# Stable Distillation: Regularizing Continued Pre-training for Low-Resource
Automatic Speech Recognition

###### Abstract

Continued self-supervised (SSL) pre-training for adapting existing SSL models
to the target domain has shown to be extremely effective for low-resource
Automatic Speech Recognition (ASR). This paper proposes Stable Distillation, a
simple and novel approach for SSL-based continued pre-training that boosts ASR
performance in the target domain where both labeled and unlabeled data are
limited. Stable Distillation employs self-distillation as regularization for
continued pre-training, alleviating the over-fitting issue, a common problem
continued pre-training faces when the source and target domains differ.
Specifically, first, we perform vanilla continued pre-training on an initial
SSL pre-trained model on the target domain ASR dataset and call it the
teacher. Next, we take the same initial pre-trained model as a student to
perform continued pre-training while enforcing its hidden representations to
be close to that of the teacher (via MSE loss). This student is then used for
downstream ASR fine-tuning on the target dataset. In practice, Stable
Distillation outperforms all our baselines by 0.8 - 7 WER when evaluated in
various experimental
settings111https://github.com/cs20s030/stable_distillation.

Index Terms—  speech recognition, self-supervised learning, self-distillation

##  1 Introduction

Self-supervised learning (SSL) for learning effective speech representations
without expensive labeled data has proven to be extremely successful for a
variety of downstream Spoken Language Processing (SLP) tasks [1]. The general
formulation of the training pipeline is to first perform large-scale upstream
pre-training of a transformer model by solving a pretext task using unlabeled
speech data and then fine-tune them on labeled datasets for diverse downstream
tasks. The pre-text task to be solved can vary, and researchers have
continuously found new state-of-the-art methods that push performance on low-
resource SLP tasks [2, 3] Despite its huge success in low-resource ASR, prior
research has shown that SSL models suffer from various drawbacks: (1) Speech
representation models learned with SSL often don’t generalize well to domain
shifts between pre-training and fine-tuning data [4], and (2) directly fine-
tuning SSL models on downstream data often leads to catastrophic forgetting if
there is a significant discrepancy between the pre-training and fine-tuning
domains [5, 6]. To overcome this, researchers have proposed continued SSL pre-
training (CP) on the downstream data to be an effective and complementary
solution to bridge upstream pre-training and downstream fine-tuning domains
[7], especially when the target domain dataset is low-resource. However, CP of
an SSL model often leads to over-fitting on the train set [8]. Fig. 1 shows
how, with increasing steps of continued pre-training on a target ASR dataset,
the test Word Error Rate (WER) keeps increasing. Over-fitting patterns in the
target domain also lead the model to forget useful general-purpose knowledge
learned in the past, leading to sub-optimal performance. While it is well
known in the deep learning community that training on low-resource data can
almost always lead a model to overfit on the train set and poorly generalize,
Purushwalkam et al. [8] discuss in detail why CP leads to over-fitting and
conclude that the key reason is the violation of the IID assumption of
optimization algorithms [9].

Fig. 1: SwitchBoard test-set WER evaluated at various steps of continued SSL
pre-training of a model already pre-trained with LibriSpeech. While vanilla CP
starts over-fitting with increasing steps, Stable Distillation avoids it by
regularization. Fig. 2: Illustration of Stable Distillation (SD). SD performs
self-distillation with a teacher model while pre-training a student on the
target ASR dataset. Both the student and the teacher models start from
identical SSL pre-trained models, pre-trained on a large-scale OOD dataset.
The teacher is additionally pre-trained on the target dataset before SD. For
evaluation, the student model is either fine-tuned end-to-end using CTC (B1)
or used as a feature extractor for fine-tuning an Encoder-Decoder model (B2).

Main Contributions. In this paper, we present Stable Distillation, a simple
and novel continued pre-training strategy to improve ASR performance on the
target domain. Our key goal is to learn representations that, while adapting
to the target domain, have not over-fitted the training dataset and are not
forgetful of knowledge acquired during the initial pre-training. Stable
Distillation, similar to other model distillation methods, employs two
individual models, a teacher $f_{pre}^{T}(.)$ and a student $f_{pre}^{S}(.)$,
both of which, in our case, are identical and pre-trained with SSL on a large-
scale out-of-domain dataset. We first train the teacher with vanilla continued
pre-training on the target downstream ASR data and solve the same pre-text
task as the original SSL model. Next, we use the teacher to regularize
continued pre-training on the student through self-distillation. Specifically,
we attempt to match the representations of the student and the teacher by
optimizing the MSE loss between both representations. Intuitively, the
additional self-distillation regularizes the distance between the initial
weight before continued pre-training and the final weight after fine-tuning.
Finally, we either fine-tune the student for ASR or use it as a feature
extractor. We conduct extensive experiments on several downstream datasets
where the domain differs from the actual pre-training data domain and show
that Stable Distillation can achieve absolute WER improvements in the range of
0.8 - 7 WER over our baselines that went through no or vanilla continued pre-
training. Additionally, we show an implicit benefit of Stable Distillation
where our method can be used for better adapting a cross-lingual model for
mono-lingual ASR fine-tuning.

##  2 Related Work

SSL in Speech. The last couple of years have seen a massive rise in SSL
research with models constantly outperforming SOTA on benchmark datasets [10,
1]. The most common pre-text tasks include instance discrimination via
contrastive learning [2], clustering [3], or reconstruction [11]. However,
despite its success, SSL models are not robust to domain shifts between pre-
training and fine-tuning datasets [4]. This calls for better and more
effective ways to adapt a pre-trained model to a target domain for downstream
fine-tuning. Continued pre-training on the downstream dataset has shown to be
an effective solution for target domain adaptation. However, it comes at a
risk of over-fitting [8]. Overall, through widely employed, continued pre-
training of SSL models is a relatively under-explored area of speech
representation learning, and we argue that more attention is required by the
research community to solve problems related to it.

Domain Adaptation. Supervised domain adaption for ASR is a well-studied
problem in literature [12]. On the contrary, unsupervised SSL model domain
adaptation to the target task dataset domain is a relatively understudied
problem in literature. Fan et al. [13] were the first to explore this task and
proposed DRAFT, which uses adapters in pre-trained SSL models for effective
continued pre-training. Though adapters help effectively mitigate the problem
of overfitting and catastrophic forgetting [14], the need and complexity of
adding extra parameters to the model impede their widespread usage. Lodagla et
al. [15] propose a pruning-assisted domain adaptation of SSL representations.
However, their framework is complex, requires multiple pre-training and fine-
tuning stages, and achieves minimal improvement in performance.

##  3 Methodology

Problem Formulation. Fig. 2 illustrates our proposed Stable Distillation. Our
problem statement is simple. Given an upstream pre-trained model $f_{pre}(.)$,
pre-trained on any unlabeled dataset $\mathcal{D}_{p}$ = ($\mathbf{X}_{pre}$)
using SSL, we would like to employ $f_{pre}(.)$ to learn ASR on a downstream
labeled dataset $\mathcal{D}_{f}$= ($\mathbf{X}_{targ}$,$\mathbf{Y}_{targ}$).
For this, we either fine-tune the upstream SSL model using CTC or use it as a
feature extractor to fine-tune a conformer-based Encoder-Decoder model to
finally obtain an ASR model $\mathcal{F}$. As discussed earlier, though
continued pre-training of $\mathcal{D}_{f}$ on $f_{pre}(.)$ can lead to
optimal performance due to the several advantages it offers, like domain
adaption to the target domain, but it also suffers from various drawbacks like
over-fitting. Thus, we seek an effective solution for CP via our proposed
Stable Distillation.

###  3.1 Stable Distillation

(1) Continue Pre-training the Teacher. The first step towards performing
Stable Distillation is to teach the teacher. We initialize our teacher by
making a copy of our pre-trained model $f_{pre}(.)$ and denote it as
$f_{pre}^{T}(.)$. $f_{pre}^{T}(.)$ is then continually pre-trained on
$\mathcal{D}_{p}$, by solving the same pre-text task that $f_{pre}(.)$ was
pre-trained on, to finally obtain $f_{cont}^{T}(.)$

(2) Self-Distillation as Regularization. As a second step, we initialize our
student by making a copy of our pre-trained model $f_{pre}(.)$, and denote it
as $f_{pre}^{S}(.)$. Next, parallel to performing continued pre-training on
the student, we perform self-distillation between $f_{pre}^{S}(.)$ and
$f_{cont}^{T}(.)$ by matching their final layer representations of downstream
dataset $\mathcal{D}_{f}$ to finally obtain $f_{dist}^{S}(.)$. Thus, for
stable distillation, we jointly optimize the MSE between student and teacher
representations and the student’s own pre-text SSL task loss as:

$\mathcal{L}_{sd}=\lVert
f_{pre}^{S}(\mathbf{X}_{targ})-f_{cont}^{T}(\mathbf{X}_{targ}))\rVert_{2}\\\
+\alpha\mathcal{L}_{pretext}(f_{pre}^{S}(\mathbf{X}_{targ}))$ (1)

where $\alpha$ is a tunable hyper-parameter used to weigh the pre-text loss
$\mathcal{L}_{pretext}$. The pre-text task is similar to the original.

(3) Final downstream fine-tuning. Finally, we take the trained student model
$f_{dist}^{S}(.)$ and fine-tune it on the target dataset $\mathcal{D}_{f}$
using either: (1) End-to-End CTC Fine-tuning: In a more conventional setup, we
fine-tune all the weights of $f_{dist}^{S}(.)$ by adding a linear CTC head and
optimizing the CTC loss. (2) We fine-tune a conformer-based encoder-decoder
model employing $f_{dist}^{S}(.)$ as an upstream feature extractor by jointly
optimizing CTC and attention-based auto-regressive loss [16]. For the latter,
all weights of $f_{dist}^{S}(.)$ are frozen.

An intuition into why Stable Distillation works. Nagarjan et al. [17] show
that the model capacity of deep networks is restricted through implicit
regularization of the $l_{2}$ distance from the initialization. Thus, the
distance can affect the generalization bounds of these networks. Mobahi et al.
[18] perform several experiments to study the regularization effect of self-
distillation. Thus, as a derivation of these findings, we use self-
distillation to improve generalization via a regularization effect on the
$l_{2}$ distance. Fig. 3 illustrates how SD minimizes the $l_{2}$ distance
between fine-tuned and CP models.

Table 1: Detailed Statistics of datasets used in our experiments. Type refers
to Conversational or Read speech.

Dataset | Language | Domain | Type | Duration
---|---|---|---|---
|  |  |  | (train, dev, test)
MSR | Gujarati | General | Conv. | 40hr, 5hr, 5hr
MSR | Tamil | General | Conv. | 40hr, 5hr, 5hr
MSR | Telugu | General | Conv. | 40hr, 5hr, 5hr
Gramvani (GV) | Hindi | Call Cent. | Conv. | 100hr, 5hr, 3hr
SwitchBoard (SWBD) | English | Call Cent. | Conv. | 30hr, 5hr, N.A.
Wall Street Journal (WSJ) | English | Finance | Read | 80hr, 1.1hr, 0.4hr

Fig. 3: Frobenius norm of the weight difference between CP ($w_{pre}$) and
fine-tuned models ($w_{fine}$) for CP of Wav2Vec2-Lb on SWBD. Table 2:
Comparison of Stable Distillation ASR results with our baselines on both Enc-
Dec and E2E evaluation settings. All results are in the format of dev / test.
$\mathcal{R}$ and $\mathcal{C}$ indicate Read and Conversational Speech.
Domain Map refers to the source pre-training $\rightarrow$ CP domain.

Pretrained | Downstream | Domain Map | No Cont. Pretrain | Vanilla Cont. Pretrain | Stable Distillation
---|---|---|---|---|---
Model | Dataset |  (_Source_ $\rightarrow$ _Target_) | Enc-Dec | E2E | Enc-Dec | E2E | Enc-Dec | E2E
XLSR-300 |  GVHindi | $\text{General}_{\mathcal{R}}\rightarrow\text{Call Cent.}_{\mathcal{C}}$ | 32.7 / 32.5 | 37.3 / 37.0 | 31.6 / 31.4 | 35.3 / 35.0 | 28.9 / 27.7 | 30.3 / 30.1
XLSR-300 |  MSRGujarati | $\text{General}_{\mathcal{R}}\rightarrow\text{General}_{\mathcal{C}}$ | 21.7 / 28.5 | 24.4 / 32.3 | 21.3 / 27.2 | 22.1 / 30.3 | 20.2 / 26.4 | 20.2 / 28.4
XLSR-300 |  MSRTamil | $\text{General}_{\mathcal{R}}\rightarrow\text{General}_{\mathcal{C}}$ | 28.1 / 27.7 | 33.4 / 32.1 | 27.8 / 26.9 | 32.2 / 31.2 | 26.7 / 25.7 | 29.1 / 28.4
XLSR-300 |  MSRTelugu | $\text{General}_{\mathcal{R}}\rightarrow\text{General}_{\mathcal{C}}$ | 28.3 / 28.8 | 34.1 / 32.8 | 28.0 / 28.3 | 32.6 / 32.0 | 27.2 / 27.1 | 29.4 / 28.1
Vakyansh |  GVHindi | $\text{General}_{\mathcal{R}}\rightarrow\text{Call Cent.}_{\mathcal{C}}$ | 34.5 / 34.3 | 33.2 / 34.2 | 32.7 / 32.5 | 31.7 / 31.5 | 30.6 / 30.4 | 30.0 / 30.1
Wav2Vec2-Lb |  SWBDEnglish | $\text{General}_{\mathcal{R}}\rightarrow\text{Call Cent.}_{\mathcal{C}}$ | 39.1 / N.A | 22.2 / N.A. | 36.2 / N.A. | 20.4 / N.A. | 31.4 / N.A. | 14.3 / N.A.
Wav2Vec2-Lb |  WSJEnglish | $\text{General}_{\mathcal{R}}\rightarrow\text{Finance}_{\mathcal{R}}$ | 12.4 / 11.6 | 11.4 / 10.9 | 11.3 / 10.6 | 10.5 / 10.0 | 10.5 / 9.8 | 9.5 / 9.1

##  4 Experimental Setup

Datasets and SSL Pre-trained models. Details on individual datasets used for
all our experiments can also be found in Table 1. We use the splits mentioned
in Table 1 for all our experiments in Table 2. Precisely, we evaluate our
approach on the MSR low resource Indian language corpus (MSR) [19], Gramvani
ASR dataset [20], SwitchBoard dataset [21] (SWBD) and the Wall Street Journal
dataset [22]. For SWBD, we take a low-resource split, the rationale behind
which is mentioned in Section 5.

For all our experiments in Table 2, we use either of: (1) Wav2Vec2 [2] pre-
trained on 960 hours of LibriSpeech [10] (Wav2Vec2-Lb), (2) XLSR-300 model
[23] pre-trained on a combination of VoxPopuli, MLS, CommonVoice, BABEL, and
VoxLingua107, or (3) Vakyansh model [24] pre-trained on speech from Hindi
YouTube videos. All these models are pre-trained on read speech from the
general domain.

Baselines. Due to the lack of prior work in this space, we compare Stable
Distillation with other commonly used pipelines that include: (1) No Continued
Pre-training: For this baseline, we use the pre-trained SSL model without any
continued pre-training on downstream dataset $\mathcal{D}_{f}$ and (2) Vanilla
Continued Pre-training: For this baseline, we perform vanilla continued pre-
training of our SSL model on downstream dataset $\mathcal{D}_{f}$.

Hyper-parameters. For stable distillation, we first perform continued pre-
training on our teacher wav2vec-2.0 for a total of 50 epochs and then perform
Stable Distillation on the student for 50 more epochs. For a fair comparison,
for our continued pre-training baseline, we pre-train the model for a total of
50 epochs. We train with a learning rate of $5e^{-4}$ using Adam optimizer.
Finally, for Stable distillation, we find $\alpha$ = 0.01 to give us the best
performance searched among $\\{0.01,0.05,0.1,0.5,1\\}$. For downstream fine-
tuning, we use a conformer-based encoder-decoder model that has 12 encoder
layers and 6 decoder layers. We train our models with a learning rate of
$1.5e^{-3}$, batch size of 64, and for a total of 100 epochs. We report the
Word Error Rate (WER) averaged over three runs with different random seeds.

##  5 Results and Analysis

Table 3: Performance comparison in Enc-Dec setting when CP $\rightarrow$ final
fine-tuning language/domain differs. Results show that SD leads to better
regularization. For Libri. we report clean $|$ other.

Model | Dataset | Vanilla Cont. Pretrain | Stable Distillation
---|---|---|---
XLSR-300 |  GVHindi $\rightarrow$ MSRTamil | 101.4 / 101.5 | 47.8 / 47.8
XLSR-300 |  GVHindi $\rightarrow$ MSRTelugu | 99.4 / 99.7 | 46.7 / 46.9
Wav2Vec2-Lb |  WSJEnglish $\rightarrow$ LibriEnglish | 18.2 / 28.8 $|$ 23.3 / 29.8 | 16.0 / 25.2 $|$ 20.1 / 27.6

Table 2 compares the performance of Stable Distillation with all our baselines
on the splits for all datasets mentioned in Table 1. For all experiments, we
follow dataset settings resembling real-world scenarios where the target
domain for CP is usually from a different domain and is low-resource compared
to the source domain that the model is already pre-trained on (see Domain Map
column in Table 2). SD, on average, outperforms our baselines by 0.8-7.7 WER
in the Enc-Dec setup and 1-7 WER in the E2E setup. Precisely, for the Enc-Dec
setup, compared to vanilla CP, we achieved an average relative WER improvement
of 7.2% and 7.1% for dev and test sets, respectively. Compared to no CP, the
improvements are 11.3% 11.1%. For the E2E setup compared to vanilla CP, we
achieved an average relative WER improvement of 13.0% and 12.9% on dev and
test sets, respectively. Compared to no CP, the improvements are 17.3% and
17.2%.
Table 3 confirms our claim that SD improves vanilla CP by adding explicit
regularization, thereby preventing overfitting on the target domain train set.
Ideally, if a model has overfitted to the target training dataset after CP, it
should perform worse if it is fine-tuned for ASR on the source dataset itself
or any other dataset where the domain or language differs. While rows 1 and 2
show examples when the CP and fine-tuning languages differ, row 3 shows that
SD leads to better performance than vanilla CP with LibriSpeech ASR when
Wav2Vec2-Lb (also pre-trained on LibriSpeech) was further pre-trained on SWBD.
Row 6 in Table 2 shows that the same model also performs better than CP with
WSJ ASR (due to effectively exploiting past knowledge). Rows 1-6 also show a
peripheral benefit of SD, which helps in effective cross-lingual to mono-
lingual adaptation of SSL models pre-trained on large-scale multi-lingual data
[25].

(a) Evaluation-set WER on SWBD on various low-resource settings for E2E setup.

(b) Evaluation-set WER on SWBD for various Enc-Dec layer configs on
Wav2Vec2-Lb.

Fig. 4: More results. Stable Distillation outperforms all baselines.

##  6 Conclusion and Future Work

In this paper, we propose Stable Distillation, a simple and effective
methodology for target domain adaptation of pre-trained SSL models. Stable
Distillation regularizes continued pre-training of an SSL model on a target
domain and prevents overfitting. We empirically show that Stable Distillation
proves to be extremely effective in various settings where the initial and
target domains differ. As part of future work, we would like to explore better
distillation procedures for continued pre-training further to push ASR
performance in trivial and simple steps.

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###### Abstract

In many analyses in Higgs, top and electroweak physics, the kinematic
reconstruction of the final state is improved by constrained fits. This is a
particularly powerful tool at $e^{+}e^{-}$ colliders, where the initial state
four-momentum is known and can be employed to constrain the final state. A
crucial ingredient to kinematic fitting is an accurate estimate of the
measurement uncertainties, in particular for composed objects like jets. This
contribution will show how the particle flow concept, which is a design-driver
for most detectors proposed for future Higgs factories, can — in addition to
an excellent jet energy measurement — provide detailed estimates of the
covariance matrices for each individual particle flow object (PFO) and each
individual jet. Combined with information about leptons and secondary vertices
in the jets, the kinematic fit enables to correct $b$\- and $c$-jets for
missing momentum from neutrinos from semi-leptonic heavy quark decays. The
impact on the reconstruction of invariant di-jet masses and the resulting
improvement in $ZH$ vs $ZZ$ separation will be presented, using the full
simulation of the International Large Detector (ILD), as an example of highly-
granular ParticleFlow optimized detector concept.

##  1 Introduction

The decays of the Higgs boson into heavy $b$ and $c$ quarks play an essential
role in the Higgs physics studies. The presence of the semi-leptonic decays
(SLD) in the $b$ and $c$ jets degrades the reconstruction of these jets [1,
fig. 8.3d]. The energy resolution of the jets can be recovered beyond the
detector resolution by using a kinematic fit as a mathematical approach [2].
The measurement uncertainties are one of the most important inputs to the
kinematic fit. In the ILD, individual particles are reconstructed with an
unprecedented knowledge of jet-level uncertainties [1].
In the last study of the Higgs self-coupling measurement at the 500 GeV ILC
[3], the invariant di-jet mass in $e^{+}e^{-}\rightarrow ZHH$ events with
$H\rightarrow b\bar{b}$ has been improved by a very simple correction to the
semi-leptonic decays and a simple parameterization of the jet energy error in
the kinematic fit.

(a)

(b)

Figure 1: Higgs mass reconstruction in the presence of ISR photon and semi-
leptonic decays: (a) The signal peak gets sharper by considering ISR photon
and correction of semi-leptonic decays. (b) The background peak is pulled
towards the signal.

Although the reconstruction of the Higgs mass is improved by this simple
correction (fig. 1(a)), the result is not satisfactory in the presence of
$ZZH/Z$ background (fig. 1(b)). In order to avoid background being pulled
towards the signal by too much flexibility in the fit, a proper neutrino
correction and a better jet error parameterization are needed. The new jet-
error parameterization has been evaluated using
$ZH/ZZ\rightarrow\mu\bar{\mu}b\bar{b}$ samples in presence of ISR photon and
$\gamma\gamma\rightarrow$ low $p_{T}$ hadrons at $\sqrt{s}$=250 GeV [4, 5].

##  2 Kinematic fitting

It was shown that by tagging charged leptons in $b$\- or $c$-jets, the semi-
leptonic decays can be found [4]. The momentum of the missing neutrino can
then be obtained up to a sign ambiguity, using the kinematics of the semi-
leptonic decay including the four-momentum of visible decay products of the
semi-leptonic decay, the mass, and the flight direction of the parent hadron.
Imposing constraints on energy and momentum conservation and/or invariant
masses of known particles will resolve the sign ambiguity by a kinematic fit.
Full details of the measurement uncertainties for each particle flow object
(PFO) as reconstructed particle candidate are provided by the Pandora particle
flow algorithm [6] used for event reconstruction in the ILD concept. The
energy and spatial resolutions of each sub-detector of ILD are propagated to
full covariance matrix for each PFO. While angular errors of the charged
particles are very well modeled using the ILD tracker (black histogram in fig.
2(a)), the angular uncertainties for the photons and neutral hadrons (blue and
red histograms in fig. 2(a)) should be scaled up by a factor of 1.3 and 1.8,
respectively, when they are propagated to form the initial covariance matrix
of the jet ($\sigma_{\mathrm{det}}$).

(a)

(b)

Figure 2: (a) Normalized residual of $\theta_{\mathrm{PFO}}$ for charged
particles (black), photons (blue) and neutral hadrons (red) (b) Pull of the
jet angle ($\theta_{\mathrm{jet}}$) from the kinematic fit when the jet
angular uncertainty ($\sigma_{\theta_{\mathrm{jet}}}$) receives contribution
from only charged particles (black), all particles (red) and when
$\sigma_{\theta_{\mathrm{PFO}}}$ is scaled up for photons and neutral hadrons
by a factor of 1.3 and 1.8, respectively, motivated from fig. 2(a)

The jet energy error has been studied in [4, 5, 7]. In the previous jet error
parameterization [7], only charged particles contributed to the jet angular
uncertainties (black histogram in fig. 2b) and the kinematic fit hypothesis
was too tight for adjusting the four-momentum of jets. Therefore, a fixed
angular uncertainty ($\sigma_{\theta_{\mathrm{jet}}}$=100 mrad) was assumed
for all jets [7]. In the new jet error parameterization, all particles
contribute to the jet angular uncertainties and hence, the angular
uncertainties are parameterized for individual jets. This significantly
improves the pull distribution of the jet angles (red histogram in fig. 2(b))
and the gain is even more drastic when $\sigma_{\theta_{\mathrm{PFO}}}$ is
scaled-up for photons and neutral hadrons (blue histogram in fig. 2(b)). In
analogous to $\theta_{\mathrm{jet}}$, the azimuthal angle of the jet
($\phi_{\mathrm{jet}}$) has similar behavior for photons and neutral hadrons.

##  3 $Z/H$ mass reconstruction

The neutrino correction – for the time being, based on cheated inputs in terms
of decay point and mass of the mother hadron, and association and momenta of
the visible decay products – in addition to the new jet error
parameterization, is applied on the introduced
$ZH/ZZ\rightarrow\mu\bar{\mu}b\bar{b}$ samples. The mass recovery by the
neutrino correction alone is shown in the blue histograms in fig. 3 for both
Higgs boson (solid) and $Z$ boson (dashed). Here the sign ambiguity is
resolved by the kinematic fit, but the di-jet invariant mass is obtained from
the pre-fit jet four-momenta. Even without applying the neutrino correction,
the di-jet invariant mass can be significantly improved by the new jet error
parametrization described in section 2 fed to the kinematic fit (the green
histograms in fig. 3). Finally, the combination of the neutrino correction and
the kinematic fit is shown in the red histograms in fig. 3. The performance of
the combination of the kinematic fit and the neutrino correction based

Figure 3: Invariant di-jet mass in $ZH$ and $ZZ$ events reconstructed by the
PFA only (black), with neutrino correction (blue), with kinematic fit (green)
and with neutrino correction and kinematic fit (red).

on reconstructed information is expected somewhere between the green and red
histograms even if the neutrino correction is less powerful when using
reconstructed information only. In all cases, the problem of pulling the $Z$
peak towards the Higgs peak shown in fig. 1 is avoided and the $ZH$/$ZZ$
separation is significantly improved with respect to the black histograms.
This will benefit any Higgs studies where event selection is done based on di-
jet masses. The impact of the neutrino correction seems much smaller for
$Z\rightarrow b\bar{b}$ than for $H\rightarrow b\bar{b}$. This is suspected to
be due to the natural width of the $Z$ boson, which is similar in size to the
effects of detector resolution.

##  4 Conclusions and Outlook

The invariant di-jet mass plays an important role in the separation of the
$ZZH$ background and the $ZHH$ signal for the Higgs self-coupling analysis.
Since $H\rightarrow b\bar{b}$ is the predominant decay mode of the Higgs
boson, the reconstruction of heavy-flavor jets highly affects the invariant
di-jet mass. A combination of a kinematic fit with a conceptual approach for a
correction of semi-leptonic decays based on a detailed reconstruction of the
decay kinematics can improve the heavy flavour jet reconstruction. The
propagation of PFO-level measurement uncertainties for all reconstructed
particles obtains a precise knowledge of the measurement errors for each
individual jet. The neutrino correction, for the time being, based on cheated
inputs as proof-of-principle, and the kinematic fit with detailed error
parameterization have been applied on $ZH/ZZ\rightarrow\mu\bar{\mu}b\bar{b}$
events. Each of the techniques considerably enhances the $ZH$/$ZZ$ separation
via the di-jet mass and their combination shows significant improvement. The
neutrino correction based on fully reconstructed information is ongoing and
both techniques will be applied to the Higgs self-coupling analysis in the
future.

## References

  * [1] The ILD Collaboration  “International Large Detector: Interim Design Report”, 2020  arXiv:2003.01116 [physics.ins-det]
  * [2] Benno List and Jenny List  “MarlinKinfit: An Object–Oriented Kinematic Fitting Package”  In _LC Notes_ Hamburg: DESY, 2009  URL: https://bib-pubdb1.desy.de/record/88030
  * [3] Claude Fabienne Dürig  “Measuring the Higgs Self-coupling at the International Linear Collider” Universität Hamburg, Diss., 2016, DESY-THESIS  Hamburg: Verlag Deutsches Elektronen-Synchrotron, 2016, pp. 246  DOI: 10.3204/PUBDB-2016-04283
  * [4] Yasser Radkhorrami and Jenny List  “Conceptual aspects for the improvement of the reconstruction of $b$\- and $c$-jets at $e^{+}e^{-}$ Higgs Factories with ParticleFlow detectors”, 2021  arXiv:2105.08480 [hep-ex]
  * [5] Yasser Radkhorrami and Jenny List  “Kinematic Fitting for ParticleFlow Detectors at Future Higgs Factories”, 2021  arXiv:2110.13731 [hep-ex]
  * [6] M.A. Thomson  “Particle flow calorimetry and the PandoraPFA algorithm”  In _Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment_ 611.1 Elsevier BV, 2009  DOI: 10.1016/j.nima.2009.09.009
  * [7] Aliakbar Ebrahimi  “Jet Energy Measurements at ILC: Calorimeter DAQ Requirements and Application in Higgs Boson Mass Measurements”, 2017  DOI: 10.3204/PUBDB-2017-11891


# A compact setup for loading magneto-optical trap in ultrahigh vacuum
environment

Kavish Bhardwaj1 Sourabh Sarkar1,2 S. P. Ram1,∗ V. B. Tiwari1,2 S. R.
Mishra1,2 1Laser Physics Applications Section, Raja Ramanna Centre for
Advanced Technology, Indore-452013, India.  2Homi Bhabha National Institute,
Anushaktinagar, Mumbai-400094, India<EMAIL_ADDRESS>
###### Abstract

We have developed a compact setup which enables loading a magneto-optical trap
(MOT) in ultrahigh vacuum (UHV) environment. Nearly $1\times 10^{8}$ atoms of
87Rb are trapped in the MOT at $\sim 2\times 10^{-10}$ Torr base pressure in
the chamber. After the MOT loading, we have successfully demonstrated working
of quadrupole magnetic trap in this chamber with a lifetime of $\sim 8$ s.

##  I Introduction

A compact and reliable source of ultra-cold atoms is an essential requirement
for several experimental investigations and device applications using cold
atoms. To produce sample of ultra-cold atoms, the cold atoms trapped in a
magneto-optical trap (MOT) Raab  _et al._ (1987); Inguscio and Fallani (2013);
Steane and Foot (1991) are subjected to evaporative cooling Mishra  _et al._
(2017) in an ultrahigh vacuum (UHV) environment. But, loading a MOT in
ultrahigh vacuum (UHV) chamber has always been a complicated task to deal
with, which requires either a double MOT setup Ram  _et al._ (2013) or a
zeeman slower device Slowe  _et al._ (2005). In first method (i.e. use of
double-MOT setup), a UHV chamber MOT (UHV-MOT) is loaded by pushing the cold
atom from a vapor chamber MOT to UHV chamber through a narrow differential
pumping tube connecting two chambers. In Zeeman slower method to load MOT in
UHV environment, a thermal atomic beam is injected in UHV chamber which is
slowed down by using a Zeeman slower device for UHV-MOT loading. Both these
methods are complicated in one or the other way. Hence, a simpler method to
load MOT in UHV environment is necessary and useful.

In this paper, we present a simple design to prepare and load MOT in UHV
chamber from thermal source of atoms (from Rb-dispenser). We demonstrated
that, even after the MOT loading, the vacuum of the chamber is preserved to
the extent that magnetic trapping of atoms in the same chamber can be
performed with good life-time of the trap. The observed life-time of the
quadrupole nagnetic trap was $\sim 8s$, which may be further improved by
optimizing the current pulse parameters applied to Rb-dispensers. Such simple
and portable cold atom setups may be useful for developing several atom-optic
devices for magnetometry Budker and Romalis (2007), atom interferometry Cronin
_et al._ (2009) and other quantum technologiesDowling and Milburn (2003).

##  II Experimental

The setup is shown schematically in Fig.1. We have used a stainless steel (SS)
cube as UHV chamber. At one end of this SS cube, a UHV compatible square
cross-section glass cell is attached (Fig. 1) using a CF35 flange. The glass
cell has clear optical access region of nearly $70$ mm $x$ 30 mm $x$ 30 mm.
The UHV-MOT and magnetic trap can be formed in this glass cell. The glass cell
is surrounded by the coils which are used to generate the required magnetic
field for MOT and magnetic trap. At other end of the SS cube, two Rb-
dispensers (Rb/NF/4.8/17FT SAES getters) are inserted via a two-pin UHV
feethrough of length 70 mm inside the chamber. These Rb-dispensers are
surrounded by a hollow glass jacket made of 2 mm thick Borosil glass having a
length of 200 mm. The jacket has a tapered opening of diameter 8 mm towards
the UHV glass cell. The base diameter of the jacket is 28 mm. The jacket is
push-fit attached to feedthrough flange (CF35) with the use of a spring coil
at glass cell flange. The hot atoms emitted by dispensers strike the glass
jacket walls multiple times before reaching the glass cell kept at UHV
pressure of $\sim 2\times 10^{-10}$ Torr. Thus atoms from dispenser are slowed
down by the walls of glass jacket before being trapped in MOT formed in the
glass cell. Earlier studies have also reported loading of MOT in UHV
environment by using more sophisticated cooling devices for hot atoms emitted
from dispensers Roach and Henclewood (2004); Moore  _et al._ (2005). The glass
jacket which we use is simpler and a passive device which can slow down hot
atoms and redirect them towards UHV-MOT region.

Figure 1:  (a): Schematic of the setup with glass jacket for formation of
magneto-optical trap (MOT) in ultrahigh vacuum environment. Two pairs of MOT
laser beams (out of three) are shown in the figure and the third pair of MOT
beams is perpendicular to plane of paper. The MOT is formed in the UHV
environment by supplying a current to the feedthrough and (b): dispenser
assembly inside the glass jacket.

A pressure of $\sim 2\times 10^{-10}$ Torr is generated in the glass cell
using a turbo-molecular pump (TMP), a sputter ion pump (SIP) and a titanium
sublimation pump (TSP). The whole setup was baked at $150^{o}C$ for 24 hours
and de-gasing of dispensers and activation of TSP has been carried out for
achieving this UHV environment. The Rb vapor is generated in the UHV chamber
by applying a DC current through the dispensers. Here, two Rb-dispensers are
kept in parallel arrangement. This parallel arrangement provides direct
contact of each dispenser to copper feedthrough rods to have a better
conductance for heat dissipation. In our setup, expected dispenser temperature
is $\sim 500^{o}$ C (estimated from the data sheet of the dispenser at 4 A
current) during the MOT loading. After MOT loading, dispenser temperature is
to be brought down quickly so that MOT and magnetic trap loading is minimally
disturbed by hot atoms from dispensers. Neglecting radiative cooling, the time
required for the dispenser to cool down is inversely proportional to
conductance. Atoms are emitted from the dispenser by heating the dispenser by
flowing $8$ A current in dispenser assembly. The atoms are finally collimated
towards glass cell via narrow opening in the glass jacket for trapping in MOT
McDowall  _et al._ (2012).

For formation of MOT, two ECDL laser (TOPTICA DL-100) operating at wavelength
$780$ nm and a laser amplifier (TOPTICA, Boosta) provides the necessary laser
requirement. Three orthogonal pairs of counter-propagating laser beams having
intensity 22 mW/cm2 and frequency of 15 MHz red-detuned to cooling transition
(${}^{5}S_{1/2}$ F = 2 to ${}^{5}P_{3/2}$ F′ = 3) of 87Rb are made
intersecting one another inside the glass cell. A quadrupole magnetic field
having axial field gradient of 10 G/cm is used for MOT formation. Along with
the cooling laser beams, we apply another pair of counter propagating re-
pumping laser beam having frequency resonant to re-pumping transition (
${}^{5}S_{1/2}$ F = 1 to ${}^{5}P_{3/2}$ F′ = 2) of 87Rb. The MOT loading was
studied by collecting fluorescence from the atoms in MOT on a calibrated
photodiode.

After loading the MOT in this setup, we have also performed the magnetic
trapping of atoms. For loading magnetic trap, the laser beams were switched-
off and quadrupole magnetic field gradient was raised from 10 G/cm to 220
G/cm. For this, the current was flown through quadrupole magnetic coils
through IGBT based current switch and was ramped to 22 A in 500 ms using a
c-RIO based electronic controller. The number of atoms in magnetic trap was
estimating by fluorescence imaging of the atom cloud in trap.

##  III Results and discussion

For the study the loading behavior of MOT in the UHV environment, we have
collected the fluorescence from MOT atom cloud on a calibrated photodiode.
Figure 2 shows the photodiode signal due to fluorescence from the atoms in the
MOT. The photodiode signal is proportional to number of atoms in the MOT.
Final equilibrium number of atoms trapped in the MOT (N) is determined by the
balance between capture rate (R) and loss rate of the MOT. The MOT loading was
performed in continuous and pulsed mode operations of current in dispenser
source.

Figure 2:  (Color online) Observed loading curves of UHV-MOT for different
values of dispenser currents in continuous mode, (a) for 6 A, 7 A, and 8 A
current in dispenser assembly and (b) for 10 A current in dispenser assembly.
In plots the experimental data are shown by continuous curves whereas the
fitted data are shown by dashed curves.

Figure 2 shows the loading curves of 87Rb UHV-MOT for different values of
current in dispensers assembly. Figure 2 (a) is for 6 A, 7 A, and 8 A values
of current in dispenser assembly. The loading time $\tau$ estimated from
fitting of the experimental data to the equation $N=N_{s}(1-e^{(-t/\tau)})$
are 150 s, 59 s and 31 s respectively for the loading curves corresponding to
6 A, 7 A and 8 A current in dispenser assembly. Here, $N$ is the instantaneous
number of atoms in the MOT, $N_{s}$ is the saturated number in the MOT and $t$
is the time. At 8 A current in the dispenser assembly, $\sim$ $7.5\times
10^{7}$ atoms are obtained in the UHV-MOT. At this value of dispenser current
(8 A in continuous mode), the vacuum inside chamber deteriorates and the
pressure reaches to a steady state value of $\sim 5.5\times 10^{-10}$ Torr
from the initial value of $\sim 2\times 10^{-10}$ Torr. At further higher
current, e.g. 10 A in continuous mode, the loading time reduces to few seconds
(Fig. 2(b)) and number of atoms increases to $\sim$ $2.5\times 10^{8}$, but
the vacuum in the chamber deteriorates very quickly (pressure rising to $\sim
8\times 10^{-10}$ Torr in few tens of second). In order to have faster loading
and less deterioration of vacuum in the chamber, we tried to load the MOT
using a structured current pulse in the dispenser assembly. A structured
current pulse used in the experiments is shown in Fig. 3 by red colour curve.
In the pulse structure, the initial part of the pulse has high current for
short duration and later part of the pulse has low current for long duration.
With this structure of current pulse, the MOT loading time reduces to $\sim
9s$ and vacuum is recovered at the end of the current pulse. The MOT loading
is shown by the blue curve in Fig. 3 using this current pulse. The pulsed
loading sequence used here, leads to the loading of $1\times 10^{8}$ atoms in
the MOT.

A major difference in MOT loading with structured current pulse and continuous
current mode comes from the use of high current in structured pulse which
increases the temperature of the dispensers. Therefore, if the next MOT
loading cycle is repeated soon without allowing the cooling of dispensers, the
temperature of the dispensers increases in accumulative way with successive
MOT loading cycles. This leads to accumulative increase of pressure in the
chamber due to increased Rb emission. Similar observations have been reported
earlier by Griffin  _et al._ (2005). Therefore, this type of MOT loading can
be preferred with low repetition rate of MOT loading.

Figure 3: (Color online) MOT loading curve (blue) with a structured current
pulse (red) in the dispenser assembly.

After successful loading of MOT in UHV environment, we demonstrated the use of
the UHV-MOT for magnetic trapping of atoms. We transferred the cold 87Rb atoms
from the MOT to a quadrupole magnetic trap formed by two coils. From the
variation in number of atoms in the magnetic trap with time (as shown in Fig.
4), the $1/e$ lifetime of the trap was $\sim$ 8 s when this MOT was loaded
with 8 A current (continuous) in the dispenser assembly. The dispenser current
was continuously ON during the magnetic trapping of the atoms. A good lifetime
of the magnetic trap indicates that a high vacuum in the chamber is
maintained. This lifetime can be further improved by taking various measures
in magnetic trapping such as blocking the residual lights going to the
chamber, blocking the Majorana losses, etc, Mishra  _et al._ (2017). A good
lifetime of the atoms in the magnetic trap can be exploited for further
experiments such as evaporative cooling Mishra  _et al._ (2017), radio-
frequency (RF) dressing Chakraborty  _et al._ (2016), Bose-Einstein
condensation Mishra  _et al._ (2017); Van Der Stam  _et al._ (2007), etc, in
the same chamber.

Figure 4:  Measured variation (circles) in number of atoms in quadrupole
magnetic trap with time. The continuous curve is an exponential decay curve
fitted to estimate the lifetime of the atoms in the magnetic trap.

##  IV Conclusion

We have developed a compact setup and used it for magneto-optical trap (MOT)
loading in ultrahigh vacuum (UHV) environment. The magnetic trapping of atoms
using this UHV-MOT is also demonstrated in this compact setup.

###### Acknowledgements.

We thank S. Singh and V. Singh for useful technical discussions. We are
thankful to Shri Deepak Sharma and Shri Bhupinder Singh for the development of
switching circuit, Shri Ayukt Pathak and Smt. Shraddha Tiwari for the
development of c-RIO based electronic controller and Shri Ajay Kak for
manufacturing glass jacket.

## Data Availability Statement

Data available on request from the authors.

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