value of the population of the excited state $\rho_{{}_{\mathrm{PP}}}$ after
the UV laser is turned on can be expressed in terms of $s$ as
$\rho_{{}_{\mathrm{PP}}}={s}/{2(1+s)}$. If we now consider the decay from that
steady-state to the $D$ state through spontaneous emission at a rate
$\Gamma_{\mathrm{DP}}=2\pi\times 1.482$ MHz [12], the measured characteristic
decay time $\tau_{\mathrm{meas}}$ can be related with
$\rho_{{}_{\mathrm{PP}}}$ as
$\tau_{\mathrm{meas}}^{-1}\approx\rho_{{}_{\mathrm{PP}}}(s)\Gamma_{\mathrm{DP}}$.
This way, by measuring $\tau_{\mathrm{meas}}$ we can retrieve the saturation
parameter $s$ without the need of estimating the detuning or the Rabi
frequency. For instance, for the maximum intensity set in Fig. 3, we obtain
$\rho_{{}_{\mathrm{PP}}}=0.46(1)$, which yields a saturation parameter of
$S=11.4(6)$. This value can be compared to an estimation using the saturation
intensity of the transition. To calculate it, we take the transition linewidth
$\Gamma_{\mathrm{SP}}=2\pi\times 21.57(2)$ [12] and the corresponding
transition frequency $\omega_{\mathrm{SP}}=2\pi\times 755.222~{}$THz, and
compute
$I_{\mathrm{sat}}={\hbar\Gamma_{\mathrm{SP}}\omega_{\mathrm{SP}}^{3}}/({12\pi
c^{2}})$, where $c$ is the speed of light, to obtain
$I_{\mathrm{sat}}=45.1\times 10^{-5}$ $\mu$W/($\mu$m)2. Then, taking the
experimental intensity for that same data point $I=5.42(12)\times 10^{-3}$
$\mu$W/($\mu$m)2, we obtain a saturation parameter $S=I/I_{\mathrm{sat}}$ of
12.0(3), which is in good agreement with the value estimated using the
characteristic decay time.

##  4 Conclusions

In this work we presented an experimental apparatus capable of performing time
dependent fluorescence measurements with transitory atomic dynamics of a
single trapped ion. The dynamics are well modeled by three-level optical Bloch
equations. This allows us to measure characteristic transient times of optical
pumping dynamics which are in the order of a few ns to 10 $\mu$s. These
measurements allow us to estimate atomic properties like the branching
fraction of excited states as well as directly measuring experimental
parameters like the efficiency of the detection system, which is normally
estimated using the single efficiencies of all optical elements. Finally, we
investigate the dependence of the transient times with the optical power and
the detuning of the probe laser, and find it in good agreement with the
simulations of the OBE.

Funding This work was supported by Agencia I+D+i Grants No. PICT 2018 - 3350
and No. PICT 2019 - 4349, Secretaría de Ciencia y Técnica, Universidad de
Buenos Aires Grant No. UBACyT 2018 (20020170100616BA), and CONICET
(Argentina).

Acknowledgments We thank F. Schmidt-Kaler for his support and generosity as
well as J. P. Paz, M. A. Latoronda, and A. J. Roncaglia for their
unconditional help and backup in the setting up of the laboratory.

Disclosures The authors declare no conflict of interest.

Data availability Data underlying the results presented in this paper are not
publicly available at this time but may be obtained from the authors upon
reasonable request.

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