# Comparative Analysis of Named Entity Recognition
in the Dungeons and Dragons Domain

Gayashan Weerasundara  Nisansa de Silva
Department of Computer Science & Engineering
University of Moratuwa, Sri Lanka
{gayashan.22<EMAIL_ADDRESS>

###### Abstract

Many NLP tasks, although well-resolved for general English, face challenges in
specific domains like fantasy literature. This is evident in Named Entity
Recognition (NER), which detects and categorizes entities in text. We analyzed
10 NER models on 7 Dungeons and Dragons (D&D) adventure books to assess
domain-specific performance. Using open-source Large Language Models, we
annotated named entities in these books and evaluated each model’s precision.
Our findings indicate that, without modifications, Flair, Trankit, and Spacy
outperform others in identifying named entities in the D&D context.

##  1 Introduction

Named Entity Recognition (NER) targets the identification and classification
of textual entities, such as names and locations. In the diverse and intricate
vocabulary of fantasy literature, like that of Dungeons and Dragons (D&D), NER
becomes challenging Zagal and Deterding (2018). D&D, a prominent fantasy
literature domain, spans content for its namesake tabletop game Peiris and de
Silva (2022, 2023); Zhou et al. (2022). These narratives inhabit fictional
realms like Forgotten Realms and Dragonlance, bursting with characters,
locations, and objects Gygax and Arneson (1974).

NER’s utility in fantasy literature is vast: from extracting information and
summarizing text to character analysis and plot creation. However,
conventional NER models, primarily trained on standard datasets like
CoNLL-2003 Tjong Kim Sang and De Meulder (2003) or OntoNotes 5.0 Weischedel et
al. (2013), might falter on fantasy texts due to their unique linguistic
attributes. Recognizing the need for domain-specific adaptation, other
specialized areas such as law (Sugathadasa et al., 2017), medicine (de Silva
et al., 2017), and the dynamic landscape of social media (de Silva and Dou,
2021) have already seen research emphasizing it. Large models, as Yao et al.
(2021) points out, can face domain adaptation challenges, stressing the need
for evaluating NER models specifically on fantasy content.

Fantasy NER has potential, especially with advancements in image generation. A
notable application might involve an image generation model leveraging NER
tags to derive prompts and subsequently produce contextually relevant images.

Our study contrasts 10 NER models across seven D&D books, each averaging
118,000 words. Manual annotations of entities were made and juxtaposed against
model outputs. Through precision assessments and named entity distribution
analyses, we glean insights into model performances in the fantasy domain. Our
key contributions include:

  * •

A pioneering, comprehensive NER model evaluation on fantasy content.

  * •

An annotated D&D book dataset for NER studies.

  * •

A deep dive into varied NER models’ strengths and pitfalls in the fantasy
realm.

  * •

Discussions on NER’s role and prospects in fantasy literature.

Following this, Section 2 delves into related NER and fantasy literature
works. Section 3 details our data and annotation process, while Section 4
unveils our methods and findings. Sections 5 and 6 respectively discuss
insights and conclude our research, and Section 7 outlines potential future
endeavors.

##  2 Related Works

NER has seen the development of various models like rule-based systems,
statistical models, neural networks, and transformer-based models Seo et al.
(2021); Liu et al. (2022); Krasnov et al. (2021). Although they’ve been
trained on standard datasets, these don’t encompass the complexities found in
domains like fantasy literature, which poses challenges due to invented names,
variable spellings, entity ambiguity, and limited resources.

We introduced a novel annotated dataset of D&D books for NER and evaluated 10
NER models, including XLM-RoBERTa Conneau et al. (2019), StanfordDeID Chambon
et al. (2023), ELECTRA Clark et al. (2020), and others.

Other studies have compared the performance of NER models on different types
of texts and languages. For example, Wang et al. (2021) compared Spacy, Flair,
m-BERT, and camemBERT on anonymizing French commercial legal cases. They found
that camemBERT performed the best overall, followed by Flair and m-BERT. SpaCy
had the lowest scores but also the fastest prediction time. Benesty (2019)
compared spaCy, Flair, and Stanford Core NLP on anonymizing English court
decisions. They found that Flair had the highest scores, followed by Stanford
Core NLP and spaCy. Shelar et al. (2020) compared rule-based, CRF-based, and
BERT-based techniques for NER on text data. They found that BERT-based
technique had the highest accuracy and recall, followed by CRF-based and rule-
based techniques. Naseer et al. (2021) compared NLTK, spaCy, Stanford Core
NLP, and BERT Devlin et al. (2018) on extracting information from resumes.
They found that BERT had the highest accuracy and F-measure, followed by
spaCy, Stanford Core NLP, and NLTK.

These studies suggest that different NER models may have different strengths
and weaknesses depending on the type, language, and domain of the text data.
Our study aims to contribute to this understanding by providing the first
systematic comparison of NER models on fantasy texts and analyzing their
performance and characteristics.

##  3 Data Collection and Annotation

This section details the data sources and annotation process utilized for our
named entity recognition (NER) task, a subtask of information extraction that
classifies named entities in unstructured text into categories such as
persons, organizations, and locations Mohit (2014).

We examined seven adventure books from the Dungeons and Dragons (D&D) realm,
listed in table 1. These books, primarily adventure-centric, were sourced from
the official DnDBeyond site, the main publication hub for D&D by Wizards of
the Coast.

Through a comprehensive analysis of these texts, we used their rich narratives
and character dynamics to benchmark and assess various NER models in this
intricate domain.

Book | Counts
---|---
| Words | Topics
Lost mine of Phandelver Baker and Perkins (2014) | 45947 | 29
Hoard of the Dragon Queen Baur et al. (2014a) | 74243 | 45
Rise of Tiamat Baur et al. (2014b) | 80065 | 48
Curse of Strahd Perkins et al. (2016) | 154519 | 62
Tomb of Annihilation Perkins et al. (2017) | 148605 | 35
Candlekeep Mysteries Perkins et al. (2021) | 141104 | 106
The Wild Beyond the Witchlight Allan et al. (2021) | 184135 | 60

Table 1: D&D adventure books

Each of our chosen books averages 118,000 words. The selection was driven by
our familiarity with these tales and the broader D&D universe. Additionally,
they span multiple genres, themes, and settings in the fantasy realm, offering
a vast array of named entities for NER.

The source books were transformed into text and organized hierarchically into
chapters, topics, and paragraphs. An example from ”The Wild Beyond the
Witchlight” is displayed in table 2.

Chapter | Topic | Paragraph | Word Count
---|---|---|---
Introduction: Into the Feywild |  Adventure Summary |  | The main
---
antagonists of
this story are
three hags…
131
| One of the
---
many novelties
of this adventure
is that…
43
| The characters
---
are drawn into
the adventure
by one of two
adventure hooks.
You choose…
31
| Chapter 1
---
describes the
Witchlight Carnival…
40
… | …
Running the Adventure |  | The Monster
---
Manual contains
stat blocks
for most of the
creatures encountered
in this…
72
| Spells and
---
equipment mentioned
in the adventure
are described
in the Player’s
Handbook…
31

Table 2: Content hierarchy in a book

We first manually perused the source books, marking named entities
hierarchically by chapter, topic, and paragraph, recording only entity counts.
Subsequently, we employed three state-of-the-art large language models: Bloom
Scao et al. (2022), OpenLLaMA Geng and Liu (2023), and Dolly Databricks
(2023), to detect named entities in each book chapter. These models, trained
on vast conversational data, can craft natural language responses, making them
apt for the intricate language patterns in D&D texts, such as neologisms and
metaphors.

After eliminating duplicates and pinpointing unique entities, we verified
these results against our initial counts. The named entities identified by the
three LLMs underwent a manual review for accuracy and consistency, adding
crucial missed entities. Table 3 contrasts the named entity counts from each
LLM, with recall metrics based on entities common across all models.

Book | Bloom | Dolly | OpenLLaMA |  Total Unique
---|---|---|---|---
|  Count |  Recall |  Count |  Recall |  Count |  Recall |  Entities
Lost Mine of Phandelver |  21 |  0.47 |  32 |  0.73 |  40 |  0.91 |  44
Hoard of the Dragon Queen |  58 |  0.89 |  62 |  0.95 |  60 |  0.92 |  65
Rise of Tiamat |  54 |  0.88 |  57 |  0.93 |  53 |  0.87 |  61
Curse Of Strahd |  92 |  0.90 |  96 |  0.94 |  101 |  0.99 |  102
Tomb of Annihilation |  101 |  0.80 |  99 |  0.79 |  112 |  0.89 |  126
Candle keep Mysteries |  60 |  0.87 |  61 |  0.88 |  64 |  0.93 |  69
The Wild Beyond Witch Light |  66 |  0.84 |  67 |  0.85 |  71 |  0.89 |  79
Table 3: Result comparison between LLMs

When annotating the resultant named entities we followed a set of annotation
guidelines that define the entity types and the annotation rules for our NER
task. The entity types that were used are:

  * •

Person: any named character or creature that can act as an agent, such as
heroes, villains, allies, enemies, etc.

  * •

Organization: any named group or faction that has a common goal or identity,
such as guilds, cults, clans, etc.

  * •

Location: any named place or region that has a geographical or spatial
dimension, such as cities, dungeons, forests, etc.

  * •

Misc: any named entity that do not belong to above mentioned categories. (This
contain important information like Spells, Artifacts, Potions etc.)

The process of annotation is done through a script, where a paragraph segment
is taken iteratively and fed into the LLMs with a template prompt.

| Please identify and list all named entities
---
in the following text using the BIO
(beginning-inside-outside) scheme:
| ”The traveling extravaganza known as
---
the Witchlight Carnival visits your
world once every eight years. You
have a dim memory of sneaking into
the carnival as a child without paying…
…pair of elves named Mister Witch and
Mister Light—were decidedly unhelpful.”
B-Organization: | Witchlight | Carnival
I-Person: | Mister | Witch
I-Person: | Mister | Light

Table 4: Process of Annotation

Following Algorithm 1 is the pseudo-code for the process in identifying named
entities:

Input: Books;

Output: Named entities;

foreach  _book_ do

segments $\leftarrow$ divideIntoSegments(book);

foreach  _segment in segments_ do

paragraphs $\leftarrow$ divideIntoParagraphs(segment);

foreach  _paragraph in paragraphs_ do

foreach  _LLM in LLMs_ do

prompt $\leftarrow$ createPrompt(paragraph);

namedEntities $\leftarrow$ LLM(prompt);

processNamedEntities(namedEntities);

end foreach

end foreach

end foreach

end foreach

removeDuplicates(namedEntities);

Algorithm 1 Named Entity Recognition using Multiple LLMs

As shown in above pseudocode, the algorithm 1 takes a set of books as input
and outputs the named entities identified by the LLMs. The algorithm iterates
over each book and divides it into segments. Each segment is further divided
into paragraphs, and each paragraph is iteratively fed into each of the LLMs
with a prompt to identify named entities. The named entities identified by
each LLM are then processed and saved. Finally, all named entities are checked
for duplicates, and those duplicates are removed.

After named entities were recognized, they were then mapped in to json objects
for storage as shown in Figure 1. Nesting of objects is done according to the
hierarchy as mentioned in table 2. Each of the named entities were nested in
an array of entities as entity objects with corresponding attributes as
mentioned bellow.

JSON object ⬇ { "book": "Candlekeep␣Mysteries", "chapter": 1, "text":
"The␣Book␣of␣Inner␣Alchemy␣is␣one␣of␣Candlekeep’s...", "entities": [ { ... },
{ "entity": "B-Location", "score": 0.9659823, "index": 8, "word":
"Candlekeep", "start": 42, "end": 51 }, ] } Figure 1: sample format of the
JSON output

##  4 Experimental Setup and Results

The experiment was conducted to identify how effective are the NER models when
using them as off the shelf models in identifying named entities for a fantasy
domain when there are no available corpora for fine tuning. For testing we
used 10 different contemporary NER midels.

Following table 5 shows the identified count of named entities for each
categories of the adventure book Candlekeep Mysteries.

Model | PER | LOC | ORG | MSC | All
---|---|---|---|---|---
XLM-RoBERTa Conneau et al. (2019) | 16 | 0 | 3 | 4 | 23
StanfordAIMI Chambon et al. (2023) | 0 | 0 | 1 | 18 | 19
ELECTRA Clark et al. (2020) | 10 | 0 | 1 | 10 | 21
WikiNEuRal Tedeschi et al. (2021) | 23 | 4 | 6 | 1 | 34
BERT Devlin et al. (2018) | 9 | 1 | 1 | 0 | 11
RoBERTaNER Baptiste (2022) | 1 | 0 | 0 | 17 | 18
BERT-CRF Souza et al. (2019) | 12 | 0 | 0 | 0 | 12
Flair Akbik et al. (2018) | 28 | 14 | 6 | 4 | 54
Spacy Honnibal and Montani (2017) | 21 | 11 | 7 | 18 | 57
Trankit Nguyen et al. (2021) | 25 | 15 | 2 | 2 | 44

Table 5: Statistics for the adventure book Candlekeep Mysteries. The NER tags
are as follows, Person: PER, Location: LOC, Organization: ORG, and
Miscellaneous: MSC

The testing approach for the NER models mirrors algorithm 1. Here, paragraphs
of input text are fed into the models without specific prompts. The resultant
output is refined by filtering out corrupted values (e.g., ”Strahd Von
Zarovich” might be mistakenly split into two distinct names) and redundant
entries, before being transitioned into the JSON structure showcased in Figure
1.

During initial processing, NER models often produce numerous erroneous
outputs. These arise from factors like incomplete word detection,
missegmentation of terms, or misinterpretation of special characters. Such
discrepancies can be mitigated using string manipulations and by cross-
referencing outputs with a pre-curated list of named entities.

Figure 2 displays entries that encountered corruption. These highlight
instances where NER models incorrectly processed and extracted entities from
the source material.

JSON object ⬇ { "entities": [ { "entity": "I-Person", "score": 0.5659823,
"index": 308, "word": "Fembris␣L#", "start": 1160, "end": 1162 }, { "entity":
"I-Person", "score": 0.51227564, "index": 309, "word": "rlancer", "start":
1162, "end": 1164 } ] } Figure 2: sample format of a corrupted JSON outputs

In the given example shown in Figure 2, the name ”Fembris Larlancer” is
erroneously divided into two distinct words, ”Fembris L#” and ”rlancer”, as a
result of corruption during the NER processing stage. This example underscores
the challenges faced during the entity extraction process and the need for
robust post-processing to ensure the accuracy and quality of the extracted
entities.

After removing corrupted and eligible named entities, duplicate entries must
be removed to do a proper comparison of performance between different models.
For this tuples of words in adjacent positions were generated and compared.
For example Mayor Lei Duvezin, Mayor Duvezin, Lei Duvezin and Duvezin all
refers to the same entity with the label Person. In cases such as above tuple
with most similarity matches will be retained as the named entity and
duplicates will be removed.

To visualize the raw named entity identification potential of each model, a
density plot was plotted with respect to count of identified named entities
with NER models. Following Figure 3 shows the density of named entities
recognized by each NER model. The hue represents the overlapping count ranges
of named entities identified in each source book.

Figure 3: Density plot for each model

Without training, NLP frameworks like Trankit Nguyen et al. (2021), Flair
Akbik et al. (2018), and Spacy Honnibal and Montani (2017) show a strong
baseline in entity recognition.

Model precision is key in performance evaluation. This is gauged by comparing
the true positive entities with actual named entities. This comparison can be
visually represented for each model across source books.

For a comprehensive model assessment across books, Kernel Density Estimation
(KDE) is used. It’s a non-parametric method estimating the probability density
function Terrell and Scott (1992):

$f(x)=\frac{1}{nh}\sum_{i=1}^{n}K\left(\frac{x-x_{i}}{h}\right)$

where:

  * •

xi are the data points

  * •

K is the kernel function, which is typically a Gaussian function or a uniform
function

  * •

h is the bandwidth, which determines the width of the kernel function and
controls the smoothness of the estimate

  * •

n is the number of data points

KDE calculates $f(x)$ through a summed kernel function $K(u)$, anchored at
data points $x_{i}$.

Figure 4 illustrates models’ efficacy over seven source books. A gradient near
1 signifies optimal performance.

In D&D, named characters, with their elaborate backstories, are central.
Assessing a model’s inclination to identify these characters over other
entities is vital. This inclination can be visualized by juxtaposing character
counts with total entities, contrasted against real metrics. Figure 5
delineates the frequency of character identification across all source books.
Meanwhile, Figure 5(a) and Figure 5(b) depict the distribution pertaining to
models and books, respectively.

Figure 4: Distribution plot for each model

In the D&D landscape, named characters, renowned for their intricate
histories, are paramount. Evaluating a model’s propensity to spot these
characters in relation to other entities is imperative due to the significant
role characters play in D&D narratives. This bias can be graphically
represented by mapping character counts against all identified entities and
contrasting them with authentic counts. By scrutinizing the named entity
counts from diverse NER models and comparing them to true values, one can
infer model behavior and efficacy. Figure 5 offers a glimpse into character
recognition frequency for different models across sourcebooks, with Figure
5(a) and Figure 5(b) charting the distributions for models and books
respectively.

(a) Models

(b) Adventure sourcebooks.

Figure 5: Frequency plots with respect to models and adventure sourcebooks

From Figure 5(b), we observe a consistent ratio between characters and other
named entities across books. This consistency allows us to downplay book
variability and focus on the insights from Figure 5(a). Notably, NLP
frameworks such as Spacy Honnibal and Montani (2017) and Flair Akbik et al.
(2018) exhibit more balanced frequency distributions, indicating a higher
character identification ratio. Although this might be unfavorable in certain
contexts, in this domain, aligning character identifications closely with
overall named entity values signals optimal performance. This suggests Spacy
and Flair perform exceptionally in an off-the-shelf setting.

Figure 6 showcases precision and recall metrics for each NER model. To
determine recall, we derived the true positive count from average unique named
entity counts, while the true count originated from LLM models, as outlined in
table 3. For precision, false positives were ascertained from misidentified
unique named entities on average.

The precision and recall values were averaged for each model across source
books, and plotted to offer a concise visualization of each NER model’s
performance.

Figure 6: Precision graph for different NER models

Evidently, Flair and Spacy outshine other NER models in precision and
performance, while Trankit Nguyen et al. (2021) excels in recall relative to
its precision.

##  5 Discussion

We undertook a Named Entity Recognition (NER) task on seven adventure books
from the esteemed Dungeons and Dragons (D&D) series. Our methodology involved
manual entity annotations in these books, which were subsequently verified
against outputs from three leading language models: Bloom, OpenLLaMA, and
Dolly.

Our annotation guidelines delineated entity types into categories like person,
organization, location, and misc. Ten NER models were subsequently employed to
gauge their efficacy in recognizing named entities within D&D. Among these,
Flair, Trankit, and Spacy emerged superior, mirroring findings from past NER-
centric studies. Conversely, StanfordDeID Chambon et al. (2023) and RoBERTaNER
Baptiste (2022) lagged in performance. A precision-centric analysis further
reiterated the dominance of Flair, Trankit, and Spacy over their counterparts.

The findings imply that while generic models can decently handle NER tasks in
specialized domains like D&D, performance inconsistencies exist across models.
Employing annotation guidelines bolsters consistency in entity recognition
across varied books and contexts. Moreover, incorporating large language
models for automated annotations can significantly mitigate the manual
intervention needed for comprehensive datasets, particularly in intricate
domains such as D&D.

However, our study bears certain caveats. We refrained from fine-tuning the
NER models specifically for D&D, so our findings are indicative of generic
model capabilities and might not capture the full potential of domain-specific
optimization. Our dataset, comprising just seven books, might not encompass
the depth and breadth of D&D narratives. The exclusive focus on Wizards of the
Coast publications could also inadvertently introduce stylistic biases.
Finally, while our study zeroes in on D&D as a fantasy subset, our insights
might not seamlessly extend to other literary domains with their unique
nuances.

##  6 Conclusion

Our exploration illuminates the remarkable potential of harnessing off-the-
shelf models for NER tasks within the D&D universe’s nuanced realm. Some
models showcase an impressive baseline in entity recognition for this domain
without extensive fine-tuning. However, there’s a compelling need for
continued research and refinement to tailor these models optimally for D&D’s
unique intricacies.

Additionally, our research serves as a foundational resource for future
inquiries. The dataset we’ve curated and our annotation guidelines stand as a
benchmark for gauging the efficiency of future NER models or techniques.
Consequently, our work not only reveals the current prowess of NER models
within the D&D context but also sets the stage for continued innovation at the
confluence of fantasy literature and artificial intelligence.

##  7 Future Works

Based on our findings and limitations, we suggest some directions for future
research. One direction is to fine-tune NER models on the D&D dataset and
comparing their performance with off-the-shelf models. Additionally, other
techniques such as transfer learning or domain adaptation could be explored to
improve the performance of NER models in the D&D domain. Another direction is
to use different data sources for NER in D&D, such as novels, comics,
podcasts, or video games. A third direction is to apply different evaluation
metrics for NER in D&D, such as F1-score, recall, accuracy, or error analysis.
Finally other aspects of NER in D&D can also be explored, such as entity
linking, coreference resolution, relation extraction, or sentiment analysis.

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# Quantitative study of enantiomer-specific state transfer

JuHyeon Lee,1 Johannes Bischoff,1 A. O. Hernandez-Castillo1, Boris
Sartakov,1,2 Gerard Meijer,1 and Sandra Eibenberger-Arias1 eibenberger@fhi-
berlin.mpg.de 1Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg
4-6, 14195 Berlin, Germany
2Prokhorov General Physics Institute, Russian Academy of Sciences,
Vavilovstreet 38, 119991 Moscow, Russia

###### Abstract

We here report on a quantitative study of Enantiomer-Specific State Transfer
(ESST), performed in a pulsed, supersonic molecular beam. The chiral molecule
1-indanol is cooled to low rotational temperatures (1-2 K) and a selected
rotational level in the electronic and vibrational ground state of the most
abundant conformer is depleted via optical pumping on the $S_{1}\leftarrow
S_{0}$ transition. Further downstream, three consecutive microwave pulses with
mutually perpendicular polarizations and with a well-defined duration and
phase are applied. The population in the originally depleted rotational level
is subsequently monitored via laser induced fluorescence (LIF) detection. This
scheme enables a quantitative comparison of experiment and theory for the
transfer efficiency in what is the simplest ESST triangle for any chiral
molecule, that is, the one involving the absolute ground state level,
$\ket{J_{K_{a}K_{c}}}=\ket{0_{00}}$. Moreover, this scheme improves the
enantiomer enrichment by over an order of magnitude compared to previous
works. Starting with a racemic mixture, a straightforward extension of this
scheme allows to create a molecular beam with an enantiomer-pure rotational
level, holding great prospects for future spectroscopic and scattering
studies.

††preprint: APS/123-QED

The two non-superimposable mirror images of a chiral molecule are referred to
as enantiomers. Their structures cannot be transformed into each other by pure
translation or rotation. Almost all physical properties of enantiomers are
identical – which makes them intrinsically challenging to separate. The
enantiomeric molecular pairs have identical energy levels except for a
theoretically predicted tiny energy difference $(\sim
10^{-11}\,\textrm{J/mol})$ induced by parity violating weak interactions [1,
2, 3]. Yet, their interactions with other chiral objects – chiral molecules
and chiral light – are dramatically different. Therefore, special care must be
taken when addressing molecular chirality in biological environments since the
functionality of biomolecules is dominated by the handedness of surrounding
molecules [4].

Since Pasteur first described optical activity, various techniques such as
optical rotation, circular dichroism, vibrational circular dichroism, and
Raman optical activity [5, 6, 7, 8] have been developed to determine
enantiomeric excess (EE) and absolute configurations of chiral molecules.
Those techniques require high-density samples, but still give rise to weak
signals because they rely on the inherently weak interaction of the molecules
with the magnetic field of the radiation. Over the past decade, instrumental
developments led to new methods which rely solely on electric dipole-allowed
transitions, including Coulomb explosion [9], photoelectron circular dichroism
[10, 11], and microwave three-wave mixing [12, 13]. All these techniques can
be applied in the gas phase and enable exploration of chiral molecules without
interference from any surrounding physical medium. In addition, it is possible
to gain insight on the interaction of the molecules with solvents by adding
these in a controlled manner [14]. Since chiral molecules retain their
handedness throughout physical processes, measurements of a sample’s
enantiomeric excess carried out in the gas phase hold for the sample in
solution or solid phase.

Beyond chiral analysis, chiral separation is a fundamental goal of chiral
studies. In the past two decades, several optical schemes to achieve quantum-
controlled chiral separation and purification have been suggested [15, 16,
17]. The chiral sensitivity of these methods is due to the fact that a $C_{1}$
chiral molecule necessarily has three non-zero electric dipole moment
components whose scalar triple products
$(\bm{\mu}_{a}\cdot(\bm{\mu}_{b}\times\bm{\mu}_{c}))$ are opposite in sign for
the two members of the enantiomeric pair [12, 13]. Therefore, it is possible
to gain insight into the chirality of a sample regardless of the initial
orientation of the molecules. These methods employ cyclic transitions in a
three-level system where the interference between two different paths can be
used to control the transfer of population in an enantiomer-specific fashion.

Recently, quantum-controlled chiral separation was experimentally demonstrated
using a method called enantiomer-specific state transfer (ESST) [18, 19]. ESST
utilizes three rotational states and three mutually orthogonally polarized
microwave (MW) pulses which address all the transitions between the states. By
using three resonant pulses with controlled phases, it is possible to create
interfering pathways to a given target state. The model of a 3-level cyclic
transition gives a qualitative understanding of ESST. However, to complete
this model, $M_{J}$ degeneracy has to be taken into account. While the spatial
degeneracy in ESST has been considered theoretically [20, 21], quantitative
comparison between experiment and theory is still lacking. For the
quantitative analysis of ESST, optimal control of the pulse sequence and pulse
length of the microwave excitations is necessary. So far, ESST has been
experimentally studied with sequences of partially overlapping MW pulses which
hampers characterizing the effects of individual MW pulses on the interrogated
molecules. In addition, poor enantiomeric enrichment makes the quantitative
analysis practically difficult. The largest enantiomeric enrichment achieved
to date is $\sim 6\%$ [19]. The two main factors that limit the size of the
population transfer are the thermal population of the three rotational energy
levels participating in ESST and the $M_{J}$ degeneracy of the involved
rotational states [20, 21].

Figure 1:  (a) Excitation scheme of the ESST experiment for the simplest triad
of rotational levels, using the z-axis for M-quantization. For polarization
directions as indicated, the allowed transitions between the levels $\ket{i}$
and $\ket{j}$ together with the electric dipole moments $\mu_{ij}$ and phases
$\varphi_{ij}$ are drawn in. Solid lines indicate transitions that participate
in ESST, dashed lines those that do not. (b) Redefined excitation scheme,
obtained by changing the basis set, resulting exclusively in two-level
systems.

The most rigorous comparison between theory and experiment can be attained by
studying the simplest triad which consists of the ground state $\ket{0_{00}}$
and two rotational levels with $J=1$ [22]. Therefore, the simplest triad
consists of either one of the following combinations: ($\ket{0_{00}}$,
$\ket{1_{01}}$, $\ket{1_{10}}$), ($\ket{0_{00}}$, $\ket{1_{11}}$,
$\ket{1_{10}}$) or ($\ket{0_{00}}$, $\ket{1_{01}}$, $\ket{1_{11}}$) in the
$\ket{J_{K_{a}K_{c}}}$ notation. The excitation scheme used for ESST in this
case is shown in Fig. 1(a) where we refer to the levels as $\ket{1}$,
$\ket{2}$ and $\ket{3}$. The wavefunctions associated with these levels,
$\ket{\Psi_{1}}$,$\ket{\Psi_{2}}$ and $\ket{\Psi_{3}}$, are characterized by
the projection of the total angular momentum on the $z$-axis. In this triad,
three resonant MW pulses are applied in the following order:
$\ket{2}\xleftarrow{\pi/2}\ket{1}\xrightarrow{\pi}\ket{3}\xrightarrow{\pi/2}\ket{2}$.
These three MW fields are linearly polarized and mutually orthogonal to each
other. Here, the $\pi/2$ pulse creates a 50:50 superposition between two
levels whereas the $\pi$ pulse inverts the population of two states.
Polarization directions and non-zero dipole moment components of the MW fields
are indicated next to each of the transitions in Fig. 1(a). The polarization
of the first $\pi/2$ pulse defines the quantization axis ($z$-direction), and
it allows $\Delta{M_{z}}=0$ transitions (blue solid line). The subsequent
$\pi$ and $\pi/2$ pulses are polarized along $x$\- and $y$-axes and thus the
selection rules are given by $\Delta{M_{z}}=\pm 1$. Therefore, the possible
transitions driven by the second MW pulse are
$\ket{\Psi_{1},M_{z}=0}\rightarrow\ket{\Psi_{3},M_{z}=\pm 1}$ (green solid
lines). The third MW pulse connects two states with $J=1$ where four
transitions are involved. Two of the transitions $\ket{\Psi_{3},M_{z}=\pm
1}\rightarrow\ket{\Psi_{2},M_{z}=0}$ (red solid lines) participate in ESST,
while the other two $\ket{\Psi_{3},M_{z}=0}\rightarrow\ket{\Psi_{2},M_{z}=\pm
1}$ (red dashed lines) do not.

Figure 2:  (a) Scheme of the experimental setup (not to scale). Jet-cooled
1-indanol is injected into the vacuum chamber through a pulsed valve. The
molecules travel through a multipass zone where they interact with the UV
depletion laser (Step I). Further downstream, three MW pulses with mutually
orthogonal polarizations are applied for ESST (Step II). The configuration of
these three horn antennae with their polarization directions is shown in the
inset. The molecules are interrogated by the same UV laser in the detection
region where the total laser induced fluorescence (LIF) intensity is measured
with a photomultiplier tube (PMT) (Step III). (b) Scheme of the electronic
excitation and emission processes. The most stable conformer of 1-indanol is
depicted together with the inertial axis system. (c) One of the simplest
triads of rotational levels of 1-indanol. Frequencies and types of each MW
field are marked. (d) Energy level scheme of the second triad used, consisting
of levels with $J=$ 2 and 3. Corresponding MW frequencies and types are also
depicted.

One can change the basis set and redefine the wavefunctions as follows:

$\displaystyle\ket{\Psi_{i}^{0}}$ $\displaystyle=$
$\displaystyle\ket{\Psi_{i},M_{z}=0}$ (1a) $\displaystyle\ket{\Psi_{i}^{\pm}}$
$\displaystyle=$
$\displaystyle\frac{1}{\sqrt{2}}\ket{\Psi_{i},M_{z}=-1}\pm\frac{1}{\sqrt{2}}\ket{\Psi_{i},M_{z}=+1}$
(1b)

with $i=1$, $2$ or $3$ for Eq.(1a) and $i=2$ or $3$ for Eq.(1b). The redefined
scheme is shown in Fig. 1(b) where levels can be described as $\ket{i^{0}}$
for $i=1$, $2$ or $3$ and $\ket{i^{\pm}}$ for $i=2$ or $3$. It can be seen
that: (i) the triangle $\ket{1^{0}}$, $\ket{2^{0}}$ and $\ket{3^{+}}$
participates in the ESST process; (ii) levels $\ket{2^{+}}$ and $\ket{3^{0}}$
constitute a closed two level system that only interacts with the last $\pi/2$
pulse; (iii) levels $\ket{2^{-}}$ and $\ket{3^{-}}$ are dark states and do not
interact with the applied field.

If relaxation processes are neglected, we can treat the ESST process as a
series of two level transitions [23]. The wavefunction of the two level system
formed by $\ket{1^{0}}$ and $\ket{2^{0}}$, for instance, can be described as
$a^{0}_{1}\ket{\Psi^{0}_{1}}+a^{0}_{2}\ket{\Psi^{0}_{2}}$, where $a^{0}_{1}$
and $a^{0}_{2}$ are the time-dependent probability amplitudes. The Bloch
equations for resonant excitation are [23]:

$\displaystyle i\hbar\derivative{a^{0}_{1}(t)}{t}$ $\displaystyle=$
$\displaystyle-\frac{\Omega_{12}}{2}e^{i\varphi_{12}}a^{0}_{2}(t)$ (2a)
$\displaystyle i\hbar\derivative{a^{0}_{2}(t)}{t}$ $\displaystyle=$
$\displaystyle-\frac{{\Omega}^{\ast}_{12}}{2}e^{-i\varphi_{12}}a^{0}_{1}(t)$
(2b)

where $\Omega_{12}=\mu_{12}\,\mathcal{E}_{12}/\hbar$ and $\varphi_{12}$ are
the Rabi frequency and phase of the electric field driving the transition,
respectively. Here, $\mu_{12}$ is the transition dipole moment and
$\mathcal{E}_{12}$ is the electric field amplitude. The general solution after
time $t$, for constant $\Omega_{12}$ and $\varphi_{12}$ is

$\displaystyle a^{0}_{1}(t)$ $\displaystyle=$ $\displaystyle
a^{0}_{1}(0)\cos\frac{\Theta(t)}{2}+i\frac{\mu_{12}}{|\mu_{12}|}e^{i\varphi_{12}}a^{0}_{2}(0)\sin\frac{\Theta(t)}{2}$
(3a) $\displaystyle a^{0}_{2}(t)$ $\displaystyle=$ $\displaystyle
i\frac{\mu^{\ast}_{12}}{|\mu_{12}|}e^{-i\varphi_{12}}a^{0}_{1}(0)\sin\frac{\Theta(t)}{2}+a^{0}_{2}(0)\cos\frac{\Theta(t)}{2}$
(3b)

where $\Theta(t)=|\Omega_{12}|\,t/\hbar$. In the simplest case where the two
upper levels $\ket{2}$ and $\ket{3}$ are empty and only the ground level
$\ket{1}$ is populated, taken as $a^{0}_{1}(0)=1$, the solution for the Bloch
equations after the first $\pi/2$ pulse are:

$\displaystyle a^{0}_{1}$ $\displaystyle=$ $\displaystyle\frac{1}{\sqrt{2}}$
(4a) $\displaystyle a^{0}_{2}$ $\displaystyle=$
$\displaystyle\frac{i\mu^{\ast}_{12}}{\sqrt{2}|\mu_{12}|}e^{-i\varphi_{12}}$
(4b)

After the $\pi$ pulse, population inversion occurs:

$\displaystyle a^{0}_{1}$ $\displaystyle=$ $\displaystyle 0$ (5a)
$\displaystyle a^{+}_{3}$ $\displaystyle=$
$\displaystyle\frac{i\mu^{\ast}_{13}}{\sqrt{2}|\mu_{13}|}e^{-i\varphi_{13}}$
(5b)

Finally, after the last $\pi/2$ pulse, the solutions are:

$\displaystyle a^{0}_{2}$ $\displaystyle=$ $\displaystyle
i\frac{\mu_{12}^{\ast}}{2|\mu_{12}|}e^{-i\varphi_{12}}(1\mp
ie^{i(\varphi_{12}+\varphi_{23}-\varphi_{13})})$ (6a) $\displaystyle
a^{+}_{3}$ $\displaystyle=$ $\displaystyle
i\frac{\mu_{13}^{\ast}}{2|\mu_{13}|}e^{-i\varphi_{13}}(1\pm
ie^{i(\varphi_{12}+\varphi_{23}-\varphi_{13})})$ (6b)

where the alternating signs for the interference term have to be used for
either of the enantiomers. As a result, ESST will be achieved both in levels
$\ket{2}$ and $\ket{3}$ whose populations will be given by
$n_{i}=|a^{-}_{i}|^{2}+|a^{+}_{i}|^{2}+|a^{0}_{i}|^{2}$ for $i=2,3$.

When there is thermal population in level $\ket{3}$, the closed two level
transition $\ket{3^{0}}\rightarrow\ket{2^{+}}$ transfers part of the
population from level $\ket{3}$ to level $\ket{2}$ with the last $\pi/2$
pulse. The thermal population in level $\ket{3}$ can be expressed as
$\mathcal{F}_{3}(T_{\text{rot}})$ times the population in level $\ket{1}$,
where $T_{\text{rot}}$ is the rotational temperature. The total populations in
levels $\ket{2}$ and $\ket{3}$ relative to the original population in level
$\ket{1}$ at the end of the ESST process are then given by:

$\displaystyle n_{2}$ $\displaystyle=$
$\displaystyle\frac{1}{2}(1\pm\sin(\varphi_{12}+\varphi_{23}-\varphi_{13}))+\frac{1}{6}\mathcal{F}_{3}(T_{\text{rot}})$
(7a) $\displaystyle n_{3}$ $\displaystyle=$
$\displaystyle\frac{1}{2}(1\mp\sin(\varphi_{12}+\varphi_{23}-\varphi_{13}))+\frac{1}{2}\mathcal{F}_{3}(T_{\text{rot}})$
(7b)

where $\pm$ and $\mp$ have to be used for either enantiomer. The closed two
level transition is thus seen to produce a phase-independent background which
for level $\ket{3}$ adds to the thermal population of the dark state.

Here we perform a quantitative study of ESST using 1-indanol. The molecules
are cooled in a supersonic expansion using Ar as carrier gas
$(T_{\text{rot}}\sim 2\,\textrm{K})$. We choose the $\ket{0_{00}}$,
$\ket{1_{01}}$, and $\ket{1_{10}}$ rotational states as target triad (Fig.
2(c)). The thermal populations of all the $M_{J}$ components of these three
levels are almost equal because their energy differences are small
$(<0.2\,\textrm{K})$. To increase the transfer efficiency of ESST, we
developed a new spectroscopic scheme consisting out of three essential Steps
(I-III) as illustrated in Fig. 2(a) and outlined below.

In Step I, a continuous-wave UV laser with an output power up to
$80\,\textrm{mW}$ and a bandwidth of $<1\,\textrm{MHz}$, is used to
selectively deplete the population of the target rotational level
$\ket{1_{01}}$ using the $\ket{2_{02}}\leftarrow\ket{1_{01}}$ R-branch line of
the origin band of the $S_{1}\leftarrow S_{0}$ electronic transition [24].
After UV excitation, the molecules predominantly radiate back to higher
vibrational levels and to other rotational levels in the $S_{0}$ state [25].
In this way, we optically pump and deplete all three $M_{J}$ components of the
$\ket{1_{01}}$ level. We reached up to $95\%$ depletion in our experiment; for
details, see the Supplemental Material.

Step II of the experiment consists of sequentially exciting three electric
dipole-allowed rotational transitions ($a$-type, $b$-type, and $c$-type) with
mutually orthogonal polarizations in the following manner:
$\ket{1_{01}}\xleftarrow{\pi/2}\ket{0_{00}}\xrightarrow{\pi}\ket{1_{10}}\xrightarrow{\pi/2}\ket{1_{01}}$.
To determine the optimal pulse duration of each MW radiation field, the
relevant Rabi oscillation curves are measured prior to the ESST measurement
(see the Supplemental Material). Typically, pulse lengths required for a $\pi$
pulse of each MW field are around $2\,\mu\textrm{s}$ and the ESST process is
completed in less than $6\,\mu\textrm{s}$. During this short time interval,
decoherence will not take place.

In Step III, laser induced fluorescence (LIF) detection is employed to probe
the population in the target rotational level $\ket{1_{01}}$. A small fraction
of the power ($10\%$) of the narrow–band UV laser is used to selectively
excite the same UV transition $S_{1}(2_{02})\leftarrow S_{0}(1_{01})$, probing
all three $M_{J}$ levels in the target state.

Figure 3:  The population of the target state $\ket{1_{01}}$ as a function of
the MW field phase $\varphi_{23}$ normalized to its original thermal
population. ESST results with depletion for (R)- and (S)-enantiomers are
marked in black and red, respectively. Predicted ESST curves are calculated
using Eq.(7a) and shown with dashed lines for each case. The ESST measurement
is also performed without depletion as depicted in gray. The slight overall
signal decrease with increasing phase corresponds to about $3\%$ signal
decrease during the measurement (about 15 minutes) and is included in the
fitting.

We perform separate measurements using enantiopure commercial samples of (R)-
and (S)-1-indanol with a stated $99\%$ purity. In order to map enantiomer
selectivity on the ESST signal, relative phases of the applied MW fields have
to be varied as expressed in Eq.(7). For this, we keep the phases of the first
two MW fields, $\varphi_{12}$ and $\varphi_{13}$, fixed and change the phase
$\varphi_{23}$ in steps of 20 degrees from 0 to 720 degrees in our
measurement. In Fig. 3, normalized ESST results are shown for the
(R)-enantiomer in black and the (S)-enantiomer in red (details on the
measurement of the normalized ESST signal are given in the Supplemental
Material). As expected, the phase of the two curves differs by 180 degrees.
From the best sine fits, the experimental amplitudes and offsets are
determined to be 0.135(6) and 0.343(4) for the (R)-enantiomer (black solid
line) and 0.128(9) and 0.340(6) for the (S)-enantiomer (red solid line),
respectively. These parameters are commonly used to determine enantiomer
enrichment ($\epsilon$) as $\epsilon/2=\textrm{amplitude/offset}$ [18].
According to this definition, we achieved 79$\%$ and 75$\%$ enantiomer
enrichment for the (R)- and the (S)-enantiomers, respectively. The same ESST
measurement for the (R)-enantiomer is also measured without depletion as
depicted in gray in Fig. 3. The comparison of both measurements on the same
$y$-scale shows the significant improvement due to the depletion process.

The dashed lines in Fig. 3 show calculated normalized ESST curves for each
case. We remove the population only from the level $\ket{1_{01}}$, whereas the
level $\ket{1_{10}}$ retains its Boltzmann population. As discussed before,
the $M_{z}$ = 0 level of $\ket{1_{10}}$ introduces background signal due to
the last $\pi$/2 pulse that connects the $\ket{1_{01}}$ and $\ket{1_{10}}$ via
a $b$-type transition. In this case, the population of the target state
$\ket{1_{01}}$ is given by Eq.(7a). Note that, in Eq.(7a), the population is
normalized to the original population in the $\ket{0_{00}}$ level, whereas the
simulation shown here is normalized to the population in the $\ket{1_{01}}$
level, assuming a Boltzmann distribution with $T_{\text{rot}}=2\,\textrm{K}$.
The predicted amplitude of the depleted ESST signal is 0.175 with an offset of
0.336. Comparison of the experiment with simulation shows that, for both
enantiomers, the amplitude of the experimental value is $\sim 20\%$ smaller
than expected while the offset agrees very well. The discrepancies between
experiment and simulation are most likely caused by the imperfect
orthogonality between the three microwave fields. The distance of the horn
antennae to the molecular beam axis is about the same as the wavelength of the
MW radiation, and we are therefore in the near-field limit where the
polarization of the microwave field is not very well defined yet. Moreover,
reflections of the MW radiation in the vacuum chamber cannot be completely
avoided, also contributing to field imperfections. In addition to these
effects, the stated $\sim 1\%$ impurity in our sample will contribute to the
observed difference.

Figure 4:  Population of the target state $\ket{3_{13}}$ as a function of the
MW field phase $\varphi_{23}$ normalized to its original thermal population.
ESST results for the (R)-enantiomer with and without depletion are marked in
black and gray, respectively. Predicted ESST curves are simulated and shown
with dashed lines for each case.

Another triad of transitions involving the rotational energy levels,
$\ket{3_{13}}$, $\ket{2_{12}}$, and $\ket{3_{22}}$ (Fig. 2(d)), is chosen for
the ESST measurement. This triad involves higher $M_{J}$ degeneracy and higher
MW frequencies due to the higher $J$ levels. Three resonant MW pulses are
applied in the following way:
$\ket{3_{13}}\xleftarrow{\pi/2}\ket{2_{12}}\xrightarrow{\pi}\ket{3_{22}}\xrightarrow{\pi/2}\ket{3_{13}}$.
For this triad, the optimum pulse durations are determined from the first
maximum in the Rabi oscillation curves, providing ”effective” $\pi$ and
$\pi/2$ pulse durations (see Supplemental Material). We measure the ESST
signal by varying $\varphi_{23}$ in steps of 20 degrees from 0 to 720 degrees
while the other two phases are kept fixed. In Fig. 4, normalized ESST results
are shown for the (R)-enantiomer with and without depleting the target state
$\ket{3_{13}}$ in black and gray, respectively. The simulated results are
shown with dashed lines for each case. We achieved $\epsilon=0.98$ for the
measurement with depletion. The ESST curves in this triad show an increased
contrast relative to Fig. 3 because the energy separation between the
$J$-levels is larger and because a larger fraction of all the involved $M_{J}$
levels can participate in the ESST process.

In summary, we quantitatively studied the ESST method by targeting the
simplest triad of rotational transitions that is available for any chiral
molecule. We observed $\sim 20\%$ lower amplitude of the ESST signal than
theoretically expected which we attribute to the imperfect polarization of the
MW fields. Depleting a target rotational state prior to the ESST process
enables significant enhancement in enantiomer enrichment. The enantiomeric
enrichment achieved in our measurement is $98\%$ which is more than an order
of magnitude larger than previously reported values. When removing thermal
populations of the two upper levels in the simplest triad, perfect ESST
efficiency can be achieved, and experiments are underway to demonstrate this.
Starting with a racemic mixture, this scheme allows to create a molecular beam
with an enantiomer-pure rotational level, holding great prospects for future
spectroscopic and scattering studies.

###### Acknowledgements.

We thank Marco De Pas, Henrik Haak, Uwe Hoppe, Sebastian Kray, Johannes
Seifert and Stefan Truppe as well as the teams of the mechanical and
electronics workshop of the Fritz-Haber-Institut for excellent technical and
laser support.

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