ignoreexclude

11institutetext: Göttingen Academy of Sciences and Humanities 22institutetext:
Tel Aviv University

# Segmenting Dead Sea Scroll Fragments
for a Scientific Image Set

Bronson Brown-deVost 11 Berat Kurar-Barakat 22 Nachum Dershowitz 22

###### Abstract

This paper presents a customized pipeline for segmenting manuscript fragments
from images curated by the Israel Antiquities Authority (IAA). The images
present challenges for standard segmentation methods due to the presence of
the ruler, color, and plate number bars, as well as a black background that
resembles the ink and varying backing substrates. The proposed pipeline,
consisting of four steps, addresses these challenges by isolating and solving
each difficulty using custom-tailored methods. Further, the usage of a multi-
step pipeline will surely be helpful from a conceptual standpoint for other
image segmentation projects that encounter problems that have proven
intractable when applying any of the more commonly used segmentation
techniques.

In addition, we create a dataset with bar detection and fragment segmentation
ground truth and evaluate the pipeline steps qualitatively and quantitatively
on it. This dataset is publicly available to support the development of the
field. It aims to address the lack of standard sets of fragment images and
evaluation metrics and enable researchers to evaluate their methods in a
reliable and reproducible manner.

###### Keywords:

Image segmentation Object detection Dead Sea Scrolls

##  1 Introduction

In 2011, the Israel Antiquities Authority (IAA) initiated a large-scale
digital imaging project to create a digital archive of their collection of
Dead Sea Scrolls—the largest collection of Dead Sea Scrolls in the world
[21].111There are several other institutions that have digitized scrolls from
their own collections, especially the Jordan Museum in Amman
https://universes.art/en/art-destinations/jordan/amman/museums/jordan-
museum/dead-sea-scrolls, the Israel Museum in Jerusalem
https://www.imj.org.il/en/wings/shrine-book/dead-sea-scrolls, the Bibliothèque
nationale de France https://gallica.bnf.fr/ark:/12148/btv1b8551261c, and a few
other collections. These are either less fragmentary than the manuscripts we
deal with from the IAA or do not supply high enough quality images. At the
time of this writing, they have digitized nearly every fragment in their
archive containing text. The scrolls,222We refer to the manuscripts in the IAA
collection as “Dead Sea Scrolls” throughout this paper, as this is probably
the most well-known designation of these ancient remains. The interested
researcher will note that the collection is largely comprised of Hebrew,
Aramaic, and a few Greek scrolls from caves in and around the area of Khirbet
Qumran on the western shore of the Dead Sea dating to the last few centuries
before the common era and briefly into the common era, but the Dead Sea
Scrolls proper include a much broader corpus including items that are not
scrolls, such as tefillin and mezuzot among other items, and also works from a
much broader time period, up into the Islamic era, written in Latin, Nabatean,
and Arabic from areas all around the Judean Desert. which are for the most
part fragmentary, were imaged at 12 wavelength data points using a custom
multispectral camera rig, built specifically for this purpose. The IAA began
publishing these images online shortly after the project began, making the
collection publicly available to both scholars and the general
public.333https://www.deadseascrolls.org.il.

The IAA has recently been reorganizing its database of images so as to make
higher resolution versions of the images available via the standard IIIF Image
API. In addition, they have an experimental front-end for scholars, which
incorporates manual transcriptions, a canvas for arranging fragments, and a
facility for manually associating regions in images with letters in
transcriptions.444https://sqe.deadseascrolls.org.il; see also [10] and [17].
The high-resolution images—as is—are satisfactory for most research purposes,
but it is necessary to work with fragments segmented out of the images in
order to test small joins and larger reconstructions. The segmentation
approach provided here seeks to address that need.

##  2 IAA Image Dataset

We have access to about 180,000 IAA images in total, which present the recto
and verso of nearly 20,000 manuscript fragments in full-color (a composite of
the multispectral images), in infrared (924nm), and in infrared with a raking
light from the right, and with a raking light from the left—all have a
resolution of $\sim$1215 PPI (we did not utilize the full multispectral data,
which has not yet been made publicly available). These images are consistent
in the camera and lighting placement and always include an XRite color target,
a Golden Thread object-level target, and a tag with the fragment’s plate
number. These three additional objects in each image may appear in various
positions, but do not change their placement within a recto or within a verso
series of images for each single fragment, as neither the camera nor the
fragment in its layout was moved between the acquisition of images (see Fig. 2
for an example).

##  3 Motivation

Segmentation of the fragments in the IAA image database is desirable for
several reasons. First and foremost, it helps us to better account for the
comprehensiveness of our access to the fragments. It enables us to more easily
compare the fragments as pictured in the current image database with earlier
series of images, mostly from the middle of the last century. This can help
reveal fragments that may have been passed over in earlier research or prove
useful for detecting earlier images of fragments that provide a view of the
fragment at a time when it was in a better preserved state. Secondly, it makes
the fragments more directly accessible to further computational analysis, such
as letter recognition. Finally, it enables scholars to more easily test
hypotheses for joins or combinations by means of digital tooling, rather than
resorting to physical manipulation of the fragile remains, which is
detrimental to their integrity.

##  4 Related Work

There are a number of large collections of fragmentary manuscripts, besides
the Dead Sea Scrolls. These include the Elephantine
papyri,555https://www.smb.museum/en/museums-institutions/aegyptisches-museum-
und-papyrussammlung/collection-research/research/erc-project-elephantine-
localizing-4000-years-of-cultural-history-texts-and-scripts-from-elephantine-
island-in-egypt. the Oxyrhynchus
papyri,666http://www.papyrology.ox.ac.uk/POxy. the Cairo
Genizah,777https://fgp.genizah.org; https://geniza.princeton.edu;
https://cudl.lib.cam.ac.uk/collections/genizah/1. and fragments found in
medieval book bindings.888https://fragmentarium.ms;
https://bwb.hypotheses.org. Most of these would also benefit from the image
treatments described here.

For much of the digitization of the Cairo Geniza fragments, a contrasting blue
background (akin to the use of a blue/green screen for chroma key compositing
in films) was used when capturing images, making segmentation trivial [22].
Artifacts were also removed from those images [24]. Early attempts at
segmenting fragment from background for the Dead Sea Scroll images were
reported in [12, 4], but were not accurate enough for handling the whole
corpus. The use of convolutional networks for semantic segmentation has become
quite standard [11, 13].

Frequently, fragment images are manually segmented, often using a tool
included in image software such as GrabCut [19]; see [7]. Segmentation is a
prerequisite before trying to piece fragments together (e.g. [6] for
parchement and [1, 16] for papyrus999Also https://ec.europa.eu/research-and-
innovation/en/projects/success-stories/all/solving-papyrus-puzzle.) or to
register verso and recto images.

Recto and verso manuscript images are aligned by affine transformation in [8].

##  5 Problematica

The process of segmenting the IAA’s images has been complicated by several
factors:

  1. 1.

Two calibration bars and a label are present in every image, but generally
never at the same location in the image frame from one fragment image set to
another. This can cause problems for certain segmentation processes when the
fragment is either very tiny and hard to detect or when the fragment has a
large support material that may touch or overlap with one or another of these
markers.

  2. 2.

The black felt background—chosen for its nonreflective property—appears very
similar to the ink on the manuscripts, problematizing differentiation between
written remains and holes in the parchment or papyrus.

  3. 3.

Many fragments are affixed to a modern support medium.  (a) This may have been
done with Japanese tissue paper for conservation purposes.  (b) Or it may have
been done for historical reasons, such as a researcher placing multiple
individual fragments on a single support either to display a proposed join or
to keep fragments in near proximity that they wished to keep together.

##  6 Methodological Overview

In consideration of these factors that complicate the segmentation operation,
we have opted for a customized pipeline approach to the problem of segmenting
our corpus of images. Specifically, we did not rely on deep learning methods
except for the bar detection task, as bars can be labeled using bounding boxes
that are relatively easy to generate. In contrast, aligning, binarization, and
segmentation tasks require pixel-level annotation, which can be particularly
challenging on high-resolution images. We have organized the steps in this
pipeline in such a way as to provide the most generally reliable process for
the corpus as a whole and have been working to include some amount of logging
and automated evaluation of possibly or probably problematic instances of
segmentation. The basic process can be outlined as follows:

  1. 1.

Isolate the calibration bars and label in the recto and verso images.

  2. 2.

Align the recto image with the mirrored verso image, ignoring the calibration
bars and label.

  3. 3.

Threshold the infrared recto and the (mirrored and aligned) verso.

  4. 4.

Union those two masks for a maximal fragment mask.

  5. 5.

Detect the backing substrate on recto and (mirrored and aligned) verso.

    1. a.

Perform an intersection on those two masks to isolate the maximal shared mask
of the backing substrate.

    2. b.

Perform morphological closing on the mask, because the backing substrate often
has a woven texture.

  6. 6.

Subtract the mask in step 5 from the mask in step 4.

  7. 7.

Get contours from the mask in step 6.

  8. 8.

Keep only contours that overlap with masked regions in both recto/verso masks
from step 4.

  9. 9.

Filter out any very tiny segmented objects based on the image resolution.
(There may be flecks of parchment or papyrus that are not suitable for further
research.)

##  7 Detailed Process

###  7.1 New Evaluation Dataset

The dataset is designed to support the development of fragment segmentation
field by providing a standard set of images and evaluation metrics. The
dataset contains a total of $139$ fragments, where $100$ fragments are
included in the train set, $20$ fragments in the validation set and $19$
fragments in the test set. To ensure the validity of our analysis, we selected
the training and testing fragments at random and verified that they were
disjoint at the manuscript level. Each set contains both color and infrared
images of recto and verso sides of the fragments. The color recto and verso
images are annotated with bounding boxes around the bars and labels using the
online AI assisted annotation platform Hasty.101010http://hasty.ai.

Additionally, the test set includes ground truth for the segmentation of recto
fragments, stored as one or multiple WKT files for each fragment. Each WKT
file contains the coordinates of the boundary contours and the coordinates of
any holes inside the boundary polygon for each piece of the fragment in the
image. This ground truth information will be useful for evaluating and
comparing the performance of different fragment segmentation methods. The
dataset is publicly available and is expected to contribute to the advancement
of the field by providing a standard benchmark.111111http://to-be-made-
available.

###  7.2 Isolate Calibration Bars and Labels

IAA images typically contain three distinct types of bars: an Xrite color
calibration bar, a Golden Thread object level target bar, and a plate-number
label. These objects are present in both the recto and verso images of a
fragment, and their positions are identical in both infrared and color images.
However, in recto and verso images, they appear in different positions. Since
these objects can occur at any location and orientation within the image,
isolating them at the beginning of the segmentation process prevents them from
contaminating any of the subsequent steps in the pipeline.

To remove the calibration bars and labels, we use a Faster Region-based
Convolutional Neural Network (Faster R-CNN) pre-trained on ImageNet but fine-
tuned with our own small training set. The motivation behind using the Faster
R-CNN method is that it is currently the state-of-the-art detection method in
computer vision. Additionally, by using Faster R-CNN, we can avoid the time-
consuming task of semantic segmentation or instance segmentation, which
require significant effort and time to label accurately, particularly on high-
resolution images. The dataset includes both recto and verso color images for
each fragment. We chose to use color images as they contain more separable
features for the network. All types of bars are boxed and labeled as “bar”
because it is not necessary for our current purposes to identify the bar type.
The region of interest (RoI) heads had a batch size per image of $128$ and
were set to only recognize one class (bar). The images are rescaled so that
their shorter side is $800$ pixels. The network was set to have a base
learning rate of $0.0001$ and was trained for $1500$ iterations on the $100$
images training set without decaying the learning rate, with five images per
batch, and evaluated on the $20$ images evaluation set with a maximum of five
detections per image at every ten iterations observing that the network is not
overfitting (Fig. 1).

Figure 1: Plot of average classification and regression losses of Faster R-CNN
for bar detection on IAA images of fragments versus training and validation
iterations.

The results of bar detection on some test set samples are visualized in Fig. 2
with similar accuracy observed in the other test results as well. These
results support the quantitative evaluation of the trained model on the
38-image test set, where it achieved an Average Precision (AP) score of
$92\%$. The AP measures the average precision at different intersection over
union (IoU) thresholds from $0.50$ to $0.95$ with a step size of $0.05$. The
low AP score (92%) is attributed to the small size of the train set. Despite
this, the results are considered sufficient for the purposes of bar detection
in the pipeline as high accuracy is not necessarily required in this step.

| Color | Infrared
---|---|---
Recto |  |
Verso |  |
Figure 2: Color images of both recto and verso of a fragment on the left, with
bar detection results overlaid. The images are also overlaid with ground truth
in yellow. The bar detection was performed only on color images, as the
network was trained on these. The results can be used for the infrared images
on the right as well, as the bar positions are identical in both image types.
The two strips of Japanese paper, or hinges, used to hold the fragment in
place can also be seen at the top. Additional paper was used by conservators
to reinforce the verso, and is visible through a hole in the parchment near
the top of the fragment. Images courtesy of Leon Levy Dead Sea Scrolls Digital
Library, Israel Antiquities Authority; photo: Shai Halevi.

###  7.3 Align Images of Recto and Verso

The alignment of the image of a fragment recto with an image of its verso
enables us most importantly to avoid interpreting ink marks on the recto as
holes, since the ink will be black on the recto but will not be detectable on
the image of the fragment verso, whereas a hole will be visible on both the
recto and verso. Two caveats apply here: A minority of fragments are
opisthographs, written on both sides [15], in which case ink may occur at the
same location on both sides of the fragment and will be interpreted here as a
hole; an imaged fragment may be a “wad”, a stack of two or more fragments that
cannot be safely separated from each other [5], with the result that the
recto/verso image set depicts the recto of the surface of the fragments
visible from the top of the stack and the verso shows only those visible from
the bottom. In the second case, the approach here cannot be used to reliably
isolate any single fragment in the wad, further progress would require either
a conservationist to separate individual fragments of the wad or a different
type of imaging or detection technology to isolate the individual items in the
stack.

The alignment of recto/verso sets is performed on the infrared images of the
fragment. First, the bars were masked using the bar detection model described
in Section 7.2. The verso image was then horizontally flipped. Next, we
carried out keypoint detection and description on the two. Keypoints are
regions with maximum variance when moved around it, and their descriptors are
vectors that describe the regions surrounding them. We then take the
descriptor of one keypoint in recto and match it with all other keypoints in
verso to find the closest two keypoints, so that we can apply a ratio test
[14] that discards many of the false matches arising from background clutter,
because, for false matches, there will likely be a number of other false
matches within similar distances. We reject all matches for which the distance
ratio is greater than $0.80$. This does not remove matches from other valid
regions. To solve this problem, we fit the alignment matrix using RANSAC
(Random Sample Consensus) method that iteratively fits the alignment matrix by
selecting a random subset of the keypoints and refining the model based on
that subset until the best model is obtained that fits the majority of the
data points within a specified error tolerance. The error tolerance in RANSAC
is a predefined threshold value that determines how far a data point can be
from the model.

The final alignment’s accuracy was evaluated based on the quantity of inliers
in the final set of keypoint matches. To enhance the outcome, the algorithm
was executed using four different feature extractors (SIFT [14], KAZE [3],
AKAZE [2], and ORB [20]) and with a threshold range from $21$ to $5$,
decremented by $2$ at each step. Analysis revealed that the optimal
combination was obtained using SIFT with a threshold of $15$, resulting in the
greatest number of inliers.

Figure 3: The $y$-axis represents the average number of inliers across the
test images, while the $x$-axis represents the threshold value. Each plot line
represents the results for a different feature extractor, with the highest
number of inliers being returned using SIFT with a threshold value of $15$.
Figure 4: Recto and flipped verso infrared images, with inliers depicted as
red circles and their corresponding match connections as colored lines. Images
courtesy of Leon Levy Dead Sea Scrolls Digital Library, Israel Antiquities
Authority; photo: Shai Halevi.

###  7.4 Image Thresholding

We preferred infrared images instead of color images because they have a
higher contrast between the fragment and the background. In contrast, color
images may have variations in lighting, shading, and color that can make
thresholding a more challenging task. We have chosen to perform the first
threshold using a dynamically calculated value. This is performed on the 8 bit
grayscale infrared images by finding the average of all pixels with a value
below 50 (i.e., all very dark pixels), to which a buffer of 10 is added. This
tends to perform very well as a floor for removing the black background in our
image set while leaving even very dark fragments or portions of fragments that
have darkened due to age and exposure to the elements. This step provides a
maximal fragment mask for the image of the fragment’s recto and the image of
the fragment’s verso (Fig. 5).

| Original | Thresholded
---|---|---
Recto |  |
Verso |  |
Figure 5: Image Thresholding. Images courtesy of Leon Levy Dead Sea Scrolls
Digital Library, Israel Antiquities Authority; photo: Shai Halevi.

###  7.5 First Mask

Since we already have the transform matrix needed to match the image of the
recto to the image of the verso, we apply this matrix to the verso mask in
order to align the two masks from step 3. The recto and verso masks are then
combined according to their union resulting in a maximal mask for the fragment
itself. The separate recto and verso masks are retained for further
refinements in step 8 (Fig. 6).

Recto | Verso | Combined
---|---|---
|  |
Figure 6: First mask.

###  7.6 Masking the Backing Substrate

The backing substrate used by the conservationists at the IAA is highly
detectable in the full-color images when they are transformed into full HSV
color-space. For our image set, we used manual testing to determine that
backing substrate occurs with HSV values between (0, 0, 100) and (255, 20,
200). We create masks for the image of the recto and the image of the verso
using all pixels that fall within that range (Fig. 7).

| Original | Backing Mask
---|---|---
Recto |  |
Verso |  |
Figure 7: Backing substrate masks. Images courtesy of Leon Levy Dead Sea
Scrolls Digital Library, Israel Antiquities Authority; photo: Shai Halevi.

#### Morphological closing.

The resulting masks tends to have many small holes due to the woven nature of
the substrate. They are improved by first discarding any tiny elements and
then performing a morphological close operation. The IAA images all have a
similar pixel density very close to 1215 PPI and a 20$\times$20 pixel ellipse-
shaped kernel appears to provide the optimal results for closing.

Often more of the backing substrate will be visible on the verso of the
fragment than the recto, in fact the entire verso of the fragment may be
covered by the backing substrate. For this reason, we use only the
intersection of the recto and verso masks. This results in a mask for only
those portions of the backing substrate that do not overlap with the
manuscript fragment or fragments (Fig. 8).

Recto | Verso | Combined
---|---|---
|  |
Figure 8: Combination of backing masks.

###  7.7 Preparing the Final Mask

The backing material mask from step 5 is subtracted from the fragment mask in
step 4. The result is a mask that should cover all of the fragment or
fragments in the images excluding any portions that only consist of the
backing material (Fig. 9).

Initial Recto | Initial Verso | Backing Mask | Final Mask
---|---|---|---
|  |  |
Figure 9: Final mask.

###  7.8 Calculating Fragment Locations

We find the contours in the final mask and sort them according to hierarchy
into separate polygons with holes. The vector shape or shapes produced here
should mainly correspond to the actual fragment or fragments in the image
set—there may be more than one manuscript fragment in an image set. The
contour detection algorithm in OpenCV may result in polygons that are invalid
topographies according to the OGC
standard,121212https://portal.ogc.org/files/?artifact_id=253556.1.11.1. which
will create problems for some algorithms for (geo-) spatial analysis. For this
reason, the results must be verified and repaired as best as possible. For
this we use the geo-repair-polygon library [9] that was created for this
purpose within the Scripta Qumranica Electronica project.131313DFG
Projektnummer 282601852; https://gepris.dfg.de/gepris/projekt/282601852,
http://qumranica.org.

###  7.9 Exclude Unwanted Fragments

We check each fragment from step 7 against the recto and the verso masks from
step 5. Any fragment polygons that do not overlap with features in _both_ the
recto and the verso masks from that step are discarded. This step removes any
small features that are not directly attached to the fragments themselves
(i.e., features that occur in different places in the recto and verso images).

###  7.10 Final Filter

In the IAA images there may be broken off flecks of parchment or papyrus that
are attached to the backing substrate, and thus will successfully be segmented
by this pipeline. Such very tiny items, however, are not profitably used
within our current research goals and are filtered out of the final collection
of results. The filtering is based, like the kernel for morphological closing
in step 5b, on the PPI of the IAA images, in this case all polygons with an
area less than 1000 are ignored (Figs. 10, 11).

Highlighted Fragment | Fragment Vector | Extracted Fragment
---|---|---
|  |
Figure 10: Extracted fragment. Images courtesy of Leon Levy Dead Sea Scrolls Digital Library, Israel Antiquities Authority; photo: Shai Halevi. Highlighted Fragments | Fragment 1 | Fragment 2 | Fragment 3
---|---|---|---
|  |  |
Figure 11: Multiple extracted fragments. Images courtesy of Leon Levy Dead Sea
Scrolls Digital Library, Israel Antiquities Authority; photo: Shai Halevi.

###  7.11 Evaluation

Fragment segmentation can be considered a semantic segmentation problem
because the goal is to segment the fragments from the background. Each pixel
of the image is assigned to a semantic class, fragment or background.
Therefore we use evaluation metrics for semantic segmentation to evaluate our
fragment segmentation results. We measure each metric (IoU, precision, recall,
F1, and accuracy) for each fragment image individually (Fig. 12) and then
calculate the average of these metric values to get the overall performance
(Table 1) of the fragment segmentation. This helps us understand how well the
results are on the entire dataset and identify any potential issues with the
individual results.

The mean Intersection over Union (IoU) was $0.97$, which indicates a high
overlap between the predicted and ground truth binary masks. The mean
precision was $0.98$ and the mean recall was $0.99$, meaning that the model
was able to detect most of the fragment pixels present in the ground truth.
The reason that the recall is lower than precision is the tendency to include
some background pixels as fragment pixels. For example, in the case of
fragment 998_9, the relatively lower precision and recall (Fig. 12) values can
be attributed to the presence of some background pixels (with Japanese paper)
being returned as fragment pixels.

Table 1: The mean values of IoU, precision, recall, F1, and accuracy, calculated for each individual fragment image. IoU |  Precision |  Recall |  F1 |  Accuracy
---|---|---|---|---
$0.9722$ |  $0.9773$ |  $0.9947$ |  $0.9857$ |  $0.9993$
Figure 12: Each bar represents the performance of a single fragment image
segmentation, with different colors representing different metrics: IoU,
precision, recall.

##  8 Summary

The nature of the Israel Antiquities Authority (IAA) digitization of the Dead
Sea Scrolls in their collection presents several difficulties for standard
approaches to automatically segment the manuscript fragments pictured from the
background and metadata elements contained in the image. We propose that a
pipeline can be used in such cases in order to isolate each difficulty and
solve it using the best, custom-tailored approach. The results of each step
are aggregated in specific ways as to reach the desired output. The individual
analytical steps outlined here may be useful for other collections of
manuscript images that would benefit from segmentation. Further, the usage of
a multi-step pipeline will surely be helpful from a conceptual standpoint for
other image segmentation projects that encounter problems that have proven
intractable when applying any of the more commonly used segmentation
techniques. Finally, we employed a ground-truth corpus in order to provide a
qualitative evaluation of our automated segmentation results.

##  9 Further Research

Considering the success of our experiments on the evaluation dataset and some
expected improvements, the plan is for the pipeline described herein to be
applied in the near future to the whole of the IAA corpus of color images and
for the results to be incorporated within its online platform. The resulting
images can then be used for some of the following purposes:  (a) to rectify
the images so that they are upright  (b) to accurately place fragments on a
canvas in reconstruction attempts  (c) to search for multiple images of the
same fragment in other sets of images—such as the much older Palestine
Archaeological Museum (PAM) images [18] (Fig. 13) (cf. [12, 4])  (d) to allow
for the registration of older images with the new ones (cf. [12, 4]); or  (e)
to align transcriptions with fragments at the glyph-level (cf. [23]).

Figure 13: PAM series image. Images courtesy of Leon Levy Dead Sea Scrolls
Digital Library, Israel Antiquities Authority; photo: Najib Anton Albina.

Segmenting fragments on the PAM images would present additional problems, as
they are available only as black and white infrared images of plates that
usually contain multiple fragments, often with shadows. See [12] for a first
attempt.

## Acknowledgments

The dataset used in this study is licensed under the Creative Commons
Attribution-NonCommercial 4.0 International (CC-BY-NC 4.0) license. All of our
derivative images must also be cited according to the paper citation.

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# Double Nuclear Spin Relaxation in Hybrid Quantum Hall Systems

M. H. Fauzi<EMAIL_ADDRESS>Center for Spintronics Research Network,
Tohoku University, Sendai 980-8577, Japan  Research Center for Physics,
Indonesian Institute of Sciences, South Tangerang City, Banten 15314,
Indonesia  William J. Munro  National Institute of Informatics, 2-1-2
Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan  NTT Basic Research
Laboratories & NTT Research Center for Theoretical Quantum Physics, NTT
Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa, 243-0198, Japan
Kae Nemoto<EMAIL_ADDRESS>National Institute of Informatics, 2-1-2
Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan  Y. Hirayama
<EMAIL_ADDRESS>Center for Spintronics Research Network,
Tohoku University, Sendai 980-8577, Japan  Department of Physics, Tohoku
University, Sendai 980-8578, Japan  Center for Science and Innovation in
Spintronics (Core Research Cluster), Tohoku University, Sendai 980-8577, Japan

###### Abstract

Recent advances in quantum engineering have given us the ability to design
hybrid systems with novel properties normally not present in the regime they
operate in. The coupling of spin ensembles and magnons to microwave resonators
has for instance lead to a much richer understanding of collective effects in
these systems and their potential quantum applications. We can also hybridize
electron and nuclear spin ensembles together in the solid-state regime to
investigate collective effects normally only observed in the atomic, molecular
and optical world. Here we explore in the solid state regime the dynamics of a
double domain nuclear spin ensemble coupled to the Nambu-Goldstone boson in
GaAs semiconductors and show it exhibits both collective and individual
relaxation (thermalization) on very different time scales. Further the
collective relaxation of the nuclear spin ensemble is what one would expect
from superradiant decay. This opens up the possibility for the exploration of
novel collective behaviour in solid state systems where the natural energies
associated with those spins are much less than the thermal energy.

It has now be widely accepted that the principles of quantum mechanics will
lead to new technologies with capabilities unlike anything seen in our purely
classical world [1, 2, 3]. There is the potential to have computational and
communication power beyond anything our conventional world can every realize
[4, 5, 6]. The principles also allow us to construct unparalleled quantum
sensing and imaging sensitivity [7, 8]. Typically such achievements could be
achieved using traditional quantum systems. However in recent years it has
been established that the hybridization of distinct quantum systems has the
potential to design composite devices with properties and attributes not
normally unavailable in the regime those systems came from [9, 10, 11]. Hybrid
quantum systems will exhibit functionalities superior to those in other sub
quantum systems (long lived memories for instance) and are likely to be
multitasking [11]. They will play important roles in engineering multi-
functional quantum devices (quantum transducers for instance) and performing
diverse quantum information processing tasks. With the state-of-the-art
quantum technology, hybrid quantum systems are being designed and engineered
using many different types of elements ranging from solids to atomic,
molecular and optical (AMO) systems [9, 10, 11, 12, 13, 14, 15, 16, 17, 18].

Hybrid quantum systems are more however than a tool to create new technologies
as they also provide the opportunity to explore quantum many body and non-
equilibrium physics in unique regimes or regimes normally not available to
those systems [11, 19, 20]. We now have the ability to explore quantum
phenomena using solid-state systems which have typically been investigated in
AMO systems [19, 21, 22, 23, 20] with the advantage that this solid-state
systems are easier to control, manipulate and measure with high accuracy. Two
recent examples include the demonstration of amplitude bistability and
superradiance using an electronic spin ensemble coupled to a microwave
resonator [19, 20]. The latter case is of particular interest here as it
involves the collective behaviour of that ensemble where the superradiant
burst of microwave photons occurred ten orders of magnitude faster than the
corresponding relaxation of a single nitrogen-vacancy center in diamonds
electron spin [20]. This enabled the dynamics of the process can be
investigated. While this was a coherence phenomena, a simple modification
using two ensembles instead of one allows it to be a truly collective quantum
phenomena with no classical analog [24, 25]. It also raises the question about
whether such collective effects can be seen in other solid-state systems which
we will explore in this context. Further by using nuclear spins one would be
operating in a regime with significant thermal background, even though the
experiment is taking place in a dilution environment [26, 27, 28].

Figure 1: Schematic illustration of our hybrid quantum systems device
operating at dilution temperatures (50 mK) used to investigate the behaviour
of nuclear spins coupled with an electronic reservoir of electrons in QH
states through the hyperfine interaction. Here two identical 20-nm wide GaAs
quantum wells, separated by a $2.2$ nm thick insulation layer, are in close
proximity to create a strongly coupled bilayer two-dimensional electron gas
system. These are indicated by the two red lines in the main illustration. The
electronic states in both layers are electrostatically controlled by applying
a gate bias between the top gate ($V_{\rm{TG}}$) and bottom gate
($V_{\rm{BG}}$). A static magnetic field $B$ is also applied along the
$Z$-axis normal to the device. The inset depicts our QH system coupled through
the hyperfine interaction to the NG boson. The nuclear spins are forming the
double-spin domains A and B (two independent ensembles) with the NG boson
operating as a reservoir. Domain A is described by the upward red arrows while
domain B with the downward blue arrows. The number of spins in each domain is
approximately the same.

The predication and subsequent demonstration of the Quantum Hall (QH) effect
establishing macroscopic quantum phenomena in solid-state two-dimensional
electron systems in the presence of high magnetic field has spawned many
important discoveries in quantum many-body electronic physics and topological
quantum matter including the quantum Hall ferromagnet and collective
excitations such as Nambu-Goldstone (NG) bosons & skyrmions [29, 30, 31, 32,
34]. However the nuclear-electron spin dynamics and its hybridization in the
QH system has been rarely explored [36]. Coupling of a nuclear spin ensemble
to a Nambu-Goldstone boson seems an ideal candidate to explore collective
effects in a solid-state hybrid quantum system [34, 24] and that would be our
focus here. We would expect to observe phenomena arising from both collective
and individual nuclear spins decoherence and so our initial focus will be on
the measured behaviour of this hybrid system - especially the dynamic ones. A
Nambu-Goldstone mode is known to cause a rapid nuclear spin relaxation rate
[33, 34, 35]. However, the way that the nuclear spin dynamics was measured in
the previous reports missed out a key feature, which we address here namely a
sudden reconfiguration of nuclear spin polarization.

Figure 2: Plot of the initialization of the double-nuclear-spin domain (a)
indicating the number of polarized nuclear spins (measured as a hyperfine
field change in mT) versus the time $\tau_{\rm{p}}$ the source-drain current
$I_{\text{sd}}$ is applied. At $\tau_{\rm{p}}=50$s, the number of up nuclear
spin polarization $J^{z}_{\uparrow}$ (down nuclear spin polarization
$J^{z}_{\downarrow}$) was $-170$ mT ($+43$ mT) respectively. For
$\tau_{\rm{p}}=400$s, they increased to $-353$ mT ($+215$ mT), a factor of 2
(5) polarization improvement respectively. As a calibration a fully polarized
sample would result in a hyperfine field near $5.3$ T [45] meaning we can
estimate the maximum percentage of spins in the up (down) domain at
approximately $6.6\%$ ($4\%$) respectively. In (b) we depict the total nuclear
spin polarization for varying pumping time $\tau_{\rm{p}}$ followed by a $5$ms
interaction the NG boson with a subsequent total magnetization measurement (in
terms of the hyperfine field strength). For ease of comparison, the initial
polarization in panel(a) is replotted together. In (c) we show the nuclear
spin relaxation dynamics versus the Dwell time to the NG boson for pumping
times $\tau_{\rm{p}}$ $=100$s ($400$s) respectively with the solid lines
providing a visual guide. It is clear that at long times the double-nuclear-
spin domains reach the same thermal equilibrium. Our minimum Dwell time
measurement is $5$ ms restricting our ability to explore the really short time
dynamics.

Let us begin by describing our nuclear spins coupled with electrons in QH
states through the Fermi contact hyperfine interaction. Our hybrid quantum
system as depicted in Fig. 1 is implemented in a GaAs-based bilayer quantum
Hall setting cooled to $50$ mK and threaded with a static magnetic field $B$
applied normal to the device. This brings the electronic state into the
quantum Hall regime where the interplay between charge, spin, and layer degree
of freedom creates non-trivial correlated electronic states [37, 38] where all
nuclear spins can be up or down for instance. For our situation here, the
initialization of our double nuclear-spin domains with different spin
orientation ($\uparrow$ and $\downarrow$) is achieved by electrical means
using a fractional quantum Hall liquid (FQHL) [39] developed at the bottom
layer, where $2/3$ of the available states in the lowest Landau level are
occupied (see also supplementary material). It exhibits two different magnetic
phases, spin polarized and unpolarized phases, which are separated by a domain
wall at the spin transition point [40]. Now the injection of a relatively
large alternating source-drain current $I_{\text{sd}}$ at the spin transition
point creates a bidirectional nuclear spin polarization due to multiple
forward scattering events between two neighboring magnetic phases [41, 42]. As
a result the double-nuclear-spin domain is generated with a state of the form
$\big{|}\text{DNSD}\big{\rangle}=|\uparrow\ldots\uparrow\rangle_{\text{A}}\otimes|\downarrow\ldots\downarrow\rangle_{\text{B}}$
where the first domain (labelled A) has all spins pointed up $\uparrow$ while
the second domain $B$ has all spins pointed down $\downarrow$. We expect the
domain to have approximately the same number of nuclear spins in them but a
little asymmetry could exist [43].

Our initial state $\big{|}\text{DNSD}\big{\rangle}$ is illustrated in Fig.
(2a) where we vary the pumping time $\tau_{p}$ to observe its effect on the
magnetization of each domain. Here the blue (red) dots represent the degree of
nuclear spin polarization of the up (down)-spin domain which are measured in
terms of a change in the hyperfine field. The degree of spin polarization
(resulting from the dynamical spin flip-flop process between the electron and
nuclear spins driven by the source-drain current $I_{\text{sd}}$) in each
domain increases with larger pumping time $\tau_{\rm{p}}$ reaching a maximum
of $6.6\%$ ($4.0\%$) respectively. Without such pumping the thermal
equilibrium polarization is much less than $1\%$.

Having described one half of our hybrid system, let us now describe the second
system which is a NG boson. The NG boson arises from a charge imbalance in the
QH state of the bilayers. We can tune this charge imbalance to realize three
different spin phases / configurations: the canted antiferromagnetic (CAF)
phase, the ferromagnetic (FM) phase and the spin-singlet (SS) phase (see
supplementary material section II on how to access a particular spin
configuration) [38, 34]. It is the CAF phase that is of interest here as it
supports a linear dispersing NG boson in the long wavelength limit [37]. The
NG boson naturally couples with the double-nuclear-spin polarized domains [44]
allowing us to create our required hybrid system (see supplementary material
section on how to initialize and calibrate the nuclear spins).

In Fig 2b we show the effect of coupling our double domain system to the NG
boson for a given pumping time before measuring the total magnetization of the
system (which indicate the degree of polarization of the hybrid system). It is
clear that this coupling has rapidly increased the degree of polarization in
the system as shown by the black dot curve - actually to a magnetization below
that associated with thermal equilibrium. This leads to the natural question
about what our system is doing and so let us now explore the dynamics of this
system. We let the double nuclear spin system and NG boson interact for a
given dwell time before we measure the polarization of the entire double
domain system using a simple magnetization measurement. We clearly observe (as
shown in Fig 2c) that the nuclear spins from the double domain system have
relaxed very rapidly (< $5$ ms) and are pointing upwards (parallel to the
direction of the applied magnetic field). They stay in the relaxed state until
around $1$s where it begins to thermalize to its original thermal steady
state. The re-thermalization is completed near $100$ s. A sudden
reconfiguration of nuclear spin polarization and its dynamics towards
equilibrium are completely different from an ordinarily independent relaxation
process.

It is apparent from Fig 2c that our hybrid system has a number of interesting
and independent timescales associated with it. Two of these are associated
with the usual dephasing [45, 46] & thermalization processes with timescales
given by $T_{2^{*}}\sim 1$ms ($T_{1}\sim 40$s) respectively [47]. These
correspond clearly to the behaviour seen in the right hand side of that sub-
figure. The left hand side of the figure, i.e. the flat region in between $5$
and $500$ ms, is however much more interesting and only occurs because of the
coupling to the NG boson associated with the CAF phase. The FM and SS phases
do not show this short term behaviour. This is due to the fact that they have
gapped modes [44] meaning the double nuclear spins exhibit normal relaxation
processes independent of the initial number of polarized nuclear spins [48]
(see supplementary material). It is thus clear our observed behaviour here is
associated with the canted antiferromagnetic (CAF) phase and its associated NG
boson. It is critical to determine how this relaxation caused by the coupling
to the NG boson varies with the size of the total nuclear spin ensemble. We
have already established in Fig 2a that the hyperfine field strength
(proportional to the number of polarized nuclear spins in the ensemble)
increases with increasing pumping time $\tau_{\rm{p}}$. Thus we can prepare
different size nuclear spin polarized ensembles which we can then let interact
with the NG boson for $5$ms before measuring the resulting polarization. In
Fig.2b we plot the total spin polarization (measured by the hyperfine field)
against the pumping time $\tau_{\rm{p}}$ after its interaction with the NG
boson. We clearly observe that the nuclear spin polarization of the total
double domain system increasing as the pumping time $\tau_{\rm{p}}$ gets
larger. It is clear from Fig. 2b-c that this short time behaviour is
associated with the form of the NG boson coupling to the double nuclear spin
domain. As such we need to explore the natural of the NG boson and its
coupling in a little more detail.

Let us discuss the QH state again briefly. When we tune the two-dimensional QH
state such that the in-plane rotational symmetry of electron spin is
spontaneously broken, an associated linear dispersing NG boson emerges. This
can be described by a continuous wave-number vector $\bm{k}=(k_{x},k_{y})$
with wavelength $\sim 0.1$mm for a nuclear-spin frequency near $10$ MHz. This
long wavelength is very important as the nuclear-spin separation is
approximately $\sim 0.5$ nm((much shorter than that of the NG boson) meaning
those nuclear spins can couple collectively to the NG boson. This is our first
hint at a collective effect where the NG boson is acting like a reservoir
[44]. It also gives us a natural way to model our overall hybrid system. For
simplicity, we assume that all the spins here are identical (only single
species to be taken into account) with spin-1/2.

Our hybrid quantum system composed of two nuclear spin ensembles and the NG
boson can be effectively described by the Dicke model where the NG boson act
as a reservoir [44]. This model indicates the generation of collective
phenomena of nuclear spins. In actual systems, however, there are individual
dissipative effects which break the collective phenomena. Examples include a
dipole-dipole interaction between nuclear spins which induces a dephasing
effect and an individual coupling between spin and other reservoir like phonon
leading to a $T_{1}$-time relaxation process. Given the presence of collective
effect involving a quantum / thermal reservoir as well as individual nuclear
spin dephasing and thermalization, it is quite natural to model this system by
a nuclear spin Born-Markov type master equation [49] of the form

$\displaystyle\dot{\rho}(t)$ $\displaystyle=$
$\displaystyle-i\omega_{\text{ns}}[J^{z}_{\text{A}}+J^{z}_{\text{B}},\rho(t)]$
(1) $\displaystyle+$
$\displaystyle\frac{\gamma^{\text{rel}}}{2}\left[(\bar{n}+1){\cal
L}(\left[J^{-}_{\text{A}}+J^{-}_{\text{B}}\right]\rho)+\bar{n}{\cal
L}(\left[J^{+}_{\text{A}}+J^{+}_{\text{B}}\right]\rho)\right]$
$\displaystyle+$
$\displaystyle\frac{\gamma^{\text{rel}}}{2}\Big{[}(\bar{n}+1)\sum_{i_{\text{A,B}}=1}^{N_{\text{A,B}}}{\cal
L}(I^{-}_{i_{\text{A,B}}}\rho)+\bar{n}\sum_{i_{\text{A,B}}=1}^{N_{\text{A,B}}}{\cal
L}(I^{+}_{i_{\text{A,B}}}\rho)\Big{]}$ $\displaystyle+$
$\displaystyle\frac{\gamma^{\text{dep}}}{2}\left[\sum_{i_{\text{A}}=1}^{N_{\text{A}}}{\cal
L}(I^{z}_{i_{\text{A}}}\rho)+\sum_{i_{\text{B}}=1}^{N_{\text{B}}}{\cal
L}(I^{z}_{i_{\text{B}}}\rho)\right],$

where
$J^{z}_{\text{A,B}}=\sum_{i_{\text{A,B}}=1}^{N_{\text{A,B}}}I^{z}_{i_{\text{A,B}}}$
are the collective spin Z-operators for the domain A (B) with
$I^{z}_{i_{\text{A,B}}}$ representing the individual nuclear spin 1/2
z-operator. Here $N_{\text{A,B}}$ are the total number of spins included in
the domain A (B) respectively (the combined number of spins in both ensembles
is $N=N_{\text{A}}+N_{\text{B}}$). Associated with these are the collective
(individual) raising $J^{+}_{\text{A,B}}$ ($I^{+}_{i_{\text{A,B}}}$) and
lowering $J^{-}_{\text{A,B}}$ ($I^{-}_{i_{\text{A,B}}}$) operators for the
nuclear spins in domain A, B respectively.The nuclear spin frequency is given
by $\omega_{\text{ns}}=\gamma_{\rm{n}}B$ where $\gamma_{\rm{n}}$ being the
gyromagnetic ratio of nuclear spins. Further $\gamma^{\text{rel}}$
($\gamma^{\text{dep}}$) in our master equation represent the damping
(dephasing) rates. Next
$\bar{n}=1/(e^{\hbar\omega_{\text{ns}}/k_{\text{B}}T}-1)$ is the Bose-Einstein
distribution functions at the energy $\hbar\omega_{\text{ns}}$ for a given
temperature $T$ where $k_{\text{B}}$ is the Boltzmann constant. In (1) the
Liouvillian ${\cal L}(X\rho)$ is given by ${\cal L}(X\rho)=2X\rho
X^{\dagger}-X^{\dagger}X\rho-\rho X^{\dagger}X$ with $X$ being an arbitrary
operator.

Our master equation given by (1) describes four basic phenomena; the Larmor
precession of nuclear spins; collective thermalization, individual
thermalization and individual dephasing (we ignore collective dephasing
effects here at present). Now solving the master equation allows us to explore
the dynamics of the overall system and we should be able to simply determine
if we can reproduce the behaviour observed in Fig 2c - especially as we
already know many of our system parameters including $\omega_{\text{ns}}$ and
the fridge temperature $T$ as well as the $T_{1},T_{2}^{*}$ relaxation times,
Our interest here will be in determining the magnetization of the double
domain system which will be proportional (up to an arbitrary scaling) to the
expectation value $S_{z}=\langle J^{z}_{\text{A}}+J^{z}_{\text{B}}\rangle$. In
Fig. 3, we show the evolution of the total spin magnetization versus dwell
time for a small sized nuclear spin ensemble (not the exact number present in
our actual system which will be approximately $10^{12}$). We do however to
ensure that the total number of spins in our model is much greater than
$\bar{n}$, otherwise the system dynamics may change. Here we choose
$N=10^{6}$. With our chosen parameters it is clear that we have a number of
distinct behaviour arising over different time scale. Those correspond to time
scale less than $1$ ms (yellow shaded region), between $1-1000$ ms and greater
than $1$ s (red shaded region). The main figure in Fig. 3 is consistent with
the experimental observations of Fig. 2(c).

Figure 3: Simulation of the total magnetization of the double domain nuclear
spin versus the interaction (dwell) time, nothing that we have an arbitrary
scaling on the y-axis. The results are presented for a) $N=10^{6}$, b)
$N=6*10^{5}$. Here we have used the parameters $\omega_{\text{ns}}/2\pi=10$
MHz, $T=50$ mK, $T_{2}^{*}\sim 1$ ms and $T_{1}\sim 40$ s. This implies that
${\bar{n}}\sim 110$ which is much less than $N$. Two distinct regions are
shown in the main figure: white (red) where individual spin dephasing
(thermalization) are the dominant behaviours. The yellow coloured inset shows
the short time behaviour where collective thermalization effects dominate.
Within the inset the black (red-dashed) curves correspond to (thermal mean
photon number ${\bar{n}}\sim 110$ (zero temperature ${\bar{n}}\sim 0$)
respectively. Little difference is seen for the two ${\bar{n}}$ as both are
much less than $N$.

We need to explore these three regions in a little more detail starting with
the short time regime shown in the inset for a total spin number $N=10^{6}$.
First and foremost the decay process we observe here occurs much faster than
either the $T_{2}^{*}$ or $T_{1}$ times associated with individual nuclear
spins. The collective thermalization term in our master equation does
reproduce such behaviour giving us strong evidence of collective and coherent
effects here. Next the individual dephasing of the nuclear spins with
associated $T_{2}^{*}\sim 1$ ms dominates in the $1-1000$ ms temporal region
where it destroys all coherence within and between the nuclear spins leaving
the double domain system in a separable state. Each of the nuclear spins are
now acting independently of each other and so collective effects do not arise.
At approximately $1$ s the effect of individual nuclear spin thermalization
begins and at approximately $100$ s the nuclear spins reach their high
temperature steady state (with a magnetization of zero). A similar behaviour
(blue curve in Fig. 3) occurs if $N$ decreases but with a different degree of
short time total magnetization is reached. The long time steady state is the
same. Our model naturally explains the observed experimental behaviour and can
give us further incites into our system dynamics.

The particularly interesting temporal behaviour arises in the short time
regime where we observe a fast decrease in the total magnetization to a little
well below zero (the magnetization associated with the long time steady
state). We only observe the resultant effect here and not it dynamics which we
can not experimentally measure. We only see the result that this collective
behaviour has caused. Our model however can also be used to explore the short
time regime in more theoretical detail. It is clear from our model (with
${\bar{n}}=0$ that the rate of thermalization scales quadratically with $N$
(rather than linear from individual spin thermalization). This is consistent
with superradiance decay. Next for ${\bar{n}}\sim 110$ we observe a very
similar quadratic short time behaviour, however as ${\bar{n}}\rightarrow N$ we
loss that quadratic behaviour. In our experiment we realistically have
$N>10^{12}$ which is much greater than the ${\bar{n}}\sim 110$ associated with
the nuclear spin operating at $50$ mK. For such a large $N$ the associated
superradiant decay time is extremely fast ($<10^{-10}$ s) and hence is
impossible to observe. Our observed experimental behaviour however is only
consistent if such collective decay had occurred.

To summarize, we have shown how collective and coherence effects arise in a
double domain nuclear spin ensemble coupled to the Nambu-Goldstone boson in a
GaAs semiconductor. The NG bosons long wavelength means both nuclear spin
ensembles couple see the same mode. This leads to superradiant like decay
event when our system is operating in the reigme ($\hbar\omega_{\text{ns}}\ll
k_{\text{B}}T$). Further it is likely that the short time dynamics will show
entanglement between the two ensembles. This will open a new paradigm in
nonlinear systems where quantum only (rather than coherent) effects are
present.

###### Acknowledgements.

We thank Yusuke Hama and Shane Dooley for valuable discussions. This work was
supported in part by the MEXT Grant-in-Aid for Scientific Research on
Innovative Areas KAKENHI Grant Number JP15H05870 (Y. H, E. Y, and K. N), MEXT
Grant-in-Aid for Scientific Research(S) KAKENHI Grant Number JP25220601 (E. Y
and K. N) and Grant-in-Aid for Scientific Research(A) KAKENHI Grant Number
JP19H00662 (W.J.M and K. N).

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