Abstract
Achieving laser cooling of molecules necessitates the establishment of a closed optical cycling transition. In contrast to atoms, molecules exhibit additional vibrational and rotational structures, which must be carefully addressed–alongside hyperfine splittings–when designing the laser frequency scheme for efficient optical cycling. In this work, we investigated optical cycling in MgF molecules on the laser cooling transition, namely 
transition between the electronic ground state (
) and the electronic excited state (
). The ground state comprises four hyperfine levels, of which two are unresolved within the excited-state linewidth; the two hyperfine levels in the excited state are also unresolved. Consequently, three laser frequencies suffice to address all transitions. This was realized by generating three independently tunable frequency components using acousto-optic modulators (AOMs). With optimized detunings, power ratios, and total beam power, simultaneous application of all three frequency components increased the total number of scattered photons by up to 
relative to the sum of the individual single-frequency signals. Applying a tilted magnetic field to remix the dark Zeeman states increased the photon yield by an additional factor of 
, leading to an overall enhancement of about sevenfold. These results provide quantitative benchmarks for MgF optical cycling and practical guidance for future molecular slowing and magneto-optical trapping experiments.
Subject terms: Optics and photonics, Physics
Introduction
Over the past decade, ultracold molecules have become promising candidates for fundamental physics research, including parity-time violation (PTV)1–4 and dark matter searches5, as well as quantum chemistry6,7, due to their rich internal energy structures and intrinsic electric dipole moments. Moreover, due to their long coherence time of rovibrational states and capability for long-range dipole-dipole interactions, these molecules have recently emerged as essential tools in quantum computation and simulation8–10.
To utilize these unique features, achieving ultracold temperatures is crucial. Fortunately, various cooling techniques, including laser cooling, have already been extensively developed for neutral atoms, and these established methods can be applied to molecular systems. Such laser cooling techniques are increasingly being applied to hydrogen-like diatomic molecules, particularly alkaline-earth monofluorides, which exhibit diagonal Franck-Condon factors (FCFs) and possess a single valence electron, enabling effective adaptation of atomic cooling methods.
In particular, extensive technical developments have been achieved with CaF molecules, including their recent loading into tweezer arrays, and the demonstration of spin-exchange interactions and entanglement11–17. SrF molecules have also been successfully captured in optical dipole traps (ODTs) and cooled down to 40 
using sub-Doppler cooling techniques18,19. Furthermore, various molecules, such as YbF, AlF, and BaF, are being actively studied using laser slowing and magneto-optical trapping (MOT) for precision measurements20–23. Additionally, novel cooling methods uniquely suited to diatomic molecules, such as radio-frequency (RF) MOTs24, blue-detuned MOTs25,26, and microwave shielding27–29, are actively being developed.
MgF shares a similar energy structure and electric dipole moments with other alkaline-earth monofluorides but offers additional advantages for laser cooling due to its lighter mass and ultraviolet (UV) transition wavelengths. Consequently, laser slowing and MOT for MgF molecules have been proposed30,31. The hyperfine-resolved spectroscopy studies were performed32, and measurements of branching fractions and decay rates of excited states involved in quasi-closed cycling transitions have also been reported33. Recently, laser-induced fluorescence (LIF) spectroscopy for cooling lines, such as 
, 
, and 
, was conducted34.
In preparation for future magneto-optical trapping (MOT) experiments with MgF, obtaining a sufficient number of scattered photons through closed-cycling transitions is essential. This study aims to optimize the photon yield for the rotationally closed transition (
) within the main transition of the 
band, which exhibits the strongest scattering.
In previous studies34,35, electro-optic modulators (EOMs) were utilized to generate frequency components corresponding to transitions from each hyperfine state of the ground state, thereby achieving a rotationally closed transition. When only the main laser was applied without vibrational repump lasers, an enhancement of the LIF signal by approximately a factor of 2.6 was reported35. However, since EOMs produce frequency components evenly spaced by the modulation frequency, and the power ratio between these components is symmetrically determined by the modulation depth, this approach significantly limits the accessible parameter space for the rotationally closed transition of the main transition.
In this study, we overcome these limitations by employing acousto-optic modulators (AOMs), which allow for independent control of the detuning and power of each frequency component. This enabled exploration of a broader parameter space. Additionally, by applying a magnetic field at a tilted angle relative to the laser polarization, we induced dark state remixing through Larmor precession, effectively mitigating these dark states.
Rotationally closed transition of 
band
The transitions forming a quasi-closed cycling transition must each satisfy rotationally closed conditions to achieve the required number of scattered photons for laser cooling. Parity and angular momentum selection rules allow the transitions between states with different rotational quantum numbers. A rotationally closed transition in the 
band can be realized by selecting the 
transition, shown in Fig. 1a.
Fig. 1.
(a) Quasi-closed cycling transitions for the rovibrational branches of MgF. Solid lines represent the transitions and their wavelengths, while dashed lines indicate dominant vibrational decay channels with their branching fractions33. (b) Fine and hyperfine energy levels of the 
transition. The black arrows indicate the rotationally closed transitions, 
, while the blue arrows represent the frequencies of the excitation lasers for 
transition. The detuning of each laser is referenced to 834294485 
, which is the frequency of the transition from 
state.
However, achieving a fully closed cycling transition is no longer feasible using a laser with a single frequency component due to the hyperfine structure of MgF. Consequently, all transitions from relevant hyperfine states must be simultaneously driven to sustain optical cycling, as shown in Fig. 1b, where the 
transitions are collectively designated as the 
transitions. Here, unprimed quantum numbers denote ground states, while primed quantum numbers refer to excited states.
To simultaneously drive the 
transitions, a total of six frequency components may appear to be required. However, due to the large natural decay rate 
of the A state33, the hyperfine splitting between 
in the excited state and between 
states in the ground cannot be resolved. Consequently, all transitions within the 
manifold can be effectively driven using three frequency components centered at the transition from 
, with detunings of 
. In this experiment, we investigated the optical cycling properties of these transitions to maximize the ratio of the LIF obtained when driving all three frequency components simultaneously to the summed LIF from each frequency component applied individually.
Experimental setup
As depicted in Fig. 2a, MgF molecules are produced by ablating a Mg target with a 532 
pulsed laser in a cryogenic system cooled below 4 
. The ablated Mg atoms then react with 
gas to form MgF. The molecules are then cooled to below 10 
through elastic collisions with He gas at 4 
. After cooling, the molecular beam exits the cryogenic system as a collimated beam and propagates to the detection region located 34 
downstream. The forward velocity of the molecular beam peaked at around 180 
, with a width of approximately 100 
, as determined from Doppler-shift spectroscopy.
Fig. 2.
(a) Schematic diagram of the experimental setup. Two AOMs generate the frequency components of the OC beam, which is delivered to the chamber via an optical fiber. The molecular beam(yellow region), produced by the CBGB(Cryogenic buffer-gas beam) source, interacts perpendicularly with the laser beam approximately 34 
downstream. The PMT records the LIF signal for 20 
after ablation. (b) Spectra obtained with different frequency configurations. The dashed lines represent the LIF signals when each single-frequency component was applied individually. The purple solid line represents the sum of the single-frequency spectra. The black solid line corresponds to the spectrum obtained when all three frequency components were applied simultaneously, i.e., the OC beam configuration. LIF signals were obtained by scanning the main laser frequency while keeping 
of each frequency component fixed. Near resonance, where all three frequency components address the hyperfine transitions, the optical cycling effect becomes evident.
Two AOMs with a resonant frequency range of 110 - 130 
were used to generate sidebands corresponding to the hyperfine structure of 
transitions. By changing the amplitudes and frequencies of the RF source applied to the AOMs, the detunings (
) and powers(
) of the carrier and sidebands were adjusted. The detunings 
are defined relative to the resonance frequency 
, corresponding to the transition from the ground state 
32. These frequency components were then combined using two beam splitters (BS), forming what we refer to as the optical cycling beam(OC beam), which is linearly polarized. The OC beam was then coupled into a polarization-maintaining fiber and delivered to the chamber, with a beam waist radius of 0.5 mm. At a standard beam power of 2 mW, the intensity corresponds to about 
, where 
.
A photomultiplier tube (PMT) detected the LIF signal when the molecular beam intersected the laser beam perpendicularly. The time-trace signals were acquired for 20 
after the ablation pulse to collect all the fluorescence from molecules with different velocities and departure times.
Unless otherwise stated (as in the section on dark-state remixing), all measurements were performed without any externally applied magnetic field, corresponding to the nominal 
G condition used in the simulations(see Methods for details on the ambient field and its effect).
Result and discussion
Figure 2b presents the LIF spectra obtained by scanning the frequency of the main laser while keeping 
and 
fixed, clearly illustrating the effect of optical cycling induced by the three frequency components. These spectra were acquired by selectively applying each frequency component individually by blocking other frequency components using mechanical shutters(single-frequency spectrum) or by applying the OC beam(OC spectrum). In addition, the sum of individual single-frequency spectra was computed and used as a reference to evaluate the effect of optical cycling. The single-frequency spectra (blue, orange, yellow dotted line in Fig. 2b), measured by applying each frequency component separately, exhibit three peaks corresponding to transitions from 
, 
, and 
, from left to right. Each of these spectra is shifted by 
due to the modulation from the AOM, and the relative peak heights vary according to 
. The 
values were tuned to be resonant with the hyperfine structure, and the power ratio 
was set in proportion to the number of magnetic sublevels.
Compared to the single-frequency spectra, both the sum of single-frequency spectra(purple solid line in Fig. 2b) and the OC spectrum(black solid line in Fig. 2b) reveal two additional peaks arising from the presence of frequency sideband components. The largest peak appears when the main laser is resonant with the transition from the 
state (i.e., at the zero point on the horizontal axis). The increase in total number of scattered photons due to the optical cycling effect can be inferred by comparing the peak heights of the sum of single-frequency spectra and the OC spectrum. As shown in Fig. 2b, a higher LIF signal was observed when all three frequency components simultaneously addressed the corresponding transitions, forming a closed-cycling transition. The following sections describe optimization of the laser parameters. Under fully optimized conditions, the LIF obtained with simultaneous driving was up to three times greater than the sum of single-frequency signals in our experimental setup.
Detunings
The detunings 
were individually scanned by changing the modulation frequency of AOM, while 
was adjusted by shifting the frequency of the main laser.
Intuitively, each frequency component should be tuned to resonate with the transitions corresponding to the 
transitions. However, in our setup, a single frequency drives both transitions from 
, whose energy splitting is approximately 0.4 
. As a result, the optimal value of 
for maximum photon scattering should be examined.
The experimental results showed that the optimal value of 
corresponded to resonance with the transition from 
. Similarly, Fig. 3a shows the optimal value of 
was found at resonance with the transition from 
, at 110 MHz, in good agreement with the rate-equation simulations. For 
, as shown in Fig. 3b, the 
and 
transitions are unresolved and thus simultaneously addressed. Off-resonant scattering from these states broadened the optimal detuning range, with the most favorable detuning found near their midpoint at approximately 
MHz. Figure 3c shows the time trace signals at the optimal detunings. The increase in LIF signal due to the optical cycling effect is evident, where the time trace of the OC beam LIF (black) exceeds that of the sum of single-frequency LIF signals (purple).
Fig. 3.
(a, b) The dependence of LIF from the OC beam as a function of (a)
and (b)
, while keeping the other components fixed at (a) (
, 
) MHz and (b) (
, 
) MHz, respectively. Solid lines indicate simulation results, and dashed lines mark transition frequencies for 
, 
, and 
. In (b), the unresolved 
and 
transitions yield a broad optimal detuning range, with the maximum scattering near 
MHz. Although not shown here, we also scanned the detuning of the 
component while fixing 
MHz and 
MHz, and found that 
MHz yielded the largest LIF signal. (c) Comparison of LIF time traces between the OC beam at the optimal detuning and the single-frequency beam. All experiments were conducted with a total laser beam peak intensity of 
(2 
), distributed in the ratio of 
.
Power ratio
The power ratio among the frequency components plays a critical role in determining the total scattering rate, as each transition differs in both its transition strength and the number of magnetic sublevels. The available laser beam power is limited in practical applications such as laser slowing or MOT. To account for this constraint, we investigated how the power should be distributed among the frequency components to achieve efficient optical cycling. The total beam power 
was fixed, and various combinations satisfying 
were used to measure the LIF signals, as shown in Fig. 4.
Fig. 4.
Plots of (a) the sum of single-frequency LIF and (b) the OC beam LIF for different combinations of 
values that satisfy a total laser beam peak intensity of 
(2 
). The color scale is identical for both plots.
The results showed that when the OC beam was applied with the optimal detunings 
, the LIF signal was consistently higher than the sum of single-frequency LIF, regardless of the power ratio configuration. The optimal power ratios for both cases were similar. Assigning a larger portion of the power to 
, which drives transitions from 
and 
, proved to be most effective. For the remaining power, allocating it to the 
transition, rather than to the 
transition, yielded a higher LIF signal. The preference for higher 
can be attributed to three factors: (1) it drives more magnetic sublevels than the other frequency components, (2) 
interacts with either 
or 
in an off-resonant manner, requiring higher power to compensate for off-resonant scattering, and (3) The saturation intensity for the transition from 
states is relatively higher than other hyperfine states due to the relatively small electric dipole matrix element. However, as the total beam power increases and the optical cycling effect strengthens, the dominance of the 
gradually diminishes. The OC beam LIF was maximized when 
and 
were equal, yielding a 
-fold increase compared to the sum of single-frequency LIF. This is attributed to the fact that the transition from the 
state has the highest saturation intensity among all possible transitions.
To provide an absolute benchmark, we estimated the number of photons scattered per molecule from rate-equation simulations that account for the Gaussian beam profile. Under optimal conditions, a single-frequency component yields about 2.3 photons per molecule, while the OC beam produces approximately 6.5 photons per molecule. The corresponding peak scattering rate with the OC beam deduced from the simulations was 
.
Total power
Lastly, we examined the saturation behavior of the optical cycling effect as a function of the total power of the OC beam under optimal detuning and power ratio conditions. As shown in Fig. 5, for the single-frequency beam, the LIF signal continues to increase with beam power, as full saturation has not yet been reached. In contrast, the LIF signal from the OC beam also increases but gradually saturates, which results from optical pumping into dark magnetic sublevels and higher vibrational states. When compared to the sum of the single-frequency signals at each total intensity, the OC beam provided the largest relative enhancement at 
(8 mW), yielding a factor of 
. At higher powers the relative gain decreased, reaching 
at 
(15 mW). The solid lines in Fig. 5 represent the results of rate equation simulations, which agree well with the experimental data(See Method). These simulations confirm that the steady-state population in the dark states increases with the total beam power.
Fig. 5.
Total power dependence of the OC beam and single-frequency beam under the condition of 
. The horizontal axis is given in units of the saturation intensity of the 
band, 
. The ratio of the OC beam LIF to the sum of single-frequency LIF reached its maximum value of 
at a total peak intensity of 
(8 mW). The solid line represents the result of rate equation simulations.
Dark state remixing
The transitions of MgF for laser cooling are a Type-II scheme, where the number of ground states (
) exceeds that of excited states (
), which inherently leads to the presence of dark magnetic sublevels in the ground state manifold. In this experiment, the laser beam was linearly polarized to drive 
-transition, so the 
states do not have allowed transitions to the excited states. These dark states can be destabilized either by modulating the laser polarization or applying a DC magnetic field at a tilted angle to the laser polarization so that Larmor precession of the electron spins mixes the magnetic sublevels.
Figure 6 shows the dependence of the OC-beam LIF on both magnetic field strength and total beam intensity. Data were taken at seven intensity values between 2–60 
and six magnetic field strengths between 0–16.5 G, for a total of 42 measurement points, and the map was constructed by interpolation. All LIF signals are normalized to the value obtained at 
(2 mW) and 
G. The detunings and power ratios were fixed at their optimized values, and the magnetic field was applied at a 
angle with respect to the laser polarization. In general, increasing the magnetic field enhances the LIF through Zeeman state remixing. At 
(2 mW), the LIF was enhanced by a factor of 
at 
G compared to 
G. However, at low intensities the signal starts to decrease again beyond about 10 G. This reduction arises from stronger off-resonant scattering caused by Zeeman shifts, combined with rapid spin precession that returns population to dark states. At higher intensities, in contrast, power broadening and the higher scattering rate mitigate these effects, allowing the fluorescence to remain high for fields above 10 G.
Fig. 6.
LIF enhancement as a function of magnetic field for various total OC beam intensities. The LIF was normalized to the value at 
and B = 0 G. Increasing the magnetic field enhances the signal, but at low intensity the enhancement decreases beyond 
G, whereas at higher intensity it is maintained. Compared to the reference case at 
and 
G, the LIF signal was enhanced by a factor of 2.2 at 
and 
G, and by a factor of 4.5 at 
and 
G.
In terms of the total number of scattered photons, higher intensities yield larger values. For example, at 
and 
G the LIF signal was enhanced by a factor of 
compared to 
at 
G. To assess the relative enhancement due to dark-state remixing, the LIF at each intensity was further normalized to the corresponding value at 
G. Under this normalization, the enhancement peaks at about sevenfold at 
and then shows a saturation trend at higher intensities.
Conclusion
We investigated optical cycling on the rotationally closed 
transition within the 
band of MgF. By generating three independently tunable frequency components with AOMs, we were able to address all relevant hyperfine transitions and optimize their detunings and power ratios. Under these optimized conditions, the fluorescence signal from the OC beam increased by a factor of 3.29 compared to the sum of single-frequency LIF.
Rate-equation simulations further indicate that this corresponds to an average of about 6.5 scattered photons per molecule in the OC configuration, compared to about 2.3 for a single-frequency component. The corresponding peak scattering rate of the OC beam is 
. The simulations also showed good agreement with the experimental data, providing a consistent description of transition dynamics and saturation behavior. The observed saturation at higher total beam power was attributed to population loss into dark magnetic sublevels and vibrational leakage.
When a tilted magnetic field was applied to remix dark states, the fluorescence increased by an additional factor of 2.22, leading to a total enhancement of 7.64 relative to the sum of single-frequency LIF.
In summary, by fully optimizing the frequency detunings, power ratios, and incorporating magnetic-field-induced dark state remixing, we established quantitative benchmarks for MgF optical cycling. These results provide practical guidance for designing laser configurations in future MgF-based molecular slowing and magneto-optical trapping experiments.
Methods
Experiment setup
Cryogenic buffer-gas beam source
The MgF molecular beam was generated using a cryogenic buffer-gas beam source, following the structure and principle similar to most molecular laser cooling experiments36,37. Ablation of the Mg target was performed using a 532 
pulsed Nd:YAG laser (Nano S 30-50, Litron Lasers) with a pulse energy of 18 
, a pulse width of <7 
, and a focused spot size diameter of 
17 
at the ablation point. The Mg target was prepared by cutting a 99.8% pure Mg rod into a disk shape.
The flow rate of He buffer gas influenced the main cell temperature, MgF production yield, and the forward velocity of the molecular beam. In this experiment, a flow rate of 3 
was optimal, as it maximized MgF production while maintaining the main cell temperature at 4 
.
During the experiment, the sample amount gradually decreased. Two primary factors contributed to this. First, the uneven surface affected the ablation efficiency as ablation pulses removed material from the target surface. This issue was mitigated by randomly scanning the ablation point with a motorized mirror mount and periodically polishing the target. Second, the minimum flow rate of the mass flow controller (MFC) for 
gas was limited to 0.05 
, which was excessively high and led to 
freezing on the inner walls of the main cell, thereby degrading the molecular beam quality. To resolve this, the MFC was modulated using pulse width modulation, ensuring that the time-averaged flow rate was maintained at 0.01 
.
The MgF molecules produced in the main cell exited as a molecular beam into the 6" CF octagonal chamber, which was connected to a beam box, where they interacted with the laser beam. The chamber was equipped with a turbo pump and was typically maintained at a vacuum level of 
Torr with the gate valve to the beam box closed. The PMT signal was digitized with a DAQ card and stored as a time trace. For each shot, the background recorded after the molecular beam had passed was averaged and subtracted from the fluorescence signal.
To characterize the forward velocity distribution, we sent a probe laser at a 
angle relative to the molecular beam and recorded the Doppler-shifted spectrum, from which the velocity profile was obtained. The forward velocity was found to increase as the beam sample degraded over time, a trend that could be mitigated by periodically opening the beam box and cleaning the inside of the main cell. The transverse velocity distribution was characterized by sending a probe beam perpendicular to the molecular beam and recording the corresponding spectra. The spectra were analyzed by fitting to a Voigt profile, which accounts for Doppler and power broadening, assuming a Gaussian velocity distribution. From these fits we obtained a transverse velocity width of approximately 
.
Laser and optics
The 359 
laser for the main transition was generated via second harmonic generation (SHG) of a Ti:Sapphire laser (SolsTis, M Squared) operating at 718 
. The SHG cavity (ECD-X, M Squared) employed an LBO crystal, achieving a maximum doubling efficiency of 30%, yielding an output power of approximately 1 
.
The main laser’s frequency was stabilized by locking the IR frequency to a wavemeter (WS8, HighFinesse) before the SHG cavity. According to the factory specifications, the absolute accuracy and measurement deviation sensitivity were 10 
and 0.4 
, respectively. The wavemeter was calibrated using a homemade ECDL locked to the D2 line of 
. Calibration was performed daily, and we continuously monitored the frequency of the ECDL during each measurement to compensate for long-term drifts on the hour scale.
The power fluctuation of the main laser was stabilized using a servo system with an AOM (ISOMAT, 80 
), reducing relative deviations to approximately 0.5%.
The polarization of the laser beams was defined by the polarization-dependent AOMs, combined with 50:50 beam splitters, and delivered to the chamber through a polarization-maintaining fiber. The input polarization was optimized with a half-wave plate and verified with a PBS to ensure stability during the experiments.
Rate equation simulation
The molecular beam emerging from the CBGB had a forward velocity centered around 
. Given the 6 mm aperture size, the beam expanded to a diameter of approximately 1.5 cm at the chamber center. Since the laser beam waist was much smaller (
mm), the effective interaction time was determined mainly by the molecular forward velocity, yielding about 
. Under these conditions, Doppler broadening from the transverse velocity distribution could be neglected, as power broadening dominated in the experiment.
All simulations correspond to the nominal 
G condition. In the experiment, the ambient magnetic field (mainly the Earth’s field of 
0.3 G) was not compensated, but its influence is negligible under our conditions. For the dark-state–forming 
manifold with 
, this field corresponds to a Zeeman splitting of about 0.2 MHz and a Larmor period of roughly 5 
. Because the laser beam radius was relatively small (
mm), the molecular interaction time with the light field was about 5.6 
–comparable to the Larmor period. At 
(2 mW), the peak photon-scattering rate reached 
. Under these conditions, optical pumping into magnetic dark states occurs much faster than remixing driven by the ambient field, so the latter plays no appreciable role during the light–molecule interaction. Consequently, we treated the condition as effectively zero-field and omitted any magnetic remixing terms in the model.
Given the short excited-state lifetime (
), the rapid spontaneous decay strongly suppresses coherent dynamics such as Rabi oscillations. Therefore, a rate-equation treatment provides an accurate description of the optical cycling process, while a full optical Bloch equation approach was not required38. The rate equations used in the simulation are given by:
 |
1 |
 |
2 |
 |
3 |
Where 
, 
, and 
represent the populations of the ground-state magnetic sublevels, excited-state magnetic sublevels, and vibrationally excited states (
), respectively. Here, 
is the branching fraction of the 
band, and 
denotes the branching ratio determined by Clebsch-Gordan coefficients.
The transition rate 
for the i-th frequency component of the OC beam, considering its detuning 
and power 
, is expressed as:
 |
4 |
 |
5 |
where 
represents the hyperfine energy splitting, 
is the saturation intensity, and 
is the electric dipole moment matrix element.
Since the laser beam has a Gaussian intensity profile, the time-dependent intensity I(t) experienced by the molecule traveling through the laser beam must be accounted for at each time step. The time range for solving the rate equations is set to scan from 
to 
relative to the intensity peak, resulting in a total scan time of 
.
Acknowledgements
Authors appreciate Donghyun Cho for his expert advice and for providing essential experimental equipment. We are especially grateful to Dongkyu Lim, whose preliminary calculations played a key role in our simulation framework. We also thank Hyunjun Jang, Hyeongtae Kim, and Zhirui Cheng for their assistance with the experimental setup.
Author contributions
E.C. supervised the project and set the direction of the experiment. K.K., S.R., Y.C., and Y.L. designed and built the experimental setup, carried out the measurements, and analyzed the data. K.K., Y.C., and Y.L. performed the simulation calculations. K.K. wrote the original draft. All authors reviewed and edited the manuscript.
Funding
The authors acknowledge support from the National Research Foundation of Korea under grant numbers RS-2022-NR119745, RS-2024-00439981, RS-2024-00431938, and RS-2023-NR068116.
Data availability
All data included in this study are available upon request by contacting the corresponding author, Eunmi Chae (echae@korea.ac.kr).
Declarations
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
All data included in this study are available upon request by contacting the corresponding author, Eunmi Chae (echae@korea.ac.kr).