# MuGI: Enhancing Information Retrieval through Multi-Text Generation
Integration with Large Language Models

Le Zhang 1,2, Qian Yang1,2, Yihong Wu2
1 Mila - Québec AI Institute
2 Université de Montréal

###### Abstract

Large Language Models (LLMs) have become a cornerstone in language
technologies, notably in information retrieval (IR). Benefiting from vast
training datasets, LLMs excel in developing nuanced understandings and
processing of natural language queries, a crucial capability required by IR.
Motivated by this, we propose a straightforward yet potent framework, Multi-
Text Generation Integration (MuGI), designed to bolster IR systems. MuGI
leverages LLMs to produce multiple pseudo references, integrating them with
queries through a dynamic repetition strategy applicable to both sparse and
dense retrievers. This training-free approach demonstrates superior
performance over traditional query expansion methods. Specifically, BM25
enhanced with MuGI outperforms advanced dense retrievers like ANCE, showing a
remarkable improvement of over 18% on the TREC DL dataset and 7.5% on BEIR.
MuGI establishes a swift and high-fidelity information retrieval pipeline,
enabling a compact 110M model to exceed the performance of larger 7B models in
in-domain tests and effectively narrowing the gap in out-of-distribution
scenarios. Our code and all generated references are made available at
https://github.com/lezhang7/Retrieval_MuGI

MuGI: Enhancing Information Retrieval through Multi-Text Generation
Integration with Large Language Models

Le Zhang 1,2, Qian Yang1,2, Yihong Wu2 1 Mila - Québec AI Institute 2
Université de Montréal

##  1 Introduction

Information retrieval (IR) is crucial for extracting relevant documents from
large databases, serving as a key component in search engines, dialogue
systems Yuan et al. (2019); Qian et al. (2021), question-answering platforms
Qu et al. (2020); Zhang et al. (2023b); Yang et al. (2023), recommendation
systems Fan et al. (2023); Zhang et al. (2023a), and Retrieval Augmented
Generation (RAG) Lewis et al. (2021); Izacard and Grave (2020); Zhang et al.
(2022); Liu (2022). IR strategies are broadly classified into sparse retrieval
and neural dense retrieval. Sparse retrieval, exemplified by BM25 Robertson et
al. (1994), calculates lexical overlaps, noted for its speed and
generalization capabilities. In contrast, dense retrieval utilizes text
embeddings from language models to perform minimum inner product searches. An
efficient IR system typically employs a two-stage process: initial retrieval
with a sparse retriever for a balance of efficiency and coverage, followed by
a re-ranking phase for refined ordering of results.

Figure 1: Performance Comparison: AMBv2 denotes the all-mpnet-base-v2 (110M)
model. In-Domain results represent averages from TREC-DL 19/20 datasets, while
OOD results are averaged across nine datasets from the BEIR benchmark. MuGI
significantly enhances BM25 and enables the smaller 110M model to outperform
the larger 7B model in in-domain evaluations, and it substantially narrows the
performance gap in OOD scenarios.

Recent advancements in Large Language Models (LLMs), notably ChatGPT, have
shown remarkable proficiency in language understanding, generation,
generalization, and reasoning Brown et al. (2020); Touvron et al. (2023).
Motivated by this progress, some studies Sun et al. (2023); Ma et al. (2023b);
Gao et al. (2022); Wang et al. (2023b) devise zero-shot techniques that
leverage LLMs for Information Retrieval (IR). These approaches generally
encompass two strategies: direct re-ranking and query rewriting. Direct Re-
ranking involves using LLMs to re-rank documents based on the query Sun et al.
(2023). However, this strategy is constrained to the re-ranking phase due to
the inherent length limitations of LLMs. Conversely, Query Re-writing aims to
resolve ambiguity and vocabulary mismatches by enhancing queries with LLM-
driven expansions Gao et al. (2022); Wang et al. (2023b).

Building on the efficacy and efficiency of LLM-based query re-writing, we
introduce the novel Multi-Text Generation Integration (MuGI), which further
harnesses the generative capabilities of LLMs. MuGI involves prompting LLMs to
generate multiple pseudo-references, which are then dynamically integrated
with the original query to enhance retrieval effectiveness. We present two
applications of MuGI: MuGI re-rank, applying MuGI exclusively for re-ranking,
and MuGI pipeline, utilizing MuGI in both initial retrieval and re-ranking
phases. Extensive experiments show that MuGI notably improves the efficacy of
both sparse and dense retrievers without the need for training. These findings
confirm MuGI’s superiority over existing Query Re-writing strategies in both
in-domain and out-of-distribution (OOD) contexts. MuGI allows lexical-based
retrieval methods, such as BM25, to outperform dense retrievers like ANCE and
DPR. Furthermore, MuGI enables a modestly sized 110M parameter retriever to
surpass the performance of more extensive 7B models in in-domain evaluations
and effectively reduce performance disparities in OOD scenarios.

##  2 Related Work

#### Information Retrieval

represents a pivotal discipline within computational linguistics, focused on
efficiently and effectively retrieving information in response to user
queries. This field has seen the development of various models and techniques,
with the Best Matching 25 (BM25) algorithm Robertson et al. (1994) standing
out as a cornerstone. BM25 advances beyond previous probabilistic models by
integrating document length normalization and non-linear term frequency
scaling, thereby refining the process of aligning queries with documents based
on relevance. The introduction of deep learning heralded the arrival of dense
retrievers like DPR Karpukhin et al. (2020), leveraging deep neural networks
to identify semantic correlations between queries and documents. Recent
advancements by Wang et al. (2023a); Ma et al. (2023a) have further enhanced
retrieval precision by optimizing generative LLMs for IR tasks, marking a
significant leap in semantic comprehension over previous approaches.

Furthermore, IR’s scope has expanded to encompass groundbreaking domains such
as RAG Lewis et al. (2021); Guu et al. (2020); Borgeaud et al. (2022). RAG
models, which improve generative models through the integration of dynamic
information retrieval, underscore IR’s evolving landscape. These models
notably elevate the quality of content generation, illustrating IR’s capacity
to transform the manner in which digital information is accessed and utilized.
This progression highlights IR’s critical role in continually enhancing
information discovery and use, indicating a move towards more advanced
retrieval systems.

Figure 2: Method overview of HyDE and query2doc, ice cube indicate models are
frozen.

#### LLMs for IR

Recent advancements have explored the potential of LLMs to bolster IR systems
Zhu et al. (2023). The application of LLMs in IR can be categorized into two
main streams: zero-shot IR using LLMs and employing LLMs as retrieval models.
For zero-shot IR, a common method is to utilize LLMs for document ranking
based on queries Sun et al. (2023); Ma et al. (2023b) or for relevance
assessment Sachan et al. (2022). Although effective, this approach is limited
by the LLMs’ input length constraints, making it more suitable for re-ranking
tasks. An alternative zero-shot IR strategy is Query Rewriting, where
techniques such as HyDE Gao et al. (2022), query2doc Wang et al. (2023b), and
LameR Shen et al. (2023) leverage LLMs to create pseudo-references or
potential answers, enhancing queries for better retrieval outcomes. Another
line of research focuses on using LLMs to generate training datasets Bonifacio
et al. (2022); Izacard et al. (2021); Wang et al. (2023a); Jeronymo et al.
(2023) and directly implementing LLMs as retrieval models Wang et al. (2023a);
Li et al. (2023).

MuGI represents an approach within the realm of Query Rewriting, utilizing
LLMs for query enhancement and thus suitable for both initial retrieval and
re-ranking phases. Different from HyDE Gao et al. (2022) and Query2Doc Wang et
al. (2023b), which primarily rely on singular text expansion (see fig. 2),
MuGI integrates multiple texts for query enhancement, as illustrated in fig.
3. Benefiting from a richer knowledge base, MuGI outperforms existing
techniques by capturing essential keywords more effectively and enriching the
background context through a adaptive query reweighting strategy. Furthermore,
MuGI excels in both in-domain and out-of-distribution evaluations,
underscoring its comprehensive applicability and effectiveness across various
retrieval contexts.

##  3 Method

###  3.1 Preliminaries

Retrieval methodologies can broadly be categorized into two distinct
approaches: lexical-based retrieval and dense retrieval.

#### Non-parametric Lexical-based Methods

The most emblematic approach among non-parametric lexical-based methods is
BM25, which primarily utilizes term frequency (TF) and inverse document
frequency (IDF) to estimate the relevance of documents to a given search
query. The relevance score of document $D$ for query $q$, denoted as
$\text{Score}(D,q)$, is determined by the following equation:

$\displaystyle\sum_{i=1}^{n}IDF(q_{i})\cdot$
$\displaystyle\frac{f(q_{i},D)\cdot(k_{1}+1)}{f(q_{i},D)+k_{1}\cdot(1-b+b\cdot\frac{|D|}{\text{avgdl}})}$
(1)

where , $f(q_{i},D)$ denotes the frequency of term $i$ in document $D$,
$IDF(q_{i})$ is the inverse document frequency of term $i$, $|D|$ represents
the length of the document, avgdl is the average document length in the
corpus, $k_{1}$ and $b$ are free parameters typically chosen via
experimentation.

#### Dense Retrieval Methods

Moving beyond term matching, dense retrieval leverages deep learning models to
understand the semantic similarity between queries and documents. This kind of
methods exploits a language model $f$ to encode both queries and documents
into embedding in a high-dimensional space. The similarity between a query and
a document is then computed using the inner product of their embedding, thus
capturing nuances beyond keyword overlap:

$\text{Similarity}(q,D)=f(q)\cdot f(D)^{T}$ (2)

Dense retrieval enables retrieving documents that are semantically related to
the query, irrespective of the exact terms used.

Both BM25 and dense retrieval methods present unique benefits in the realm of
IR. BM25 stands out for its speed and robust generalization to out-of-
distribution settings Thakur et al. (2021), making it a dependable option for
initial retrieval within extensive databases. Dense retrieval methods excel in
identifying semantic relationships between queries and documents. However,
these methods fall short in speed and generalization due to the reliance on
complex neural network models. Consequently, dense retrieval methods are often
preferred during the re-ranking stage.

###  3.2 Multi-Text Generation Integration

Figure 3: Method overview of MuGI. Left part is initial retrieval using sparse
retriever BM25, right part indicates re-ranking output from first stage given
enhance Dense Query using a dense retriever.

Recognizing that both lexical-based and dense retrieval methods depend on a
certain degree of information overlap between the query and document, we
introduce the Multi-Text Generation Integration (MuGI) method. This innovative
approach aims to augment the query’s information content by leveraging
multiple samplings from LLMs. MuGI enriches queries with additional background
information and broadens the keyword vocabulary to encompass out-of-domain
terms, thereby bridging the semantic gap between queries and documents on both
retrieval and re-ranking phases. Figure 3 provides an illustrative overview of
MuGI.

Figure 4: Zero-Shot Prompting for Relevant Passage Generation: This approach
differs from the few-shot methods in query2doc. It emphasizes generating
contextually relevant and diverse content to enhance background knowledge
density, without requiring answer passages, through multiple generations.

Upon receiving a query q, MuGI initially applies a zero-shot prompt (see fig.
4) technique to generate a set of pseudo-references, denoted as
$R=\\{r_{1},r_{2},r_{3},...,r_{n}\\}$. This strategy diverges from the
query2doc approach by omitting few-shot examples, thereby broadening the
diversity and enhancing the relevance of the generated text. Both sparse and
dense retrievers are improved through the integration of the query with these
pseudo-references:

#### MuGI for Sparse Retriever

This component is responsible for assessing relevance through the analysis of
lexical overlaps between the query and the references. Given the typically
longer length of documents compared to queries, achieving a careful balance to
ensure each element’s appropriate influence is crucial (Wang et al., 2023b;
Shen et al., 2023). The variability in the length of queries and the generated
passages renders a static rate of repetition ineffective. Therefore, for the
sparse retriever, exemplified by tools like BM25 that function based on
discrete word counts, we employ an adaptive strategy in repeating queries.
This strategy is calibrated to the length of the pseudo-references, guided by
a proportionality ratio $p$. The overarching goal is to enrich the query with
extensive background knowledge, thereby improving its representation and the
retrieval effectiveness. Different from the previous methods Wang et al.
(2023b); Gao et al. (2022) that rely on a single pseudo reference, MuGI
integrates multiple pseudo references to substantially enrich the query. The
query format adapted for the sparse retriever thus incorporates these elements
in the following manner:

$\displaystyle
t=\left\lfloor\frac{\mathrm{len}(r_{1}+r_{2}+\ldots+r_{n})}{\mathrm{len}(q)\cdot
p}\right\rfloor$ (3) $\displaystyle
q^{+}_{sparse}=\text{concat}(\\{q\\}*t,r_{1},r_{2},r_{3}...,r_{n})$ (4)

#### MuGI for Dense Retriever

MuGI also benefits the dense retrievers in Reranking stage. As dense
retrievers are neural-based models that ascertain semantic relevance through
the inner product of text embeddings, they do not necessitate a balance
between the query and references. The query format for dense retrieval is
structured as follows:

$\displaystyle q^{+}_{dense}=\text{concat}(q,r_{1},r_{2},r_{3},...,r_{n})$ (5)

#### MuGI Pipeline:

Direct retrieval from databases using dense retrievers is often slow and
impractical due to the computational demands of generating text embeddings
with neural language models. An efficient and effective strategy involves
initially retrieving coarse results via sparse retrieval, followed by a fine-
grained reordering using a robust neural dense retriever. Leveraging the
benefits our MuGI method offers at both stages, we have developed a pipeline.
This pipeline initially retrieves the top 100 references from the database
using $q^{+}_{sparse}$ on sparse retrieval. Subsequently, these 100 references
are re-ranked using $q^{+}_{dense}$ on a small dense retrieval model.

##  4 Experiments

###  4.1 Setup

Methods | In-domain | Out-of-Domain
---|---|---
DL19 | DL20 | Covid | NFCorpus | Touche | DBPedia | SciFact | Signal | News | Robust04 | BEIR (Avg)
Supervised
ANCE | 64.5 | 64.6 | 65.4 | 23.7 | 24.0 | 28.1 | 50.7 | 24.9 | 38.2 | 39.2 | 36.8
DPR | 62.2 | 65.3 | 33.2 | 18.9 | 13.1 | 26.3 | 31.8 | 15.5 | 16.1 | 25.2 | 22.5
DocT5query | 64.2 | - | 71.3 | 32.8 | 34.7 | 33.1 | 67.5 | 30.7 | 42.0 | 43.7 | 44.5
Unsupervised
HyDE | 61.3 | 57.9 | 59.3 | - | - | 36.8 | 69.1 | - | 44.0 | - | -
BM25 | 50.6 | 48.0 | 59.5 | 30.8 | 44.2 | 31.8 | 67.9 | 33.1 | 39.5 | 40.7 | 43.4
\+ query2doc | 66.2 | 62.9 | 72.2 | 34.9 | 39.8 | 37.0 | 68.6 | - | - | - | -
\+ LameR | 67.1 | 62.7 | 72.5 | - | - | 38.7 | 73.5 | - | 49.9 | - | -
\+ MuGI | $\textbf{70.4}^{\text{+19.8}}$ | ${\textbf{64.4}}^{\text{+16.4}}$ | $\textbf{72.9}^{\text{+13.4}}$ | $\textbf{37.4}^{\text{+6.6}}$ | $\textbf{46.1}^{\text{+1.9}}$ | $\textbf{42.7}^{\text{+10.9}}$ | $\textbf{74.0}^{\text{+6.1}}$ | $\textbf{36.0}^{\text{+2.9}}$ | $\textbf{50.0}^{\text{+10.5}}$ | $\textbf{49.2}^{\text{+8.5}}$ | $\text{{51.0}}^{\text{+7.6}}$

Table 1: Retrieval Results (nDCG@10) Best performing overall system(s) are
marked bold.

#### Implementation Details

We use passages from ChatGPT3.5-turbo for dense queries and ChatGPT4-turbo for
sparse retrieval111The version of GPT selected is 1106, aiming for enhanced
performance. We adhere to the default hyperparameters provided by GPT for
passage generation. For each query, five passages are generated and
concatenated with the original query to construct an expanded query for BM25
retrieval, wherein we set the proportionality ratio $p$ in eq. 3 to 5. For
dense queries, given the maximum input token limit of 512 for dense queries,
we concatenate three passages with the original query. We select a diverse
array of dense retrieval models as our backbone, including ALL-MPNET-BASE-V2,
BGE-Large-EN-v1.5, Ember-v1, and  E5-Mistral-instruct, with parameter counts
ranging from 110M to 3B. For evaluation, we use nDCG@10 as the metric and
perform re-ranking on the top 100 results from the initial retrieval phase.
All experiments are conducted using the Pyserini toolkit Lin et al. (2021).

#### Datasets

We evaluate MuGI on the TREC DL19 Craswell et al. (2020) and DL20 Craswell et
al. (2021) datasets for in-domain analysis, and on nine low-resource datasets
from BEIR Thakur et al. (2021) for out-of-distribution (OOD) evaluation,
following Sun et al. (2023).

###  4.2 Retrieval Results

The initial retrieval phase requires pre-indexing of all passages and queries
Lin et al. (2021) and using efficient search tools such as Faiss Johnson et
al. (2019). Given the computational costs associated with deploying large
models, this stage pragmatically focuses on the assessment of compact dense
models. Specifically, we evaluate the efficiency and effectiveness of models
such as DPR Karpukhin et al. (2020) and ANCE Xiong et al. (2020), which offer
a balance between performance and computational demand. We also compare MuGI
with other query rewriting methods, including HyDE Gao et al. (2022),
Query2Doc Wang et al. (2023b), and LameR Shen et al. (2023) The results are
shown in Table 1. In the in-domain evaluation, MuGI demonstrates superior
performance compared to all baseline models and existing query rewriting
techniques. Specifically, it enhances the performance of BM25 on the TREC DL
19/20 dataset by 19.8% and 17% in nDCG@10, respectively. In OOD scenarios,
dense retrievers generally exhibit a decline in performance compared to in-
domain evaluations, a trend likely influenced by their poor generalization
capabilities and the short, ambiguous nature of queries found in the BEIR
benchmark Thakur et al. (2021). In contrast, augmenting BM25 with query
rewriting techniques demonstrates robust performance, with the rewritten
queries introducing key vocabularies that aid BM25 in more effectively
identifying relevant passages. Notably, MuGI further enhances BM25’s
generalization capabilities, surpassing all other query rewriting methods.
MuGI achieves an average nDCG@10 of 51% across nine low-resource BEIR
benchmarks, marking a 7.6% improvement over the base BM25 and outperforming
other query-rewriting methods across all datasets. These findings also
highlight the significant potential of non-parametric methods in OOD retrieval
tasks, corroborating observations made in prior studies (Thakur et al., 2021;
Sun et al., 2023) The improvements in both in-domain and OOD evaluation are
attributed to MuGI’s proficiency in generating essential vocabularies through
multiple samplings from LLMs, coupled with its innovative adaptive query-
references reweighting strategies.

###  4.3 Rerank Results

Methods | #Param | In-domain | Out-of-Domain
---|---|---|---
DL19 | DL20 | Covid | NFCorpus | Touche | DBPedia | SciFact | Signal | News | Robust04 | BEIR(Avg)
Dense Retriever + BM25 re-rank
monoBERT | 340M | 70.5 | 67.3 | 70.0 | 36.9 | 31.8 | 41.9 | 71.4 | 31.4 | 44.6 | 49.4 | 47.2
monoT5 | 220M | 71.5 | 67.0 | 78.3 | 37.4 | 30.8 | 42.4 | 73.4 | 31.7 | 46.8 | 51.7 | 49.1
monoT5 | 3B | 71.8 | 68.9 | 80.7 | 39.0 | 32.4 | 44.5 | 76.6 | 32.6 | 48.5 | 56.7 | 51.4
Cohere Rerankv2 | API | 73.2 | 67.1 | 81.8 | 36.4 | 32.5 | 42.5 | 74.4 | 29.6 | 47.6 | 50.8 | 49.5
Dense Retriever + LLM API (Query Re-writing)
E5-Mistral-instruct | 7B |  |  |  |  |  |  |  |  |  |  |
\+ BM25 re-rank |  | 70.0 | 66.7 | 81.4 | 36.0 | 29.5 | 42.4 | 75.8 | 32.8 | 53.0 | 52.8 | 50.5
\+ MuGI re-rank |  | 74.7 | 72.0 | 85.3 | 40.0 | 31.2 | 46.9 | 76.7 | 33.3 | 54.3 | 57.0 | $\textbf{53.1}^{\text{+2.6}}$
\+ MuGI pipeline |  | $\text{74.5}^{\text{+4.5}}$ | $\textbf{73.5}^{\text{+1.5}}$ | $\textbf{87.3}^{\text{+5.9}}$ | $\text{39.6}^{\text{+3.6}}$ | $\textbf{31.2}^{\text{+1.7}}$ | $\text{45.9}^{\text{+3.5}}$ | $\text{76.4}^{\text{+0.6}}$ | $\textbf{33.4}^{\text{+0.6}}$ | $\text{53.3}^{\text{+0.3}}$ | $\textbf{57.2}^{\text{+4.4}}$ | $\text{53.0}^{\text{+2.5}}$
Ember-v1 | 335M |  |  |  |  |  |  |  |  |  |  |
\+ BM25 re-rank |  | 71.3 | 64.5 | 80.3 | 35.8 | 31.6 | 41.7 | 75.2 | 32.0 | 48.8 | 51.3 | 49.6
\+ MuGI re-rank |  | 75.9 | 71.0 | 84.9 | 38.8 | 33.5 | 46.1 | 76.7 | 32.2 | 49.6 | 54.3 | $52.0^{\text{+2.4}}$
\+ MuGI pipeline |  | $\textbf{76.8}^{\text{+5.3}}$ | $\textbf{71.1}^{\text{+6.6}}$ | $\text{83.0}^{\text{+2.7}}$ | $\text{38.6}^{\text{+2.8}}$ | $\text{32.2}^{\text{+0.6}}$ | $\text{45.2}^{\text{+3.5}}$ | $\textbf{76.9}^{\text{+1.7}}$ | $\textbf{32.3}^{\text{+0.3}}$ | $\textbf{51.5}^{\text{+2.7}}$ | $\textbf{56.0}^{\text{+4.7}}$ | $\textbf{52.0}^{\text{+2.4}}$
BGE-Large-EN-v1.5 | 335M |  |  |  |  |  |  |  |  |  |  |
\+ BM25 re-rank |  | 70.7 | 64.9 | 79.6 | 35.4 | 29.8 | 41.7 | 74.1 | 28.8 | 49.4 | 49.2 | 48.5
\+ MuGI re-rank |  | 75.0 | 70.6 | 83.5 | 37.5 | 30.3 | 45.9 | 74.7 | 28.8 | 49.9 | 51.5 | $\text{50.3}^{\text{+1.8}}$
\+ MuGI pipeline |  | $\textbf{77.2}^{\text{+6.5}}$ | $\textbf{71.3}^{\text{+6.4}}$ | $\textbf{83.3}^{\text{+3.7}}$ | $\textbf{39.2}^{\text{+3.8}}$ | $\textbf{30.4}^{\text{+0.6}}$ | $\textbf{46.0}^{\text{+4.3}}$ | $\textbf{75.4}^{\text{+1.3}}$ | $\text{28.8}^{\text{+0.0}}$ | $\textbf{53.2}^{\text{+3.8}}$ | $\textbf{53.3}^{\text{+4.1}}$ | $\textbf{51.2}^{\text{+2.7}}$
AMB-v2 | 110M |  |  |  |  |  |  |  |  |  |  |
\+ BM25 re-rank |  | 68.3 | 64.2 | 75.8 | 34.3 | 28.9 | 37.6 | 68.0 | 29.8 | 52.0 | 51.4 | 47.2
\+ query2doc |  | 70.2 | 66.5 | 78.3 | 34.4 | 26.4 | 39.2 | 67.6 | 28.9 | 52.2 | 52.7 | 47.5
\+ MuGI re-rank |  | 73.5 | 69.3 | 81.3 | 34.4 | 26.7 | 41.2 | 67.6 | 28.7 | 54.2 | 55.4 | $\text{48.7}^{\text{+1.5}}$
\+ MuGI pipeline |  | ${\textbf{77.1}}^{\text{+8.8}}$ | $\textbf{\text{74.2}}^{\text{+10.0}}$ | ${\textbf{81.3}}^{\text{+5.5}}$ | $\textbf{37.0}^{\text{+2.7}}$ | $\textbf{28.9}^{\text{+0.0}}$ | $\textbf{44.0}^{\text{+6.4}}$ | $\textbf{70.1}^{\text{+2.1}}$ | $\textbf{29.8}^{\text{+0.0}}$ | $\textbf{53.9}^{\text{+1.9}}$ | $\textbf{57.0}^{\text{+5.6}}$ | $\textbf{{50.3}}^{\text{+3.1}}$

Table 2: Re-rank Results (nDCG@10) on TREC and BEIR. Best performing are
marked bold. All modelsre-rank the same BM25 top-100 passages if otherwise
stated. MuGI re-rank on BM25+MuGI top 100 outputs. MuGI pipeline suggests
application of MuGI on both initial retrieval and dense retrieval.

Re-ranking is a process that reorders passages retrieved by sparse retrievers
using sophisticated dense models. Unless stated otherwise, we re-rank the top
100 passages retrieved by BM25. We incorporate leading baselines from the MTEB
Re-ranking leaderboard Muennighoff et al. (2022), including MonoT5 Nogueira et
al. (2020), E5base Wang et al. (2022), Cohere Re-rank-v2, Ember-v1, BGE Xiao
et al. (2023), and e5-mistral-7b-instruct Wang et al. (2023a). We introduce
two applications of MuGI: MuGI re-rank, for re-ranking BM25+MuGI’s top 100
outputs, and MuGI pipeline, for using MuGI in both initial retrieval and re-
ranking stages (as detailed in section 3.2).

The results in table 2 highlight MuGI’s significant impact on re-ranking
performance in two key aspects. Firstly, the BM25 and MuGI combination
(BM25+MuGI) enhances initial ranking results, thereby improving re-ranking
efficiency. Secondly, applying MuGI in the re-ranking stage yields superior
outcomes, consistently enhances all strong dense retrieval models. Notably,
integrating AMB-v2 with the MuGI pipeline achieves the highest performance in
in-domain (IID) evaluation, with over a 9% improvement compared to basic re-
ranking approaches. In OOD scenarios, AMB-v2 with MuGI re-rank shows a 1.5%
improvement over basic re-ranking (+BM25 re-rank). The MuGI pipeline further
enhances performance to 50.3%, a 3.1% increase, surpassing most larger
supervised models with basic re-ranking. We observe that MuGI has a lesser
effect on instruction-tuned models. Larger models such as E5-Mistral-instruct
and Ember-v1, trained with dataset containing prefix instructions, are less
compatible with generated references, leading to more modest improvements
compared to models like AMB-v2 that are not instruction-tuned. MuGI
demonstrates significant advancements in both in-domain and OOD evaluations.
Remarkably, BM25+MuGI outperforms most dense retrievers in OOD contexts,
attributed to the limited generalization capacity of dense retrievers in these
scenarios. This is particularly due to BEIR queries often being short and
semantically ambiguous, which poses challenges in aligning queries and
passages in feature space, even with pseudo passages. Conversely, BM25,
focusing on lexical overlaps, shows robust performance in BEIR tests when
integrated with MuGI. This indicates that the documents generated by MuGI
closely mimic the quality of gold-standard passages, enhancing BM25’s
effectiveness.

##  5 Analysis

###  5.1 Important Factors affecting MuGI

In this section, we present analysis and ablations on several factors that
influence MuGI, all experiments are based on ALL-MPNET-BASE-V2 models:

Figure 5: BM25 + MuGI ablation study (nDCG@10) on query repetition strategy
and number of passages for intergration. Left figure illustrates adaptive
repetition ratio while right figure illustrates constant repetition times of
query.

Figure 6:  AMBv2+MuGI pipeline ablation study (nDCG@10) on different
integration strategies. Re-rank on Top 100/1000 results from BM25+MuGI.

#### Hyper-parameters for Sparse Retrieval

In sparse retrieval contexts, the reweighting between the query and generated
passages is pivotal for robust performance. This study on TREC DL19
investigates the impact of varying the proportionality ratio $p$ and the
efficacy of a constant repetition strategy, as depicted in fig. 6. Employing a
constant repetition strategy, which entails repeating the query a fixed number
of times before concatenating it with generated passages, exhibits
limitations. The findings presented in fig. 6 suggest that incorporating
additional passages enhances performance, attributed to the enrichment of
relevant vocabulary. Nonetheless, this improvement reaches a plateau after the
integration of five passages, indicating that the Language Model’s ability to
generate relevant content maxes out at this juncture, with no further key
terms being produced. Conversely, an adaptive strategy with a proportionality
ratio $p$ set to 5 demonstrates more consistent outcomes. Coincidentally,
constant repetition times highlight that maintaining a ratio of about 5
between the number of passages and the query optimizes results. However,
identifying an optimal constant repetition time is labor-intensive, suggesting
that our adaptive repetition strategies might provide more efficient and
effective performance enhancements.

#### Integration Pattern for Dense Retrieval

In our analysis of dense retrieval mechanisms, we investigated multiple
methods for integrating queries and passages, as illustrated in fig. 6.
Utilizing the query directly for re-ranking (labelled as q’) showed reasonable
effectiveness. However, the inclusion of a single passage with the query
(denoted as qr1’) substantially improved outcomes. The best performance was
achieved by incorporating all three passages. Notably, the straightforward
concatenation of the query with three passages (qr1r2r3’) outperformed the
strategy of alternating the query and passages (qr1qr2qr3’).

#### Influence of Large Language Models

We utilized LLMs of varying sizes across three distinct application methods in
our approach, as outlined in table 3. Our study focused on leading-edge, open-
source LLMs222Selections were made prioritizing ”chat” and 4-bit or AWQ
quantized models for computational efficiency. from the LMSYS Arena
leaderboard Zheng et al. (2023) to create pseudo references. The analysis
indicates that, generally, larger LLMs deliver superior performance,
particularly noting enhancements in OOD scenarios for sparse methods
($\text{MuGI}_{S}$) and in in-distribution scenarios for dense models
($\text{MuGI}_{R}$ and $\text{MuGI}_{P}$).

Unexpectedly, certain open-source LLMs, even those outperforming GPT-3.5 Turbo
in standard metrics Zheng et al. (2023); Hendrycks et al. (2021); Huang et al.
(2023), underperformed in producing quality pseudo references compared to
GPT-3.5. This variance might be attributed to their more limited knowledge
storage capacities. Furthermore, empirical data reveals that sparse retrievers
benefit more from the extensive and detailed references generated by GPT-4,
showing a performance increase of 3% in IID and 1.4% in OOD situations. In
contrast, dense retrievers prefer the succinct references from GPT-3.5,
possibly due to longer references from GPT-4 exceeding the dense retrievers’
token limit (usually 512 tokens), which reduces the number of references and
key vocabularies in the expanded query. The most effective results were
achieved by combining GPT-4 with sparse retrievers and GPT-3.5 with dense
retrievers, capitalizing on the unique strengths of each model.

###  5.2 Mechanism behind Query Expansion

We present analysis to further illustrate how generated pseudo references
enhance IR.

Methods | $\text{MuGI}_{S}$ | $\text{MuGI}_{R}$ | $\text{MuGI}_{P}$
---|---|---|---
IID | OOD | IID | OOD | IID | OOD
Qwen1.5-7B | 62.2 | 43.7 | 69.2 | 48.5 | 70.3 | 48.6
Qwen1.5-14B | 62.3 | 47.6 | 71.2 | 48.6 | 71.3 | 48.7
Qwen1.5-72B | 65.6 | 49.2 | 71.3 | 48.4 | 73.7 | 49.2
Yi-6B | 61.6 | 47.5 | 71.0 | 48.6 | 71.1 | 48.3
Yi-34B | 62.9 | 48.6 | 71.2 | 48.4 | 74.1 | 49.2
GPT3.5-Turbo | 64.4 | 49.6 | 71.3 | 48.6 | 74.2 | 49.6
GPT4-Turbo | 67.4 | 51.0 | 71.4 | 48.7 | 73.4 | 49.9
GPT-Hybrid | 67.4 | 51.0 | 71.4 | 48.7 | 75.7 | 50.3

Table 3: nDCG@10 Results Using AMBv2 with References from Diverse LLMs.
$\text{MuGI}_{S}$ denotes BM25+MuGI, $\text{MuGI}_{R}$ signifies MuGI Re-rank,
and $\text{MuGI}_{P}$ refers to the MuGI Pipeline. GPT-Hybrid refers to sparse
retrieval using GPT4 and dense retrieval using GPT3.5-1106.

#### Key Vocabularies Overlap

We demonstrate that pseudo references created by LLMs include "key words"
critical for identifying the target passage within a corpus. To establish a
"Ground Truth Reference (GT REF)," we compile all passages rated as perfectly
relevant (relevance level 3) from the corpus. Similarly, we aggregate all
pseudo references generated by LLMs for a specific query to create a "Pseudo
Reference (PSE REF)." For each query’s gold references, we identify the top 10
highest Inverse Document Frequency words present in these references as key
vocabularies. We then assess the frequency overlap of these key vocabularies
between the query and GT REF, and between PSE REF and GT REF. As indicated in
fig. 7, there is a significant overlap of key words between GT REF and PSE REF
in both IID and OOD situations, surpassing the overlap between the query and
GT REF. This finding suggests that pseudo references enhance lexical retrieval
by integrating additional "key vocabularies" crucial for pinpointing the
target passage within the corpus.

Figure 7: Key Words Overlap Distribution

#### Similarity of Text Embedding

Figures 8 and 9 show the cosine similarity distribution between relevant
documents and the queries, both in their original form (‘q’) and augmented
with MuGI (‘q+’), in in-distribution and out-of-distribution scenarios,
respectively. The text embeddings are calculated using BGE-Large-EN-v1.5. The
plots’ width at various points reflects the density of sample distribution
across similarity scores, with broader sections indicating a higher
concentration of samples within a specific score range. The black dots denote
the similarity scores for individual samples. Both figures demonstrate that
the similarity between relevant documents and the queries augmented with MuGI-
generated passages (‘q+’) is significantly higher compared to the original
queries (‘q’). The enhancement in similarity scores becomes especially notable
when comparing ‘q’ with ‘q+r1’. Furthermore, incorporating additional passages
(‘q+r1r2’, ‘q+r1r2r3’) progressively increases the similarity score with the
relevant document. These findings imply that MuGI can enrich queries with
contextually relevant content thus bridging the semantic gap between queries
and documents.

Figure 8: Similarity scores between relevant documents and query on In-Domain
dataset. ‘q+r1r2r3’ represents concatenation of query with three generated
passages. Figure 9: Similarity scores between relevant documents and query on
OOD dataset.

##  6 Conclusion

This paper introduces Multi-Text Generation Integration (MuGI) method, a
technique that significantly improves information retrieval by merging query
with multiple generated passages through a dynamic re-weighting strategy. Our
empirical findings indicate that MuGI not only enhances both sparse and dense
retrieval model performance but also sets a new standard in in-domain contexts
and enables BM25 to outperform 7B LLM-based retrievers in out-of-distribution
(OOD) evaluations. Importantly, MuGI reduces the performance disparity between
large (7B) and smaller (110M) models in OOD settings, establishing itself as
an effective and efficient information retrieval solution with the support of
LLMs. The paper further includes a detailed analysis and extensive ablation
study to underscore its effectiveness.

## Limitation

The proposed method offers substantial improvements in information retrieval
performance. Nonetheless, a shared limitation across query rewriting
approaches, ours included, is the increased inference time due to the
generation of extra passages with LLMs. Retrieval-Augmented Generation
presents a potential solution by interleaving the retrieval and generation
processes, potentially mitigating this issue, which requires further
exploration.

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# Optical interface for a hybrid magnon-photon resonator

Banoj Kumar Nayak*00footnotetext: *These authors contributed equally to this
work. Andrew and Erna Viterbi Department of Electrical Engineering, Technion,
Haifa 32000 Israel  Cijy Mathai  Andrew and Erna Viterbi Department of
Electrical Engineering, Technion, Haifa 32000 Israel  Dekel Meirom  Andrew and
Erna Viterbi Department of Electrical Engineering, Technion, Haifa 32000
Israel  Oleg Shtempluck  Andrew and Erna Viterbi Department of Electrical
Engineering, Technion, Haifa 32000 Israel  Eyal Buks  Andrew and Erna Viterbi
Department of Electrical Engineering, Technion, Haifa 32000 Israel

###### Abstract

We study optical detection of magnetic resonance of a ferrimagnetic sphere
resonator, which is strongly coupled to a microwave loop gap resonator.
Optical fibers are employed for coupling the sphere resonator with light in
the telecom band. We find that magnetic resonance can be optically detected in
the region of anti-crossing between the loop gap and the ferrimagnetic
resonances. By measuring the response time of the optical detection we rule
out the possibility that microwave induced heating is responsible for the
optical detectability.

Magnons are widely employed in a variety of devices Hill_S227 ; Lecraw_1311 ;
Kumar_435802 ; Sander_363001 ; Vedmedenko_453001 ; Chumak_244001 ;
rezende2020fundamentals , including narrow band oscillators Ryte_434 , filters
Tsai_3568 , and parametric amplifiers Kotzebue_773 . Magnons can couple with
microwave (MW) photons Zhang_156401 ; Zhu_2005_06429 , optical photons Bai_1 ;
Demokritov_441 ; Zhang_123605 ; Osada_223601 ; Stancil_Spin ; Kajiwara_262 ;
Haigh_133602 ; Sharma_094412 ; Hisatomi_207401 ; Pantazopoulos_104425 ;
Hisatomi_174427 , phonons Sinha_432 ; Zhang_e1501286 , and with
superconducting qubits Tabuchi_405 ; Lachance_e1603150 ; Lachance_070101 ;
Wolski_2005_09250 . Hybrid magnon devices may help developing optical channels
linking remote quantum computers Kaur_032404 ; Huebl_127003 ; Tabuchi_083603 .

Here we study a hybrid system composed of a MW loop gap resonator (LGR)
strongly coupled to a ferrimagnetic sphere resonator (FSR) made of yttrium
iron garnet (YIG) Cherepanov_81 ; Serga_264002 . Optical fibers are employed
for transmitting light in the telecom band through the sphere. The frequency
of the hybrid FSR-LGR system is controlled using an externally applied
magnetic field (generated by a magnetized Neodymium). We explore magneto-optic
(MO) coupling and Faraday rotation of optical polarization, and demonstrate
optical detection of magnetic resonance (ODMR) of the hybrid FSR-LGR system.
ODMR of FSR has been demonstrated before in Chai_021101 , by coupling a
tapered optical fiber to whispering gallery modes of an FSR. However, the ODMR
method that has developed in Chai_021101  is based on heating induced by MW
driving, and consequently the response time of this method is relatively long
(on the order of a second). As is shown below, the response time of our ODMR
method, which is not based on heating, is significantly shorter (limited by
the ring down time of the FSR, which is about $1\mathrm{\mu s}$).

Figure 1: Experimental setup. Optical components [ErS (Erbium source), TL
(tunable laser), PC (polarization controller), OSA (optical spectrum analyzer)
and PD (photodetector)] and fibers are red colored, and MW components [LA
(loop antenna), S (splitter), C (circulator), VNA (vector network analyzer),
SA (spectrum analyzer), SG (signal generator), and LIA (lockin amplifier)] and
coaxial cables are blue colored. The LA is weakly coupled to the FSR-LGR
system. Optical fibers are installed on both sides of the FSR for transmission
of light through the sphere. Components outlines by a thick black line (TL, PD
and LIA) are used only for the measurements presented in Fig. 3.

The experimental setup, which is schematically shown in Fig. 1, is designed to
allow exploring the MO coupling between MW and optical photons, which is
mediated by FSR magnons. In Fig. 1, optical components and fibers are red
colored, whereas blue color is used to label MW components and coaxial cables.

A MW cavity made of an LGR allows achieving a relatively large coupling
between magnons and MW photons Froncisz_515 ; Zhang_205003 ; Mathai_054428 .
The LGR is fabricated from a hollow concentric aluminium tube. A sapphire
strip of $260\mathrm{\mu m}$ thickness is inserted into the gap in order to
increase its capacitance, which in turn reduces the frequency $f_{\mathrm{c}}$
of the LGR fundamental mode krupka_387 . An FSR made of YIG having radius of
$R_{\mathrm{s}}=125\mathrm{\mu m}$ is held by two ceramic ferrules inside the
LGR. The applied static magnetic field $\mathbf{H}$ is controlled by adjusting
the relative position of the magnetized Neodymium using a motorized stage. The
LGR-FSR coupled system is encapsulated inside a metallic rectangular shield
made of aluminum (represented by the black colored rectangle in Fig. 1). The
cavity is weakly coupled to a loop antenna (LA). More information about the
FSR-LGR hybrid system, including its fabrication and magnetic energy density
distribution, can be found in Ref. Mathai_054428 .

Figure 2: Continuous wave measurements. In both (a) and (c) the ErS is
employed as a source, and the optical transmission measurement is performed
using the OSA. (a) Measured optical spectrum data as a function of SG
frequency $f$ with SG power of $20$ dBm relative to measured optical spectrum
corresponding to smallest SG frequency in the plot, with a fixed magnetic
field of $H=140.13\mathrm{mT}$, showing Fabry–Pérot oscillation near the FSR-
LGR resonance. (b) VNA reflection $\left|S_{11}\right|^{2}$ in dB units as a
function of frequency $f$ and magnetic field $H$ with input power of $-30$
dBm. (c) Optical intensity (in arbitrary units) measured at a specific
wavelength of $\lambda=1524.292\mathrm{nm}$ as a function of SG frequency $f$
and magnetic field $H$, with SG power of $20$ dBm.

A vector network analyzer (VNA) is employed for measuring the MW reflection
coefficient $\left|S_{11}\right|^{2}$. The plot shown in Fig. 2(b) exhibits
$\left|S_{11}\right|^{2}$ in dB units as a function of the externally applied
magnetic field $H$ and VNA frequency $f$. The measurement is performed in the
region of anti-crossing between the LGR fundamental mode at frequency
$f_{\mathrm{c}}=3.9235\mathrm{GHz}$ and the Kittel mode FSR frequency
$f_{\mathrm{s}}$ , which is given by
$f_{\mathrm{s}}=\gamma_{\mathrm{g}}H/\left(2\pi\right)$, where
$\gamma_{\mathrm{g}}/2\pi=27.98~{}\mathrm{GHz}~{}\mathrm{T}^{-1}$ is the
gyromagnetic ratio Jin_thesis ; Fletcher_687 .

The frequencies $f_{\pm}$ of the hybrid FSR-LGR eigen modes are given by
Sainz_de_los_Terreros_1906

$f_{\pm}=\frac{f_{\mathrm{c}}+f_{\mathrm{s}}}{2}\pm\sqrt{\left(\frac{f_{\mathrm{c}}-f_{\mathrm{s}}}{2}\right)^{2}+g^{2}}\;.$
(1)

where $g$ is the FSR-LGR coupling coefficient Wang_224410 ; Mathai_67001 . The
overlaid black dashed lines in Fig. 2(b) are calculated using Eq. (1). A
fitting procedure yields the value $g/\left(2\pi\right)=16\mathrm{MHz}$. Note
that in general, $g$ is proportional to the FSR volume.

In the telecom band (wavelength $\lambda\simeq 1.5\mathrm{\mu m}$) YIG has an
optical absorption coefficient $\alpha$ of about
$\alpha=\left(0.5\mathrm{m}\right)^{-1}$ Wood_1038 , a Verdet constant
$A_{\mathrm{V}}$ of about $A_{\mathrm{V}}=5\times
10^{-5}\mathrm{mT}^{-1}\mathrm{\mu m}^{-1}$ Onbasli_1 ; Jooss_651 , and a
polarization beating length $l_{\mathrm{P}}$ in magnetic saturation of about
$l_{\mathrm{P}}=7.\,0\mathrm{mm}$ Zhang_591 ; Onbasli_1 ; Donati_372 . YIG
spheres can be employed for making optical circulators and isolator in the
telecom band Yokohama_746l ; Okamoto_36 . An optical cavity can be constructed
to enhance Faraday rotation Stone_849 ; Chang_8526 .

In our setup telecom light is transmitted through the FSR using single mode
optical fibers. The FSR serves as a thick optical lens having focal length of
$F_{\mathrm{FSR}}=\left(1/2\right)n_{0}R_{\mathrm{s}}/\left(n_{0}-1\right)$,
where $n_{0}=2.19$ is YIG refractive index in the telecom band Okamoto_36 ;
Yokohama_746 , A graded index fiber (GIF) is attached to the tip of one the
the fibers that are installed near the FSR (see Fig. 1). The length of the GIF
is $0.1p_{\mathrm{g}}$, where $p_{\mathrm{g}}=1\mathrm{mm}$ is the GIF pitch.
Focusing is achieved by displacing both fibers along the optical axis and
maximizing the fiber to fiber transmission $T_{\mathrm{F}}$, which for the
current device under study is $T_{\mathrm{F}}=0.59$.

Spontaneous emission from an Erbium doped fiber is used as the optical source
for the measurements presented in Fig. 2. The Erbium source (ErS) intensity
peaks near wavelength of $1530\mathrm{nm}$. A polarization controller (PC) is
employed to manipulate the light transmitted through the FSR. An optical
spectrum analyzer (OSA) having resolution of $0.004\mathrm{nm}$ is used to
probe the transmitted light. All fibers are single mode having $125\mathrm{\mu
m}$ clad diameter and $9\mathrm{\mu m}$ core diameter.

Figure 3: LIA measurements. (a) VNA reflection $\left|S_{11}\right|^{2}$ in dB
units as a function of frequency $f$ and magnetic field $H$. The VNA input
power is $-10$ dBm. (b) LIA measured voltage amplitude (in arbitrary units) as
a function of SG frequency $f$ and magnetic field $H$, with SG power of $-10$
dBm. In both (a) and (b) the TL wavelength is $1530.87\mathrm{nm}$ and power
is $-2.6$ dBm. (c) The dependence of LIA measured voltage amplitude
$V_{\mathrm{LIA}}$ (in arbitrary units) on LIA modulation frequency
$f_{\mathrm{AM}}$. For this measurement, the TL wavelength is set to
$1538.556\mathrm{nm}$ and TL power is set to $6$ dBm.

The OSA is employed for probing the transmitted light in the range
$1520\mathrm{nm}$ to $1540\mathrm{nm}$, as a function of MW driving frequency
$f$ applied to the LA, with a fixed magnetic field of $140.13\mathrm{mT}$ [see
Fig. 2(a)]. In this measurement, a signal generator (SG) operating at $20$ dBm
serves as a source [see Fig. 1, and note that a circulator (C) and a MW
spectrum analyzer (SA) are used to probe the back reflected MW signal]. The
measured optical transmission shown in Fig. 2(a) reveals Fabry–Pérot
oscillation near the FSR resonance $f_{\mathrm{s}}$. The wavelength period of
the Fabry–Pérot oscillation is observed to be $1.77\mathrm{nm}$. The
oscillation is attributed to an optical cavity formed between both fibers
coupled to the FSR due to Fresnel reflection at the fibers’ tips. The measured
spacing of $1.77\mathrm{nm}$ allows estimating the distance between the fibers
to be $700\mathrm{\mu m}$.

To study the dependence on both the MW frequency $f$ as well as magnetic field
$H$, the optical intensity is recorded at wavelength $1524.292\mathrm{nm}$
[see Fig. 2(c)], at which the transmission is maximized [see Fig. 2(a)]. The
SG frequency is varied from $3.8\mathrm{GHz}$ to $4.05\mathrm{GHz}$, and the
power is set to $20$ dBm. The measured optical intensity peaks near the Larmor
resonance, i.e. when $f\simeq f_{\mathrm{s}}$. Note that the splitting between
$f_{+}$ and $f_{-}$ cannot be resolved in Fig. 2(c) due to anisotropy-induced
Kerr nonlinearity Mathai_054428 .

Next we explore the response time of the above-discussed ODMR method. This is
done in order to determine the role played by MW induced heating, which has a
relatively long time scale Chai_021101 . To that end, we perform experiments
using a lockin amplifier (LIA). Components outlines by a thick black line in
the setup sketch shown in Fig. 1 (TL, PD and LIA) are used only for the LIA
measurements presented in Fig. 3. A tunable laser (TL) is used instead of the
high bandwidth ErS. The OSA is replaced with a photodetector (PD) to measure
the optical intensity. The LIA reference signal is used to amplitude modulate
(AM) the SG signal at a modulation frequency $f_{\mathrm{AM}}$, and the PD
signal output is fed into the LIA input port. For LIA measurement shown in
Fig. 3(c), the tunable laser wavelength is set to $1538.556\mathrm{nm}$, which
corresponds to the second highest optical intensity in the spectrum shown in
Fig. 2(a).

Both the VNA measurement shown in Fig. 3(a) and the LIA measurement shown in
Fig. 3(b) are performed with MW power of $-10$ dBm and TL optical power of
$-2.6$ dBm. Figure 3(c) shows a plot of LIA voltage amplitude
$V_{\mathrm{LIA}}$ (in arbitrary units) as a function of modulation frequency
$f_{\mathrm{AM}}$. The measured dependency on $f_{\mathrm{AM}}$ indicates that
the ODMR response time is on the order of a microsecond. This observation
suggests that the response time is limited by FSR damping, and it rules out
the possibility that heating plays a dominant role in the underlying mechanism
allowing the ODMR.

In summary, ODMR of FSR is demonstrated in the telecom band, and the
possibility that MW induced heating is the underlying mechanism is ruled out.
The ODMR method is compatible with ultra low temperatures (due to the very low
optical absorption of YIG in the telecom band), and thus it may help
developing an optical interface for superconducting qubits Tabuchi_405 ;
Lachance_e1603150 ; Lachance_070101 ; Wolski_2005_09250 .

This work was supported by the Israeli science foundation, the Israeli
ministry of science, and by the Technion security research foundation.

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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