# Transformers to Fight the COVID-19 Infodemic

Lasitha Uyangodage‡, Tharindu Ranasinghe§, Hansi Hettiarachchi♡,
‡Department of Information Systems, University of Münster, Germany
§Research Group in Computational Linguistics, University of Wolverhampton, UK
♡School of Computing and Digital Technology, Birmingham City University, UK
<EMAIL_ADDRESS>
###### Abstract

The massive spread of false information on social media has become a global
risk especially in a global pandemic situation like COVID-19. False
information detection has thus become a surging research topic in recent
months. NLP4IF-2021 shared task on fighting the COVID-19 infodemic has been
organised to strengthen the research in false information detection where the
participants are asked to predict seven different binary labels regarding
false information in a tweet. The shared task has been organised in three
languages; Arabic, Bulgarian and English. In this paper, we present our
approach to tackle the task objective using transformers. Overall, our
approach achieves a 0.707 mean F1 score in Arabic, 0.578 mean F1 score in
Bulgarian and 0.864 mean F1 score in English ranking 4th place in all the
languages.

##  1 Introduction

By April 2021, coronavirus(COVID-19) pandemic has affected 219 nations around
the world with 136 million total cases and 2.94 million deaths. With this
pandemic situation, a rapid increase in social media usage was noticed. In
measures, during 2020, 490 million new users joined indicating a more than 13%
year-on-year growth Kemp (2021). This growth is mainly resulted due to the
impacts on day-to-day activities and information sharing and gathering
requirements related to the pandemic.

As a drawback of these exponential growths, the dark side of social media is
further revealed during this COVID-19 infodemic Mourad et al. (2020). The
spreading of false and harmful information resulted in panic and confusions
which make the pandemic situation worse. Also, the inclusion of false
information reduced the usability of a huge volume of data which is generated
via social media platforms with the capability of fast propagation. To handle
these issues and utilise social media data effectively, accurate
identification of false information is crucial. Considering the high data
generation in social media, manual approaches to filter false information
require significant human efforts. Therefore an automated technique to tackle
this problem will be invaluable to the community.

Targeting the infodemic that occurred with COVID-19, NLP4IF-2021 shared task
was designed to predict several properties of a tweet including harmfulness,
falseness, verifiability, interest to the general public and required
attention. The participants of this task were required to predict the binary
aspect of the given properties for the test sets in three languages: Arabic,
Bulgarian and English provided by the organisers. Our team used recently
released transformer models with the text classification architecture to make
the predictions and achieved the 4th place in all the languages while
maintaining the simplicity and universality of the method. In this paper, we
mainly present our approach, with more details about the architecture
including an experimental study. We also provide our code to the community
which will be freely available to everyone interested in working in this area
using the same methodology111The GitHub repository is publicly available on
https://github.com/tharindudr/infominer.

##  2 Related Work

Identifying false information in social media has been a major research topic
in recent years. False information detection methods can be mainly categorised
into two main areas; Content-based methods and Social Context-based methods
Guo et al. (2020).

Content-based methods are mainly based on the different features in the
content of the tweet. For example, Castillo et al. (2011) find that highly
credible tweets have more URLs, and the textual content length is usually
longer than that of lower credibility tweets. Many studies utilize the lexical
and syntactic features to detect false information. For instance, Qazvinian et
al. (2011) find that the part of speech (POS) is a distinguishable feature for
false information detection. Kwon et al. (2013) find that some types of
sentiments are apparent features of machine learning classifiers, including
positive sentiments words (e.g., love, nice, sweet), negating words (e.g., no,
not, never), cognitive action words (e.g., cause, know), and inferring action
words (e.g., maybe, perhaps). Then they propose a periodic time-series model
to identify key linguistic differences between true tweets and fake tweets.
With the word embeddings and deep learning getting popular in natural language
processing, most of the fake information detection methods were based on
embeddings of the content fed into a deep learning network to perform the
classification Ma et al. (2016).

Traditional content-based methods analyse the credibility of the single
microblog or claim in isolation, ignoring the high correlation between
different tweets and events. However, Social Context-based methods take
different tweets in a user profile or an event to identify false information.
Many studies detect false information by analyzing users’ credibility Li et
al. (2019) or stances Mohammad et al. (2017). Since this shared is mainly
focused on the content of the tweet to detect false information, we can
identify our method as a content-based false information identification
approach.

##  3 Data

The task is about predicting several binary properties of a tweet on COVID-19:
whether it is harmful, whether it contains a verifiable claim, whether it may
be of interest to the general public, whether it appears to contain false
information, etc. Shaar et al. (2021). The data has been released for three
languages; English, Arabic and Bulgarian 222The dataset can be downloaded from
https://gitlab.com/NLP4IF/nlp4if-2021. Following are the binary properties
that the participants should predict for a tweet.

  1. I

Verifiable Factual Claim: Does the tweet contain a verifiable factual claim?

  2. II

False Information: To what extent does the tweet appear to contain false
information?

  3. III

Interest to General Public: Will the tweet have an effect on or be of interest
to the general public?

  4. IV

Harmfulness: To what extent is the tweet harmful to the society?

  5. V

Need of Verification: Do you think that a professional fact-checker should
verify the claim in the tweet?

  6. VI

Harmful to Society: Is the tweet harmful for the society?

  7. VII

Require attention: Do you think that this tweet should get the attention of
government entities?

##  4 Architecture

The main motivation for our architecture is the recent success that the
transformer models had in various natural language processing tasks like
sequence classification Ranasinghe and Hettiarachchi (2020); Ranasinghe et al.
(2019); Pitenis et al. (2020), token classification Ranasinghe and Zampieri
(2021a); Ranasinghe et al. (2021), language detection Jauhiainen et al.
(2021), word context prediction Hettiarachchi and Ranasinghe (2020a);
Hettiarachchi and Ranasinghe (2021) question answering Yang et al. (2019) etc.
Apart from providing strong results compared to RNN based architectures
Hettiarachchi and Ranasinghe (2019); Ranasinghe et al. (2019), transformer
models like BERT Devlin et al. (2019) provide pretrained multilingual language
models that support more than 100 languages which will solve the multilingual
issues of these tasks Ranasinghe et al. (2020); Ranasinghe and Zampieri
(2021b); Ranasinghe and Zampieri (2020).

For sequence classification tasks transformer models take an input of a
sequence and outputs the representations of the sequence. There can be one or
two segments in a sequence which are separated by a special token [SEP] Devlin
et al. (2019). In this approach we considered a tweet as a sequence and no
[SEP] token is used. Another special token [CLS] is used as the first token of
the sequence which contains a special classification embedding. For text
classification tasks, transformer models take the final hidden state h of the
[CLS] token as the representation of the whole sequence Sun et al. (2019). A
simple softmax classifier is added to the top of the transformer model to
predict the probability of a class $c$ as shown in Equation 1 where $W$ is the
task-specific parameter matrix. In the classification task all the parameters
from transformer as well as W are fine tuned jointly by maximising the log-
probability of the correct label. The architecture of transformer-based
sequence classifier is shown in Figure 1.

$p(c|\textbf{h})=softmax(W\textbf{h})$ (1)

Figure 1: Text Classification Architecture

|  Model |  I |  II |  III |  IV |  V |  VI |  VII |  Mean
---|---|---|---|---|---|---|---|---|---
English | roberta-base | 0.822 | 0.393 | 0.821 | 0.681 | 0.461 | 0.235 | 0.251 | 0.523
bert-base-cased | 0.866 | 0.461 | 0.893 | 0.740 | 0.562 | 0.285 | 0.303 | 0.587
Arabic | bert-multilingual-cased | 0.866 | 0.172 | 0.724 | 0.400 | 0.557 | 0.411 | 0.625 | 0.536
arabert-v2 | 0.917 | 0.196 | 0.782 | 0.469 | 0.601 | 0.433 | 0.686 | 0.583
arabert-v2-tokenized | 0.960 | 0.136 | 0.873 | 0.571 | 0.598 | 0.424 | 0.678 | 0.606
Bulgarian | bert-multilingual-cased | 0.845 | 0.098 | 0.516 | 0.199 | 0.467 | 0.303 | 0.196 | 0.375

Table 1: Macro F1 between the algorithm predictions and human annotations for
development set in all the languages. Results are sorted from Mean F1 score
for each language.

|  Model |  I |  II |  III |  IV |  V |  VI |  VII |  Mean
---|---|---|---|---|---|---|---|---|---
English | Best System | 0.835 | 0.913 | 0.978 | 0.873 | 0.882 | 0.908 | 0.889 | 0.897
InfoMiner | 0.819 | 0.886 | 0.946 | 0.841 | 0.803 | 0.884 | 0.867 | 0.864
Random Baseline | 0.552 | 0.480 | 0.457 | 0.473 | 0.423 | 0.563 | 0.526 | 0.496
Arabic | Best System | 0.843 | 0.762 | 0.890 | 0.799 | 0.596 | 0.912 | 0.663 | 0.781
InfoMiner | 0.852 | 0.704 | 0.774 | 0.743 | 0.593 | 0.698 | 0.588 | 0.707
Random Baseline | 0.510 | 0.444 | 0.487 | 0.442 | 0.476 | 0.584 | 0.533 | 0.496
Bulgarian | Best System | 0.887 | 0.955 | 0.980 | 0.834 | 0.819 | 0.678 | 0.706 | 0.837
InfoMiner | 0.786 | 0.749 | 0.419 | 0.599 | 0.556 | 0.303 | 0.631 | 0.578
Random Baseline | 0.594 | 0.502 | 0.470 | 0.480 | 0.399 | 0.498 | 0.528 | 0.496

Table 2: Macro F1 between the InfoMiner submission and human annotations for
test set in all the languages. Best System is the results of the best model
submitted for each language as reported by the task organisers Shaar et al.
(2021).

##  5 Experimental Setup

We considered the whole task as seven different classification problems. We
trained a transformer model for each label mentioned in Section 3. This gave
us the flexibility to fine-tune the classification model in to the specific
label rather than the whole task. Given the very unbalanced nature of the
dataset, the transformer models tend to overfit and predict only the majority
class. Therefore, for each label we took the number of instances in the
training set for the minority class and undersampled the majority class to
have the same number of instances as the minority class.

We then divided this undersampled dataset into a training set and a validation
set using 0.8:0.2 split. We mainly fine tuned the learning rate and number of
epochs of the classification model manually to obtain the best results for the
development set provided by organisers in each language. We obtained $1e^{-5}$
as the best value for learning rate and 3 as the best value for number of
epochs for all the languages in all the labels. The other configurations of
the transformer model were set to a constant value over all the languages in
order to ensure consistency between the languages. We used a batch-size of
eight, Adam optimiser Kingma and Ba (2014) and a linear learning rate warm-up
over 10% of the training data. The models were trained using only training
data. We performed early stopping if the evaluation loss did not improve over
ten evaluation rounds. A summary of hyperparameters and their values used to
obtain the reported results are mentioned in Table 3. The optimized
hyperparameters are marked with ${\ddagger}$ and their optimal values are
reported. The rest of the hyperparameter values are kept as constants. We did
not use any language specific preprocessing techniques in order to have a
flexible solution between the languages. We used a Nvidia Tesla K80 GPU to
train the models. All the experiments were run for five different random seeds
and as the final result, we took the majority class predicted by these
different random seeds as mention in Hettiarachchi and Ranasinghe (2020b). We
used the following pretrained transformer models for the experiments.

### bert-base-cased

\- Introduced in Devlin et al. (2019), the model has been trained on a
Wikipedia dump of English using Masked Language Modelling (MLM) objective.
There are two variants in English BERT, base model and the large model.
Considering the fact that we built seven different models for each label, we
decided to use the base model considering the resources and time.

### roberta-base

\- Introduced in Liu et al. (2019), RoBERTa builds on BERT and modifies key
hyperparameters, removing the next-sentence pretraining objective and training
with much larger mini-batches and learning rates. RoBERTa has outperformed
BERT in many NLP tasks and it motivated us to use RoBERTa in this research
too. Again we only considered the base model.

### bert-nultilingual-cased

\- Introduced in Devlin et al. (2019), the model has been trained on a
Wikipedia dump of 104 languages using MLM objective. This model has shown good
performance in variety of languages and tasks. Therefore, we used this model
in Arabic and Bulgarian.

### AraBERT

Recently language-specific BERT based models have proven to be very efficient
at language understanding. AraBERT Antoun et al. (2020) is such a model built
for Arabic with BERT using scraped Arabic news websites and two publicly
available Arabic corpora; 1.5 billion words Arabic Corpus El-khair (2016) and
OSIAN: the Open Source International Arabic News Corpus Zeroual et al. (2019).
Since AraBERT has outperformed multilingual bert in many NLP tasks in Arabic
Antoun et al. (2020) we used this model for Arabic in this task. There are two
version in AraBERT; AraBERTv0.1 and AraBERTv1, with the difference being that
AraBERTv1 uses pre-segmented text where prefixes and suffixes were splitted
using the Farasa Segmenter Abdelali et al. (2016).

##  6 Results

When it comes to selecting the best model for each language, highest F1 score
out of the evaluated models was chosen. Due to the fact that our approach uses
a single model for each label, our main goal was to achieve good F1 scores
using light weight models. The limitation of available resources to train
several models for all seven labels itself was a very challenging task to the
team but we managed to evaluate several.

As depicted in Table 1, for English, bert-base-cased model performed better
than roberta-base model. For Arabic, arabert-v2-tokenized performed better
than the other two models we considered. For Bulgarian, with the limited time,
we could only train bert-multilingual model, therefore, we submitted the
predictions from that for Bulgarian.

As shown in Table 2, our submission is very competitive with the best system
submitted in each language and well above the random baseline. Our team was
ranked 4th in all the languages.

##  7 Conclusion

We have presented the system by InfoMiner team for NLP4IF-2021-Fighting the
COVID-19 Infodemic. We have shown that multiple transformer models trained on
different labels can be successfully applied to this task. Furthermore, we
have shown that undersampling can be used to prevent the overfitting of the
transformer models to the majority class in an unbalanced dataset like this.
Overall, our approach is simple but can be considered as effective since it
achieved 4th place in the leader-board for all three languages.

One limitation in our approach is that it requires maintaining seven
transformer models for the seven binary properties of this task which can be
costly in a practical scenario which also restricted us from experimenting
with different transformer types due to the limited time and resources.
Therefore, in future work, we are interested in remodeling the task as a
multilabel classification problem, where a single transformer model can be
used to predict all seven labels.

## Acknowledgments

We would like to thank the shared task organizers for making this interesting
dataset available. We further thank the anonymous reviewers for their
insightful feedback.

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##  Appendix A Appendix

A summary of hyperparameters and their values used to obtain the reported
results are mentioned in Table 3. The optimised hyperparameters are marked
with ${\ddagger}$ and their optimal values are reported. The rest of the
hyperparameter values are kept as constants.

Parameter | Value
---|---
learning rate‡ | $1e^{-5}$
number of epochs‡ | $3$
adam epsilon | $1e^{-8}$
warmup ration | 0.1
warmup steps | 0
max grad norm | 1.0
max seq. length | 120
gradient accumulation steps | 1

Table 3: Hyperparameter specifications


# Laser frequency stabilization by modulation transfer spectroscopy and
balanced detection of molecular iodine for laser cooling of 174Yb

Álvaro M.G. de Melo1, Hector Letellier1, Apoorva Apoorva1, Antoine
Glicenstein1, Robin Kaiser1,∗
1Université Côte d’Azur, CNRS, INPHYNI, 17 Rue Julien Lauprête, 06200 Nice,
France

###### Abstract

We report laser frequency stabilization by the combination of modulation
transfer spectroscopy and balanced detection of a relatively weak hyperfine
transition of the R(158)25-0 line of molecular iodine (127I2), which is used
as a new frequency reference for laser trapping and cooling of 174Yb on the
${}^{1}S_{0}-{}^{3}P_{1}$ transition. The atomic cloud is characterized by
time-of-flight measurements, and an on-resonance optical depth of up to 47 is
obtained. We show laser noise reduction and characterize the short-term laser
frequency instability by the Allan deviation of the laser fractional
frequency. The minimum measured value is 3.9 ×$10^{-13}$ at
$0.17\text{\,}\mathrm{s}$ of averaging time.

<EMAIL_ADDRESS>
##  1 Introduction

Atoms with two valence electrons, i.e. alkaline-earth like metals, have
attracted the attention of the laser cooling community since the end of the
last century [1, 2, 3, 4, 5] and their applications have ranged from precision
measurements [6] to quantum computing [7]. Among them, strontium and ytterbium
have been the species often chosen due to their internal structure allowing
the use of a dipole-allowed transition at $461\text{\,}\mathrm{nm}$ and
$399\text{\,}\mathrm{nm}$, respectively, to slow down atoms from the atomic
source in combination with a narrow closed transition
(${}^{1}S_{0}-{}^{3}P_{1}$) of linewidths $2\pi\cdot 7$
$\text{\,}\mathrm{kHz}$ and $2\pi\cdot 182$ $\text{\,}\mathrm{kHz}$. These
narrow transitions can be used to achieve high optical depths at low
temperatures.

Compared to broad line magneto-optical traps (MOT) such as Rubidium with a
$2\pi\cdot 6$ $\text{\,}\mathrm{MHz}$ linewidth and easy-to-use spectroscopic
absorption cells, one challenge in realizing an ytterbium MOT operating on the
${}^{1}S_{0}-{}^{3}P_{1}$ intercombination line is to stabilize the laser
frequency, due to its linewidth ($\Gamma_{g}=2\pi\cdot 182$
$\text{\,}\mathrm{kHz}$) and the difficulty of realizing an appropriate Yb
spectroscopic cell [8] to perform usual saturated absorption spectroscopy on
the ${}^{1}S_{0}-{}^{3}P_{1}$ transition. As $\Gamma_{g}$ is below commercial
wavemeter’s precision[10], different techniques were used by several groups to
circumvent such difficulties. Frequency modulated (FM) spectroscopy of the
atomic beam has been used in [11], resulting in a short-term frequency
stability of less than $1\text{\,}\mathrm{MHz}$. Other groups have stabilized
the laser to a cavity line that is locked to another stable reference [12, 13,
9]. Such methods have shown to be efficient, however dependent on the atomic
flux or cavity stability.

Similarly to what is done for alkalis using a gas cell to perform
spectroscopy, molecular iodine (127I2), has also been used to stabilize the
laser used to load an Yb MOT on the ${}^{1}S_{0}-{}^{3}P_{1}$ transition[14].
The frequency reference was a convenient 127I2 hyperfine transition in the
P(49)24-1 rotational line. The required frequency shift to reach the
$1.3\text{\,}\mathrm{GHz}$ shifted 174Yb ${}^{1}S_{0}-{}^{3}P_{1}$ transition
has been realized using three acousto-optic modulators (AOMs), two of them in
double-pass configuration. In this work we show that a simple configuration
can be implemented by choosing a different 127I2 transition and combining the
robustness of modulation transfer spectroscopy (MTS) with respect to
temperature and laser power fluctuations to the common-noise rejection
achieved by balanced detection. The details on the experimental scheme,
spectroscopy of molecular iodine and laser frequency stabilization feedback
loop are given in section 2. In section 3, we present the implementation of an
Yb MOT with 2 ×$10^{8}$ atoms operating on the ${}^{1}S_{0}-{}^{3}P_{1}$
intercombination transition that was obtained with the laser stabilized by the
proposed method. We also give details on the laser noise reduction and
characterize the short-term instability of the laser frequency by means of the
Allan deviation of the laser’s fractional frequency.

##  2 Laser frequency stabilization scheme and iodine spectroscopy

Among the various laser locking (i.e. frequency stabilization) techniques
available, we have chosen the so-called modulation transfer spectroscopy
(MTS), where the pump beam is modulated in a saturated absorption spectroscopy
configuration. In this technique the modulation of the pump field is
transferred to the probe by a four-wave mixing (FWM) process as explained in
[15]. MTS is generally chosen due to its robustness to temperature drifts and
laser intensity fluctuations [16]. Moreover, the increase of frequency
stability by MTS in a balanced detection, i.e. when the saturated absorption
profile is subtracted by a linear absorption signal as depicted in Fig.1, was
reported in [18]. Therefore, we employ MTS in a balanced configuration to
stabilize the laser frequency to a relatively weak 127I2 line that is
convenient for laser cooling of 174Yb atoms on the ${}^{1}S_{0}-{}^{3}P_{1}$
line.

###  2.1 Experimental scheme

The laser system (Toptica TA-SHG pro) consists of a diode laser that generates
around $50\text{\,}\mathrm{mW}$ at $1112\text{\,}\mathrm{nm}$ before being
amplified by a tapered amplifier to up to $1.8\text{\,}\mathrm{W}$ and finally
a second-harmonic generation (SHG) cavity that delivers up to
$1.3\text{\,}\mathrm{W}$ at around $556\text{\,}\mathrm{nm}$. After the SHG
cavity, the beam is divided into two by inserting a half-wave plate and a
polarizing beam splitter (PBS) inside the laser box (not depicted). In Fig.1,
it can be seen that one beam is sent to a free space output and the other one
to a fiber output. The fiber output is connected to a fibered AOM (AOM 2,
Brimrose TEM-150-9-60-556-2FP-HP), that is used to shift the laser frequency
near resonance to the 174Yb ${}^{1}S_{0}-{}^{3}P_{1}$ transition as well as to
provide time control of the amplitude of the MOT beams. After AOM 2, the beam
is further split by a 2$\times$6 fiber splitter to generate the six MOT beams.
The free space output depicted is used for laser frequency stabilization via
MTS on 127I2 using AOM 1 to perform the necessary frequency modulation for
MTS. Therefore, the laser beams used for the MOT do not suffer from any
residual frequency modulation, in contrast to the case when the laser diode
current is modulated.

Figure 1: Simplified experimental scheme for the frequency stabilisation of
the laser used to load a MOT on the 174Yb ${}^{1}S_{0}-{}^{3}P_{1}$ line. The
laser beam is split into two inside the laser system, both outputs (a fibered
and a free space) are shown. The free space output is divided into two
different beams by PBS 1. One beam passes through AOM 1 where it is diffracted
and modulated to be used as the pump on the MTS, while the other optical beam
is further split into two by PBS 3. The reflection of PBS 3 is the probe for
the MTS and the transmission is the beam used to perform linear spectroscopy
of 127I2. The difference between the MTS probe and the linear absorption is
sent to a RF mixer to be demodulated to generate the error signal that is sent
as a feedback to the laser controllers. The fibered output is diffracted by
AOM 2 before being split into six by a fiber splitter before being sent to the
glass cell to perform the MOT.

The transmission of PBS 1 is diffracted and modulated by AOM 1, and the -1
diffracted order is used as the pump beam for saturated absorption
spectroscopy. The pump beam at the position of the cell has a power of
$300\text{\,}\mathrm{mW}$ and a full width at $1/e^{2}$ of
$0.75\text{\,}\mathrm{mm}$. AOM 1 is driven by a direct digital synthesizer
(2023A Aeroflex). The synthesizer’s carrier frequency
($80\text{\,}\mathrm{MHz}$) is modulated by a $200\text{\,}\mathrm{kHz}$
sinusoidal signal generated by a function generator (B$\&$K Precision 4052)
with a modulation index of 10. It is important to note that the -1 diffracted
order of AOM 1 includes separated beams of frequency shifts defined by the
driver’s carrier frequency ($\Delta_{1}=$ $-80\text{\,}\mathrm{MHz}$) and the
sidebands ($-79.8\text{\,}\mathrm{MHz}$ and $-80.2\text{\,}\mathrm{MHz}$, for
the first sidebands) generated by frequency modulation of this carrier signal
[17]. As the AOM is positioned close enough to the spectroscopic cell the
carrier and the first sidebands are almost superposed along their propagation
through the 10-cm spectroscopic cell. The transmission of PBS 2 is further
split into two beams by another half-wave plate and PBS 3. The transmission is
used to perform linear spectroscopy of 127I2 and is measured by the input PD+
of a free space balanced photodetector (Thorlabs PDB210A/M). The reflection of
PBS 3 is aligned counterpropagating to the pump beam and plays the role of the
probe beam in saturated absorption spectroscopy, which is measured by the
second input (PD-) of the photodetector. The spectroscopic cell is slightly
tilted to avoid undesired pump beam reflections reaching PD- and is kept at
room temperature without any cooling or heating system. Each probe beam has a
power of $1\text{\,}\mathrm{mW}$ and a full width at $1/e^{2}$ of
$0.75\text{\,}\mathrm{mm}$ at the spectroscopic cell.

The second output of the function generator is sent to the local oscillator
(LO) input of the RF mixer to perform the demodulation of the subtraction of
the signal measured by PD+ and PD-. Finally, it is amplified and demodulated
to generate an error signal that is sent to a PID controller (FALC 110), which
has a high bandwidth ($\sim$ $10\text{\,}\mathrm{MHz}$) output and a slow
integrator output with a bandwidth of $10\text{\,}\mathrm{kHz}$. The slow
integrator output is used to suppress long-term drifts and is fed back to the
voltage applied to a piezo actuator holding the grating (FALC’s slow
integrator output). The fast feedback closes the loop controlling the laser
diode’s current (FALC’s high bandwidth output).

###  2.2 Iodine spectroscopy

(a)

(b)

(c)

Figure 2:  (a) Saturated absorption spectroscopy of P(49)24-1 and R(158)25-0
127I2 lines (in blue) and error signals generated by MTS (in red) for a laser
scan rate of $147\text{\,}\mathrm{MHz}\text{\,}{\mathrm{s}}^{-1}$. The origin
of the frequency axis is the center of the $a_{10}$ R(158)25-0 transition. The
strong lines between $-1500\text{\,}\mathrm{MHz}$ and
$-400\text{\,}\mathrm{MHz}$ are the 21 hyperfine transitions of the P(49)24-1
line. The weak lines shown from $-400\text{\,}\mathrm{MHz}$ to
$300\text{\,}\mathrm{MHz}$ are 14 of the hyperfine transitions of the
R(158)25-0 line. The green vertical dashed lines indicates the $a_{1}$ and
$a_{21}$ lines of P(49)24-1, the $a_{10}$ line of R(158)25-0 and the 174Yb
${}^{1}S_{0}-{}^{3}P_{1}$ intercombination transition (b) Zoom of (a) from
$-550\text{\,}\mathrm{MHz}$ to $1800\text{\,}\mathrm{MHz}$. (c) Zoom of (a)
from $-80\text{\,}\mathrm{MHz}$ to $80\text{\,}\mathrm{MHz}$.

The saturated absorption signal measured by PD- (in blue) and the MTS error
signal (in red) are shown in Fig.2 for a laser frequency scan rate of
$147\text{\,}\mathrm{MHz}\text{\,}{\mathrm{s}}^{-1}$. The strong lines between
$-1500\text{\,}\mathrm{MHz}$ and $-400\text{\,}\mathrm{MHz}$ in Fig.(2a)
correspond to the 21 hyperfine components of the P(49)24-1 rotational line,
one of them already used as a frequency reference for laser cooling of
Ytterbium atoms as reported in [14]. Precision spectroscopy of the P(49)24-1
127I2 line was recently performed and reported in [19], where the absolute
frequencies of the hyperfine transitions were measured using an optical
frequency comb with an uncertainty of $7\text{\,}\mathrm{kHz}$ and with
frequency shifts due to laser power
($-2.6\text{\,}\mathrm{kHz}\text{\,}{\mathrm{mW}}^{-1}$) and iodine pressure
($-1.8\text{\,}\mathrm{kHz}\text{\,}{\mathrm{Pa}}^{-1}$). In Fig.2, we have
used these results in order to calibrate our frequencies assuming a linear
scanning of the frequency of our laser and chose the center of our frequency
axis at the $a_{10}$ R(158)25-0 hyperfine line (set at
$0\text{\,}\mathrm{MHz}$ on Fig.2). We choose to stabilize the frequency of
our laser on the $a_{10}$ hyperfine transition of the R(158)25-0 line,
defining thus a frequency reference for our laser used for laser cooling of
174Yb atoms as presented in the next section. The choice of this line is
motivated by the fact that it is a mere $191\text{\,}\mathrm{MHz}$ away from
the 174Yb ${}^{1}S_{0}-{}^{3}P_{1}$ frequency. The frequency-difference of the
pump beam in the MTS by AOM 1 ($\Delta_{1}$) with respect to the probe beam
shifts the frequency of the saturation peak by $\Delta_{1}/2=$
$-40\text{\,}\mathrm{MHz}$ [20]. We use the +1 diffraction order for AOM 2
with a frequency-shift of $\Delta_{2}=$ $151\text{\,}\mathrm{MHz}$. Combining
the frequency shifts due to AOM 1 and AOM 2 we thus shift the laser frequency
near the 174Yb resonance, with a total frequency-shift with respect to the
$a_{10}$ hyperfine transition of the R(158)25-0 line of
$\Delta=\Delta_{2}-\Delta_{1}/2=$ $191\text{\,}\mathrm{MHz}$.

Fig.2b is a zoom of Fig.2a from $-550\text{\,}\mathrm{MHz}$ to
$400\text{\,}\mathrm{MHz}$ that allows to compare the amplitude of the
$a_{10}$ hyperfine component of the R(158)25-0 line with respect to the
hyperfine components of the P(49)24-1 line. Fig.2c, a zoom of Fig.2a from
$-80\text{\,}\mathrm{MHz}$ to $80\text{\,}\mathrm{MHz}$, is centered at the
$a_{10}$ hyperfine component of the R(158)25-0 line. The small amplitude of
this line with respect to the P(49)24-1 hyperfine lines is probably the main
reason why it was not yet exploited as a frequency reference for experiments
using the ${}^{1}S_{0}-{}^{3}P_{1}$ transition of 174Yb atoms, despite being
closer to 174Yb transition. In Fig.3, we show a scan around the saturated
absorption peak, highlighting the small amplitude of the absorption signal (in
blue). The relative amplitude of the line, i.e. the amplitude of the peak with
respect to the background divided by the background amplitude, is smaller than
1%, meaning that it is below the laser’s power stability over seconds. This is
the main reason why MTS is more suitable to our experiment than frequency-
modulation (FM) spectroscopy. In FM spectroscopy, the background of the error
signal depends on fluctuations of the spectroscopic signal resulting in
fluctuations of the error signal in time. In MTS the background level is very
robust to signal’s fluctuation [23], MTS is also very suitable to perform
wideband locking as reported in [24]. MTS has been widely used with acousto-
optic modulators performing the pump beam frequency modulation by modulating
the carrier frequency of the AOM driver [17, 25]. In red, we show the MTS
error signal (without averaging) after being amplified by the FALC, which is
the signal sent as a feedback to the laser’s current and piezo controllers as
well as the signal used to measure the laser frequency instability
(considering the gain applied by the FALC) that will be shown in the next
section.

Absolute frequency measurements of the 176Yb ${}^{1}S_{0}-{}^{3}P_{1}$ line
were reported in [21, 22], with isotope shifts also reported allowing to
connect to the frequency of the 174Yb ${}^{1}S_{0}-{}^{3}P_{1}$ line. Even
though the goal of the present paper is not to perform an absolute frequency
measurement of the 174Yb ${}^{1}S_{0}-{}^{3}P_{1}$ line, we note that the
$40\text{\,}\mathrm{MHz}$ discrepancy between the two reported values in [21,
22] can be addressed by our work with sufficient precision. Indeed, relying on
the absolute frequency $\nu_{a21}$ of the $a_{21}$ hyperfine transition of
P(49)24-1 127I2 line reported in [19] ($\nu_{a21}=$
$539\,385\,938\,687\text{\,}\mathrm{kHz}$) and exploiting the measured
absolute frequencies of the $a_{1}$ and $a_{21}$ hyperfine transitions of
P(49)24-1 127I2 lines to calibrate our scanning rate, we get for the frequency
$\nu_{a10}$ of the $a_{10}$ R(158)25-0 hyperfine line an absolute frequency of
$\nu_{a10}=$ $539\,386\,406(6)\text{\,}\mathrm{MHz}$, with an estimated
precision of $6\text{\,}\mathrm{MHz}$ in our frequency scan. Adding our AOM
induced frequency shift of 191MHz (taking into account the laser detuning of
$-1.1\text{\,}\mathrm{MHz}$) we obtain for the frequency of the
${}^{1}S_{0}-{}^{3}P_{1}$ line of 174Yb a value of $\nu_{174}=$
$539\,386\,597(6)\text{\,}\mathrm{MHz}$. This is consistent within the
precision of our estimation with the value of
$539\,386\,600\text{\,}\mathrm{MHz}$ reported in [22] but in discrepancy with
the value of $539\,386\,560\text{\,}\mathrm{MHz}$ reported in [21].

Figure 3: The saturated absorption spectroscopy of the $a_{10}$ hyperfine
component of the R(158)25-0 line, measured by PD-, is shown in blue for a
laser frequency scan rate of
$6.65\text{\,}\mathrm{GHz}\text{\,}{\mathrm{s}}^{-1}$. The data shown in blue
is an average of 100 samples and stresses the small relative amplitude of the
line. The MTS error signal (in red) measured at the output of the FALC for the
same laser frequency scan rate but without averaging.

##  3 Results

###  3.1 Magneto-optical trap

In this section we present the realization of a MOT of 174Yb operating on the
narrow ${}^{1}S_{0}-{}^{3}P_{1}$ transition, illustrating the convenient
frequency stabilization of our laser to the $a_{10}$ hyperfine component of
the R(158)25-0 line. Neutral ytterbium atoms are generally laser cooled by
making use of two transitions, the one at $399\text{\,}\mathrm{nm}$ is dipole-
allowed and has a broad linewidth ($\Gamma_{b}=2\pi\cdot$
$29\text{\,}\mathrm{MHz}$) which makes it suitable for slowing down and
capturing a large range of velocity classes and it is, therefore, the
transition used for Zeeman slowers. The narrow transition can then be used in
a second cooling step due to its narrower linewidth ($\Gamma_{g}=2\pi\cdot$
$182\text{\,}\mathrm{kHz}$) that allows to obtain colder atomic clouds with a
Doppler temperature of $4\text{\,}\mathrm{\SIUnitSymbolMicro K}$ for the
bosonic isotopes (i.e. in the absence of sub-doppler cooling). The absence of
any Zeeman degeneracy in ground state of the bosonic isotopes of Yb makes them
suitable to perform experiments aiming at verify the existence of 3D
localization of light as proposed in [26]. In our experiment, as explained in
[27], we use an oven with an array of micro-tubes to produce a collimated beam
of Yb. We trap the atoms on a MOT operating on the broad
${}^{1}S_{0}-{}^{1}P_{1}$ transition, which allows, due to its larger natural
linewidth ($\Gamma_{b}$), to capture atoms in a larger range of velocity
classes from the atomic beam. To further increase the number of atoms captured
by the MOT we make use of a slowing beam, i.e. a laser beam counterpropagating
to the atomic beam, but without a Zeeman slower. With this system, we obtain
up to 1 ×$10^{9}$ atoms in a MOT operating on the ${}^{1}S_{0}-{}^{1}P_{1}$
transition at $399\text{\,}\mathrm{nm}$ (blue MOT). This blue MOT is loaded
using $72\text{\,}\mathrm{mW}$ of total laser power split in three pairs of
counterpropagating beams of waist $22\text{\,}\mathrm{mm}$ and detuned by
$-$2$\Gamma_{b}$, a slowing beam of power $200\text{\,}\mathrm{mW}$ and
detuned by $-$9.6 $\Gamma_{b}$ and an axial magnetic field gradient of
$20\text{\,}\mathrm{G}\text{\,}{\mathrm{cm}}^{-1}$ for $1\text{\,}\mathrm{s}$.

(a)

(b)

Figure 4:  (a) Absorption images of the atomic cloud for times of flight of 5,
10 ,15 and $20\text{\,}\mathrm{ms}$. (b) Square of the rms width of the MOT
along an horizontal axis as a function of the square of time of flight (blue
dots) and a fit of the data (in orange). The number of atoms is 2 ×$10^{8}$,
the MOT width at t=0 ms is $262\text{\,}\mathrm{\SIUnitSymbolMicro m}$, the
on-resonance optical depth is $b_{0}=47$ and the temperature calculated from
the curve fit is $60\text{\,}\mathrm{\SIUnitSymbolMicro K}$ (with a $R^{2}$
coefficient of the fit of 0.99). Error bars are not included as they are too
small to be visible at this scale.

To transfer the atoms from this blue MOT to our MOT on the narrow
intercombination line, we reduce the axial magnetic field gradient to
$4\text{\,}\mathrm{G}\text{\,}{\mathrm{cm}}^{-1}$ and turn off the blue MOT
and slowing beams. The $555.8\text{\,}\mathrm{nm}$ laser beam has a waist of
$9\text{\,}\mathrm{mm}$, $5\text{\,}\mathrm{mW}$ of total power split in the
three pairs of counterpropagating beams, and is detuned by $-$6 $\Gamma_{g}$
from atomic resonance. We turn this lasers on for $40\text{\,}\mathrm{ms}$ to
transfer the atoms to the MOT operating in the ${}^{1}S_{0}-{}^{1}P_{1}$
transition (green MOT). We characterize this green MOT by a time of flight
technique and absorption imaging on the ${}^{1}S_{0}-{}^{1}P_{1}$ transition.
We therefore turn off all laser beams and the magnetic field gradient during a
time of flight (TOF) at which the atomic cloud experiences a free expansion
and fall. After this time of flight, absorption images are obtained by a weak
probe beam resonant with the ${}^{1}S_{0}-{}^{1}P_{1}$ transition. Images for
TOF of 5, 10, 15, and $20\text{\,}\mathrm{ms}$ are shown in Fig.4a(a),
illustrating the free fall of the cloud in the grativational field and its
expansion due to its residual temperature. A quantitative analysis is done by
plotting the square of the rms width of the MOT ($\sigma$) as a function of
the square of the TOF (see Fig. 4a(b) (blue circles)). The fit (dashed orange
curve) of the data by the equation [28, 29]

$\sigma^{2}(t)=\frac{k_{B}T}{m}t^{2}+\sigma_{0}^{2},$ (1)

where $m$ is the atomic mass and $k_{B}$ is the Boltzman constant, allows us
to extract the temperature of the cloud ($T\sim$
$60\text{\,}\mathrm{\SIUnitSymbolMicro K}$) and its intial size at $t=$
$0\text{\,}\mathrm{(}$$\sigma_{0}\sim$ $262\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ along the horizontal axis). We also retrieve the number of atoms from
these absorption images with $N\sim$ 2 ×$10^{8}$. The on-resonance optical
depth ($b_{0}$) of the MOT, defined as $b_{0}=\frac{3N}{(k\sigma)^{2}}$ where
$k$ is the wavenumber of the light resonant to the ${}^{1}S_{0}-{}^{3}P_{1}$
transition, is thus 47. Which confirms that the obtained atomic cloud can be
used to perform experiments on collective effects in cold atomic samples [30,
31]. The temperature is about twice the expected from Doppler cooling theory,
which we attribute to multiple scattering in the atomic cloud or transverse
spatial intensity fluctuations of the MOT beams as reported in [32, 33].
Further improvements of our MOT will exploit schemes allowing to increase the
number of captured atoms in the blue MOT by shielding them using a resonant
beam on the ${}^{1}S_{0}-{}^{3}P_{1}$ transition [34] and by simultaneously
operating the MOT on both transitions in a core-shell geometry [35].

###  3.2 Noise reduction and laser frequency instability

After this illustration of the convenient locking transition, we now turn to a
more detailed description of the reduction of noise and frequency instability
of the laser by our MTS frequency stabilization scheme. The effectiveness of a
laser frequency stabilization system can be analyzed in the frequency domain.
The noise of the error signal can be measured and converted to frequency noise
power spectral density by using the error signal as a frequency discriminator.
The error signal, before being amplified, has a typical peak-to-valley
amplitude of $10\text{\,}\mathrm{mV}$ and its width (from the peak to the
valley) is $5\text{\,}\mathrm{MHz}$. Hence, the slope of
$0.5\text{\,}\mathrm{MHz}\text{\,}{\mathrm{mV}}^{-1}$ is used to convert
fluctuations of the error signal (in units of mV) to frequency. We note that
collisional (pressure) broadening present at room temperature can be reduced
in iodine spectroscopy [36] by cooling the spectroscopy cell, leading to a
narrower frequency discriminator, but this comes along with a reduced
amplitude of the signal requiring thus a longer spectroscopic cell.

In Fig. 5 we show the noise power spectral density of the laser measured by
the error signal noise in blue for the case where the laser is free-running,
i.e. no feedback was being sent neither to the piezo nor to the current
controllers, and in red for the stabilized laser, when both slow and fast
feedback loops are closed. We observe a noise reduction up to
$30\text{\,}\mathrm{kHz}$. The white noise part of the free-running spectrum
(starting at around $300\text{\,}\mathrm{Hz}$) corresponds to the intensity
noise level of the laser after the frequency SHG cavity, as reported in [37],
therefore we attribute this plateau to residual amplitude noise (after PD+ -
PD-). We note that the noise power spectral density shown in Fig. 5 not only
captures the frequency noise of the laser, but residual amplitude noise also
contributes to this signal. Nevertheless, the noise reduction shown in Fig. 5
(for frequencies below $1\text{\,}\mathrm{kHz}$) is an indication of the
effectiveness of the feedback loop.

In order to go beyond the analysis of the noise power spectral density, we
extract information from the feedback loop by analyzing the Allan deviation of
the laser fractional frequency. Although the Allan deviation is still limited
by amplitude noise for integration times below $3\text{\,}\mathrm{ms}$, the
higher values characterize the frequency instability of the laser for
averaging times up to $1\text{\,}\mathrm{s}$ which is a relevant timescale for
the operation of our experiments involving cold atoms.

Figure 5: Laser noise power spectral density measured from the residual error
signal for the free-running (blue) and stabilized (red) laser. The figure
shows a noise reduction until $30\text{\,}\mathrm{kHz}$, with a white noise
level above $300\text{\,}\mathrm{Hz}$ dominated by laser intensity noise. The
data shown is an average of 20 data samples.

The Allan deviation of an oscillator’s fractional frequency is a measure of
its frequency instability [38]. We can extract the fractional frequency of the
laser from the error signal as the latter is proportional to the frequency
fluctuations of the laser, which allows it to be used to characterize the
laser’s short-term instability [39, 40, 41], as shown in Fig.6 by the
overlapping Allan deviation [42] of the laser’s fractional frequency for
averaging times ranging from $2.5\text{\,}\mathrm{\SIUnitSymbolMicro s}$ to
$0.6\text{\,}\mathrm{s}$. The blue points correspond to a free-running laser
and the red points to the locked laser with both slow and fast feedback loops
closed. For very low averaging times, below
$20\text{\,}\mathrm{\SIUnitSymbolMicro s}$, the laser frequency instability is
the same for both cases. However, above $20\text{\,}\mathrm{\SIUnitSymbolMicro
s}$ the Allan deviation of the stabilized laser decreases until
$0.17\text{\,}\mathrm{s}$, while it increases for the free-running case after
$1.3\text{\,}\mathrm{ms}$. We note that the data used to extract the Allan
deviation shown in Fig.6 have been obtained with slightly different parameters
of the fast feedback loop than those for the data shown in Fig. 5, in
particular with an additional slow integrator element of the FALC on the fast
circuit branch switched on for the Allan deviation. The minimum Allan variance
measured is 3.9 ×$10^{-13}$ at $0.17\text{\,}\mathrm{s}$, indicating that the
laser frequency stabilization scheme introduced in section 2 can be used for
laser cooling of 174Yb atoms in the ${}^{1}S_{0}-{}^{3}P_{1}$ intercombination
line, as shown in the present work.

Figure 6: Allan deviations of the fractional frequency of the laser calculated
by the residual error signal for a free-running (blue) and stabilized (red)
laser. The feedback loop starts to be effective at an averaging time of
$20\text{\,}\mathrm{\SIUnitSymbolMicro s}$ with an Allan variance of the
stabilized laser of 3.9 ×$10^{-13}$ at $0.17\text{\,}\mathrm{s}$.

##  4 Conclusion

In conclusion, we have performed modulation transfer spectroscopy of the
P(49)24-1 and R(158)25-0 lines of molecular iodine. The hyperfine components
of the R(158)25-0 line are more convenient as a frequency reference for laser
cooling of 174Yb, the most naturally abundant ytterbium isotope, because of
its smaller frequency separation in comparison to the hyperfine components of
the P(49)24-1 line. We have shown that a laser frequency stabilization
technique based on the combination of modulation transfer spectroscopy and
balanced detection allows us to stabilize the laser frequency on one of the
hyperfine transitions of the R(158)25-0 line, despite its small relative
amplitude. The experimental configuration presented can be applied either to
enhance the laser frequency stability, as shown in [18], or to achieve laser
frequency stabilization in transitions that are relatively weak, as shown in
the present work. We have loaded a MOT, operating in the
${}^{1}S_{0}-{}^{3}P_{1}$ line of 174Yb, with 2 ×$10^{8}$ atoms and we have
measured a temperature of $60\text{\,}\mathrm{\SIUnitSymbolMicro K}$ by time-
of-flight measurements. The on-resonance optical depth of 47 indicates that
the obtained atomic cloud can be used to perform experiments on collective
effects with narrow atomic transitions, and the results of these experiments
will be a benchmark of this system to the study of localization of light by
cold atoms in three dimensions [26, 43]. The overlapping Allan deviation of
the laser fractional frequency was measured for the free-running and the
stabilized laser and it emphasizes that the stabilized laser is suitable to
perform laser cooling of 174Yb in the narrow intercombination line
(${}^{1}S_{0}-{}^{3}P_{1}$). Future development of the work presented in this
paper will include a deeper study of the impact of laser frequency
stabilization onto residual amplitude noise due to the SHG cavity in the laser
and possible additional feedforward loops to reduce such amplitude noise.

This work was performed in the framework of the European project ANDLICA, ERC
Advanced grant No. 832219. We also acknowledge support from the project
OPTIMAL granted by the European Union by means of the Fond Européen de
développement régional, FEDER. We thank Claus Zimmermann and Raphaël Saint-
Jalm for fruitful discussions and critical reading of the manuscript.

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