††thanks: Present address: Korea Astronomy and Space Science Institute,
Daejeon 34055, Republic of Korea.††thanks: corresponding author††thanks:
corresponding author††thanks: Present address: Samsung Electronics, Gyeonggi-
do 16677, Republic of Korea.††thanks: Present address: Department of Physics,
Sungkyunkwan University, Suwon 16419, Republic of Korea.††thanks:
corresponding author††thanks: corresponding author

# Extensive search for axion dark matter over 1 GHz with CAPP’s Main Axion
eXperiment

Saebyeok Ahn  Center for Axion and Precision Physics Research, Institute for
Basic Science (IBS), Daejeon 34051, Republic of Korea  JinMyeong Kim
Department of Physics, Korea Advanced Institute of Science and Technology
(KAIST), Daejeon 34141, Republic of Korea  Center for Axion and Precision
Physics Research, Institute for Basic Science (IBS), Daejeon 34051, Republic
of Korea  Boris I. Ivanov  Center for Axion and Precision Physics Research,
Institute for Basic Science (IBS), Daejeon 34051, Republic of Korea  Ohjoon
Kwon  Center for Axion and Precision Physics Research, Institute for Basic
Science (IBS), Daejeon 34051, Republic of Korea  HeeSu Byun  Center for Axion
and Precision Physics Research, Institute for Basic Science (IBS), Daejeon
34051, Republic of Korea  Arjan F. van Loo  RIKEN Center for Quantum Computing
(RQC), Wako, Saitama 351-0198, Japan  Department of Applied Physics, Graduate
School of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656,
Japan  SeongTae Park  Center for Axion and Precision Physics Research,
Institute for Basic Science (IBS), Daejeon 34051, Republic of Korea  Junu
Jeong  Center for Axion and Precision Physics Research, Institute for Basic
Science (IBS), Daejeon 34051, Republic of Korea  Soohyung Lee  Center for
Axion and Precision Physics Research, Institute for Basic Science (IBS),
Daejeon 34051, Republic of Korea  Jinsu Kim  Center for Axion and Precision
Physics Research, Institute for Basic Science (IBS), Daejeon 34051, Republic
of Korea  Çağlar Kutlu  Center for Axion and Precision Physics Research,
Institute for Basic Science (IBS), Daejeon 34051, Republic of Korea  Andrew K.
Yi  Department of Physics, Korea Advanced Institute of Science and Technology
(KAIST), Daejeon 34141, Republic of Korea  Center for Axion and Precision
Physics Research, Institute for Basic Science (IBS), Daejeon 34051, Republic
of Korea  Yasunobu Nakamura  RIKEN Center for Quantum Computing (RQC), Wako,
Saitama 351-0198, Japan  Department of Applied Physics, Graduate School of
Engineering, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
Seonjeong Oh  Center for Axion and Precision Physics Research, Institute for
Basic Science (IBS), Daejeon 34051, Republic of Korea  Danho Ahn  Center for
Axion and Precision Physics Research, Institute for Basic Science (IBS),
Daejeon 34051, Republic of Korea  SungJae Bae  Department of Physics, Korea
Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic
of Korea  Center for Axion and Precision Physics Research, Institute for Basic
Science (IBS), Daejeon 34051, Republic of Korea  Hyoungsoon Choi  Department
of Physics, Korea Advanced Institute of Science and Technology (KAIST),
Daejeon 34141, Republic of Korea  Jihoon Choi  Center for Axion and Precision
Physics Research, Institute for Basic Science (IBS), Daejeon 34051, Republic
of Korea  Yonuk Chong  SKKU Advancd Institute of Nano Technology (SAINT) and
Department of Nano Engineering Sung Kyun Kwan University (SKKU), Suwon 16419,
Republic of Korea  Woohyun Chung<EMAIL_ADDRESS>Center for Axion and
Precision Physics Research, Institute for Basic Science (IBS), Daejeon 34051,
Republic of Korea  Violeta Gkika  Center for Axion and Precision Physics
Research, Institute for Basic Science (IBS), Daejeon 34051, Republic of Korea
Jihn E. Kim  Department of Physics, Seoul National University, 1 Gwanak-Ro,
Seoul 08826, Republic of Korea  Younggeun Kim  Center for Axion and Precision
Physics Research, Institute for Basic Science (IBS), Daejeon 34051, Republic
of Korea  Byeong Rok Ko<EMAIL_ADDRESS>Center for Axion and Precision Physics
Research, Institute for Basic Science (IBS), Daejeon 34051, Republic of Korea
Lino Miceli  Center for Axion and Precision Physics Research, Institute for
Basic Science (IBS), Daejeon 34051, Republic of Korea  Doyu Lee  Center for
Axion and Precision Physics Research, Institute for Basic Science (IBS),
Daejeon 34051, Republic of Korea  Jiwon Lee  Department of Physics, Korea
Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic
of Korea  Center for Axion and Precision Physics Research, Institute for Basic
Science (IBS), Daejeon 34051, Republic of Korea  Ki Woong Lee  Center for
Axion and Precision Physics Research, Institute for Basic Science (IBS),
Daejeon 34051, Republic of Korea  MyeongJae Lee  Center for Axion and
Precision Physics Research, Institute for Basic Science (IBS), Daejeon 34051,
Republic of Korea  Andrei Matlashov  Center for Axion and Precision Physics
Research, Institute for Basic Science (IBS), Daejeon 34051, Republic of Korea
Pallavi Parashar  Department of Physics, Korea Advanced Institute of Science
and Technology (KAIST), Daejeon 34141, Republic of Korea  Center for Axion and
Precision Physics Research, Institute for Basic Science (IBS), Daejeon 34051,
Republic of Korea  Taehyeon Seong  Center for Axion and Precision Physics
Research, Institute for Basic Science (IBS), Daejeon 34051, Republic of Korea
Yun Chang Shin  Center for Axion and Precision Physics Research, Institute for
Basic Science (IBS), Daejeon 34051, Republic of Korea  Sergey V. Uchaikin
<EMAIL_ADDRESS>Center for Axion and Precision Physics Research, Institute
for Basic Science (IBS), Daejeon 34051, Republic of Korea  SungWoo Youn
<EMAIL_ADDRESS>Center for Axion and Precision Physics Research, Institute
for Basic Science (IBS), Daejeon 34051, Republic of Korea  Yannis K.
Semertzidis  Center for Axion and Precision Physics Research, Institute for
Basic Science (IBS), Daejeon 34051, Republic of Korea  Department of Physics,
Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141,
Republic of Korea

###### Abstract

We report an extensive high-sensitivity search for axion dark matter above 1
GHz at the Center for Axion and Precision Physics Research (CAPP). The cavity
resonant search, exploiting the coupling between axions and photons, explored
the frequency (mass) range of 1.025 GHz (4.24 $\mu$eV) to 1.185 GHz (4.91
$\mu$eV). We have introduced a number of innovations in this field,
demonstrating the practical approach of optimizing all the relevant parameters
of axion haloscopes, extending presently available technology. The CAPP 12 T
magnet with an aperture of 320 mm made of Nb3Sn and NbTi superconductors
surrounding a 37-liter ultralight-weight copper cavity is expected to convert
DFSZ axions into approximately $10^{2}$ microwave photons per second. A
powerful dilution refrigerator, capable of keeping the core system below 40
mK, combined with quantum-noise limited readout electronics, achieved a total
system noise of about 200 mK or below, which corresponds to a background of
roughly $4\times 10^{3}$ photons per second within the axion bandwidth. The
combination of all those improvements provides unprecedented search
performance, imposing the most stringent exclusion limits on axion–photon
coupling in this frequency range to date. These results also suggest an
experimental capability suitable for highly-sensitive searches for axion dark
matter above 1 GHz.

axion dark matter, cavity haloscope, Josephson parametric amplifier, quantum-
limited low-noise amplifier, low temperature thermalization

††preprint: APS/123-QED

##  I Introduction

Dark matter, which is evident in many astronomical observations, is generally
accepted to be one of the major substances in our universe, making up
approximately 85% of matter and strongly influencing the formation and
evolution of galaxies [1, 2]. However, the mysterious hypothetical substance
has eluded decades of dedicated searches. It remains invisible and its
identity unknown. The possible candidates for dark matter include individual
heavy particles, such as weakly interacting massive particles [3, 4],
coherently oscillating waves such as axions (in generic, axion-like particles)
[5, 6], or astronomical objects such as primordial black holes [7, 8]. Among
these, axions are theoretically promising particles that were originally
proposed to solve a fundamental problem in strong interactions, known as the
strong-CP problem. The Charge-Parity (CP) symmetry that is expected to be
violated according to quantum chromodynamics (QCD) of the Standard Model (SM),
appears to be conserved in nature, as indicated by the absence of an electric
dipole moment (EDM) for the neutron [9] and proton [10]. An elegant solution
to this naturalness problem is the Peccei-Quinn (PQ) mechanism, where the CP-
violating term in the QCD Lagrangian, referred to as $\bar{\theta}$, is
promoted to a scalar field by introducing a new U(1) global symmetry as a
minimal extension of the SM [11]. The symmetry becomes spontaneously broken at
some energy scale, dynamically relaxing the $\bar{\theta}$ parameter to zero,
thus resolving the strong-CP problem. The Goldstone boson associated with the
spontaneous symmetry breaking is the axion [12, 13]. The mass and coupling
(strength of axion–photon interaction) are inversely proportional to the
symmetry breaking scale $f_{a}$, also known as the decay constant. Since
searches for the standard axion at $f_{a}\sim v_{\rm EW}$ (electroweak scale)
have yielded null results, attention has shifted to detecting “invisible”
axions with very large $f_{a}$, i.e., with very small mass and very weak
coupling to ordinary matter.

The unique properties of the QCD axion turn out to provide a suitable
explanation for the missing matter of the universe with a cosmological
constraint on the decay constant $f_{a}\lesssim 10^{12}$ GeV, which imposes a
boundary of $\gtrsim 1\,\mu{\rm eV}$ on the mass ($\gtrsim 0.25\,{\rm GHz}$ on
the frequency) [14, 15, 16]. Depending on the production and evolution of the
cosmic axion field, there are two possible scenarios for axion cosmology. In
the pre-inflationary scenario, where cosmic inflation selects a single patch
of the universe free of topological defects, the PQ symmetry breaking results
in a homogeneous initial misalignment value of the axion field throughout the
observable universe and determines the axion relic (present) density with a
mass within a wide range as low as 1 peV/$c^{2}$, where $c$ is the speed of
light, accounting for the present abundance of dark matter [17, 18].
Alternatively, the post-inflationary axion field embraces many patches and
thus takes on multiple initial values, resulting in topological defects that
additionally contribute to axion production. Using a spatially averaged
initial misalignment value, recent QCD lattice calculations and simulations
have been able to predict the axion mass within a relatively narrow range from
$\mathcal{O}(10^{1})$ to $\mathcal{O}(10^{2})~{}\mu$eV [19, 20, 21].

At present, dark-matter axions are assumed to be in a virialized state (a sort
of thermalization process without energy loss from the total system) with
their velocity following the Maxwell–Boltzmann distribution. This results in a
dispersion of $\sim 10^{-3}c$, which in turn yields an average quality factor
of $1.0\times 10^{6}$ for an observer on earth [22].

Although feeble, the QCD axion can interact with SM particles through
anomalous couplings to gluons. Depending on the type of particles contributing
to the anomalous loop, there are two general classes of invisible axion
models: Kim-Shifman-Vainshtein-Zakharov (KSVZ) with a newly introduced heavy
quark carrying the PQ charge [23, 24] and Dine-Fischler-Srednicki-Zhitnitsky
(DFSZ) with ordinary quarks and leptons carrying the charge [25, 26]. The
electromagnetic interaction has been widely accepted for practical searches,
since it mediates axion–photon coupling, providing an experimental signature,
i.e., photons, which can be detected with existing well-developed detection
technologies.

The detection principle, first suggested by Sikivie [27], relies on the
macroscopic version of the (inverse) Primakoff effect, where a classical
magnetic field serves as a sea of virtual photons with which axions interact
and convert into real photons. The photon frequency corresponds to the total
energy of the detected axion. There are several types of search strategies
depending on the source of the axion. These include: (i) haloscope searches
for dark matter axions in the galactic halo (CAPP [28, 29, 30, 31, 32], ADMX
[33, 34, 35], HAYSTAC [36, 37, 38], QUAX [39, 40], ORGAN [41, 42], MADMAX
[43], DM Radio [44], CAST-CAPP [45], etc.), (ii) helioscopes pointing at the
Sun to look for solar axions (CAST [46] and IAXO [47]) and (iii) light-
shining-through-the-wall schemes, which are configured to generate and detect
axions in the lab (OSQAR [48] and ALPS (II) [49, 50]). Among these, the cavity
haloscope method provides the most sensitive approach, particularly in the
microwave region.

A cavity haloscope consists of a microwave resonator immersed in a strong
magnetic field where axions induce photons which couple with one of the cavity
resonant modes, e.g., the TM010 mode for a cylindrical geometry. The expected
power of the axion–photon conversion is given by

$P_{a\gamma\gamma}=8.7\times 10^{-23}\,{\rm
W}\left(\frac{g_{\gamma}}{0.36}\right)^{2}\left(\frac{\rho_{a}}{0.45\,{\rm
GeV/cm^{3}}}\right)\left(\frac{\nu_{a}}{1.1\,{\rm
GHz}}\right)\left(\frac{B_{\textrm{rms}}}{10.3\,{\rm
T}}\right)^{2}\left(\frac{V}{37\,{\rm
L}}\right)\left(\frac{G}{0.6}\right)\left(\frac{Q_{c}}{10^{5}}\right),$ (1)

where $g_{\gamma}$ is the model-dependent coupling coefficient with a value of
$-$0.97 and 0.36 for the KSVZ and DFSZ models, respectively, $\rho_{a}$ is the
axion density in the local dark-matter halo, $\nu_{a}$ is the axion Compton
frequency, and $B_{\textrm{rms}}$ is the externally applied magnetic field.
$V$ and $Q_{c}$ are the volume and quality factor of the cavity, and $G$ is
the form factor associated with the resonant mode, providing a measure of how
well the external magnetic field is matched with the electric field associated
with the relevant cavity mode. Assuming that local dark matter is composed
solely of DFSZ axions, a cavity haloscope with the experimental parameters
used in Eq. (1) would expect about 120 photons/s to be converted in the cavity
and about 30 photons/s to be picked up by a critically coupled receiver
antenna. A measure of experimental sensitivity is given by the signal-to-noise
ratio (SNR),

${\rm SNR}\equiv\frac{P_{a\gamma\gamma}}{\delta P_{\rm
sys}}=\frac{P_{a\gamma\gamma}}{k_{B}T_{\rm sys}}\sqrt{\frac{\Delta
t}{\Delta\nu}},$ (2)

where $\delta P_{\rm sys}(=P_{\rm sys}/\sqrt{\Delta\nu\Delta t}$) denotes
fluctuations in system noise power over a bandwidth $\Delta\nu$ during an
integration time $\Delta t$, and $P_{\rm sys}(=k_{B}T_{\rm sys}\Delta\nu$)
describes the Johnson-Nyquist noise with the Boltzmann constant $k_{B}$ and
the equivalent noise temperature $T_{\rm sys}$. Since the axion mass is
unknown a priori and the allowed mass range is vast, a fast search speed with
a given sensitivity becomes the figure of merit for the experimental design.
The relevant quantity is obtained by inserting Eq. (1) into Eq. (2) as

$\frac{d\nu}{dt}=1.2\,{\rm\frac{GHz}{year}}\left(\frac{0.6}{\eta}\right)\left(\frac{5}{snr}\right)^{2}\left(\frac{0.2\,{\rm
K}}{T_{\rm sys}}\right)^{2}\left(\frac{P_{a\gamma\gamma}}{8.7\times
10^{-23}\,{\rm W}}\right)^{2}\left(\frac{10^{5}}{Q_{c}}\right),$ (3)

where $\eta$ is the data acquisition (DAQ) efficiency and $snr$ is the target
SNR value. Major R&D efforts have been made to increase the search rate by
maximizing the figure of merit ($\mathcal{FOM}\equiv
B_{\textrm{rms}}^{4}V^{2}G^{2}Q_{c}/T^{2}_{\rm sys}$), the metric that defines
the strength of the experiment for a given frequency.

The Center for Axion and Precision Physics Research (CAPP) of the Institute
for Basic Science (IBS) was established in October 2013 at the Korea Advanced
Institute of Science and Technology (KAIST) in Daejeon, Republic of Korea.
IBS-CAPP’s main focus has been cavity haloscope searches utilizing multiple
experimental setups designed for different mass regions. Among them, CAPP-MAX
(Main Axion eXperiment), formerly known as CAPP-12TB, is the most sensitive
(flagship) experiment at CAPP, taking advantage of available cutting-edge
technologies learned from smaller experiments running in parallel. The main
components of the system include a superconducting solenoid with a center
field of 12 T, based on a $\rm Nb_{3}Sn$ superconducting magnet (inner) and a
regular $\rm NbTi$ superconducting magnet (outer), built by Oxford Instruments
[51]. A cryogenic dilution refrigerator (DR) with a measured cooling power of
1 mW at 90 mK is capable of reaching a base temperature of 5.6 mK. The
detector comprises a 37-liter lightweight copper cavity connected to a readout
chain consisting of flux-driven Josephson parametric amplifiers [52] (JPA),
followed by a series of linear semiconductor amplifiers. This experiment has
recently reported a search using unprecedented sensitivity to probe DFSZ axion
physics above 1 GHz [32, 53] of about 20 MHz. In this paper, we report new
results from an extended search for invisible axion dark matter with CAPP-MAX,
the first search at or near DFSZ sensitivity over a large frequency range of
more than 100 MHz above 1 GHz.

The remainder of this paper is organized as follows. In Sec. II, we introduce
the major experimental equipment including the 12 T superconducting magnet and
the wet-type cryogenic dilution refrigerator system. Their manufacturing
specifications and the actual measurements of the relevant parameters such as
magnetic field and base temperature are provided. Section III describes the
detection system consisting of the microwave cavity and readout electronics,
featuring quantum-noise-limited amplifiers (QNLA) in the first stage of the
chain. The characteristics and quality of the individual components are
presented in sufficient detail, with particular focus on noise calibration and
cavity performance. Section IV is dedicated to the automated data acquisition
and monitoring system, specifically designed for continuous data flow and
high-efficiency real-time monitoring of the entire system. Section V presents
the analysis procedure and the results. The analysis follows the standard
procedure commonly adopted in the community and is similar to the analysis
reported in our previous searches [32, 53, 28, 29, 30, 31]. Finally, we
highlight the importance of the experimental results and provide a perspective
for our near-future work in Sec. VI.

##  II Major equipment

###  II.1 Magnet

The $\mathcal{FOM}$ in axion haloscope searches is dominated by the strength
and volume of the magnet, making it the key factor in CAPP-MAX. Our
superconducting magnet, classified as “wet”, necessitates direct contact with
liquid helium (LHe) to keep the coils in the superconducting state. It has
three main characteristics:

  1. 1.

The cylindrical magnet used in our experiment, manufactured by Oxford
Instruments [51], can operate at a central magnetic field of 12 $\mathrm{T}$
when cooled to a temperature of 4.2 $\mathrm{K}$ using LHe. In Fig. 1, the
magnetic field map in the cavity region is shown in the plot on the left. The
total energy content of the magnet, when fully energized to 12 $\mathrm{T}$,
is 5.562 MJ.

  2. 2.

The solenoidal magnet used in CAPP-MAX has a cold bore diameter of 320
$\mathrm{mm}$. The magnet is composed of two different low-temperature
superconductors: Nb3Sn for the inner coil and NbTi for the outer one. These
coils are nested together to form a concentric solenoid. The inner coil has a
length of 560 $\mathrm{mm}$, while the outer has a length of 640
$\mathrm{mm}$. Taking into account the dimensions of the coil and the
radiation shields of the dilution refrigerator insert (see Section III), the
experiment can accommodate a cylindrical cavity with a volume of 37 liters
inside the solenoidal magnet’s bore. The average root mean square (rms)
magnetic field along the magnet axis over this volume measures 10.55
$\mathrm{T}$.

  3. 3.

The field cancellation region is located 750 $\mathrm{mm}$ above the center of
the magnet, and has both diameter and length dimensions of 100 $\mathrm{mm}$
in cylindrical coordinates. The cancellation coil is connected in series with
the main solenoid, sharing the same power supply and superconducting short
circuit. Within this region, the generated magnetic fields are weaker than
$10^{-2}$ $\mathrm{T}$, as illustrated on the right of Fig. 1. The presence of
this cancellation region is of utmost importance to ensure the proper
operation of the JPAs, which serve as the initial-stage RF amplifier, as well
as for the required microwave circulators and other RF components in the
setup.

Figure 1:  Magnetic-field distributions in the cavity region (left) and
cancellation region (right), respectively. The coordinates $z$ and $r$ refer
to the longitudinal and radial axes of the solenoid, correspondingly. The
black outline on the left corresponds to the location of the cavity, while on
the right it corresponds to the location of the JPA assembly. The magnet
dimensions are given in the text.

The combination of three characteristics discussed above are unparalleled
worldwide, allowing us to conduct axion dark-matter searches with increased
sensitivity [32, 53]. These distinctive features not only enabled our current
research but also pave the way for continued investigations into axion dark
matter at higher frequencies.

The magnet can be safely ramped up at a rate of 0.13 $\mathrm{T}$/min without
any load inside the magnet bore. In addition, the magnet system also
incorporates a crucial feature known as persistent-mode operation, which
allows it to operate without the need of an external power supply once it has
been ramped up.

This persistent-mode operation significantly reduces the evaporation rate of
LHe to 30 liters/day, compared to 40 liters/day during driven-mode operation.
The decay rate of persistent mode operation is approximately 30 parts per
million per day, which has no practical impact on a typical axion-haloscope
search schedule.

The magnet system underwent a quench test to evaluate its response before
delivery by Oxford Instruments [54, 51]. It has been successfully installed
inside a vapor shield cryostat, with a height of approximately 3.3
$\mathrm{m}$. The cryostat provides a useful volume of 478 liters for
containing the LHe. The magnet system was delivered to the CAPP experimental
hall in March 2020. However, due to the impact of the COVID-19 pandemic, the
commissioning run was delayed until August of the same year and finally
completed in December 2020. The magnet was powered up in spring 2021 and has
been maintained at a cold temperature, with only one instance of raising its
temperature above 100 $\mathrm{K}$ up to summer 2023.

Our magnet weighs approximately 1200 $\mathrm{kg}$, and it is most convenient
to keep it on a Low Vibration Pad of our experimental hall during operation
and during the period between experiments. This necessity requires us to move
the DR up and down during the installation and warming-up procedures.

###  II.2 Cryogenics

One of the critical factors in Eq. (2) is the system noise temperature, which
is comprised of various components, including the cavity, the initial
amplifier stages, passive RF components, cable and connector losses, among
others. To minimize the impact of these effects, it is essential to reduce
their physical temperature. Furthermore, certain components, such as QNLA,
operate only under cryogenic conditions, and their added noise depends on
their physical temperatures. High-electron-mobility-transistor (HEMT)
amplifiers, while functional over a wide temperature range, exhibit their best
noise properties below 10 $\mathrm{K}$ [55, 56]. Therefore, having cryogenic
equipment capable of cooling these crucial components in the readout circuit
is essential to achieve the best performance of the system.

The determination of how low we need to cool our critical components can be
derived from our target frequency range, which, for CAPP-MAX at this stage,
falls between 1 and 2 GHz. According to the standard quantum limit, the noise
temperature ($T_{\rm SQL}=\hbar\omega/k_{B}$) for a frequency of 1 GHz is 48
mK, one component of which is the added amplifier noise of 24 mK for 1 GHz
($T_{\rm add,min}=\hbar\omega/2k_{B}$). This provides us with guidance on the
cooling temperatures required for our components to achieve optimal
performance. Temperatures below 30 mK can be achieved with a standard dilution
refrigerator.

Another part of our system that requires cryogenic temperatures is the
superconducting magnet, manufactured by Oxford Instruments and featuring a
complex design (see Sect. II.1). During a warm-up phase of the magnet to 100
K, in order to remove solidified nitrogen and oxygen from the main dewar, the
outer vacuum chamber (OVC) was pumped to improve the isolation and remove any
penetrating gas. This process improved vacuum isolation and reduced the helium
gas pressure in the main dewar by a factor of 6.

We utilize a Leiden Cryogenics DRS1000M [57] dilution refrigerator, which
offers a nominal cooling power of approximately 1.3 mW at a temperature of 120
m$\mathrm{K}$, (marked as Dilution refrigerator on Fig. 2). The DR is equipped
with three clear 25-m$\mathrm{m}$-diameter tubes extending from the top of the
DR down to the 4 $\mathrm{K}$ stage, which is used for wiring purposes. Three
24-pin Fischer connectors [58] facilitate connections to the mixing chamber
(MXC), while one of the connectors is used for wiring to the 4 $\mathrm{K}$
plate. The wiring is constructed of phosphor-bronze twisted pairs. Two
differential lines are used to control the piezo actuators, and they are made
of copper wire that runs from the room-temperature (RT) flange down to the 4
$\mathrm{K}$ plate. From the 4 $\mathrm{K}$ plate down to the MXC, four and
five differential pairs made out of NbTi wires are connected in parallel to
enable the supply of high-current pulses, with amplitudes reaching a few
amperes, to the piezo actuators.

Figure 2:  Comprehensive view of the detector setup within the cryostat. It
includes a cross-sectional view of the main Dewar containing LHe and the
inserted dilution refrigerator (outlined in black). The HEMT package is
located on the 4 K plate, while the microwave isolator is located on the Cold
plate. The cavity and MXC assembly are affixed to the gold-plated copper
extension of the mixing chamber via four gold-plated copper thermalization
rods. The Still radiation shield is linked to the Still extension. The cavity
has two temperature sensors to monitor top and bottom temperatures and two
piezo actuators to adjust the cavity resonance and coupling coefficient.

All RF connections that run from the RT flange to the 4 $\mathrm{K}$ plate are
constructed using 0.034-inch-diameter CuNi cables. One of these cables is kept
as spare and kept terminated inside the DR. The next four cables that connect
the system inputs are made of 0.047-inch-diameter BeCu cables, while the
output cable is constructed from superconducting 0.034-inch-diameter NbTi
cables. All interconnections between cables are made using gold-plated SMA
connectors and bulkheads are constructed of brass and BeCu.

The DR is equipped with five standard temperature sensors from Leiden
Cryogenics, which are used to monitor the temperature and control it through a
proportional-integral-differential (PID) controller. We used an additional 10
channels to accurately measure the following temperatures: 4 $\mathrm{K}$
plate, two HEMT amplifiers, two microwave circulators thermally anchored to
the cold plate, the top and bottom of the cavity, and the extension of the
mixing chamber. One of the thermometers was attached to the piezo rotator
within Run 4 and later on it was placed at the cold plate within Run 5.

The inner vacuum chamber (IVC) shield maintains a temperature at the level of
LHe, while inside, there is an immersed gold-plated radiation shield with a
temperature ranging from approximately 550 to 800 m$\mathrm{K}$ during the
refrigerator operation. Due to space constraints, we have opted not to use the
radiation shield that is typically thermally connected to the refrigerator’s
cold plate. This is one of the reasons why the base temperature is higher than
the one specified in the manual.

Figure 3:  Schematic view of the helium gas recovery system (GRS) operating in
two modes shown with blue and orange dashed outlines: mode A – Data taking and
mode B – DR inserting and main dewar maintenance. In the first configuration
mode, the main recovery line is followed by the manual valve (V1), the two He
gas recovery bags and the Cryomech He compressor (model HRCP), the six high-
pressure tanks, the purifier (model HRSMP-Purifier), the three cold heads
(CH1–CH3) (model PT415) charged by the Cryomech He compressors (model CP1110)
placed on the top of the 500-liter non-magnetic He liquefier (model LHeP60),
and the liquid-cryogen level monitor (model LM-510) with PID control. In the
second mode, the He closed-cycle operation is used. The main dewar is followed
by the manual valve (V2), the reliquefier (RL) (model HeRL60), the three Cold
Heads (CH1–CH3) (model PT420-RM), charged by the 3 Cryomech compressors (model
CPA1114). The pressure and temperature control unit with PID from Stanford
research systems (model CTC100) is used. The output of the reliquefier is
followed by the evacuated-jacket metal nozzle. The 1 $\mathrm{K}$ pot is
followed by the manual valve (V3), by the Cryomech 1 K pot compressor (model
PHRS1E350006), and is connected to the input of the RL.

The DR is immersed in a LHe cryostat, which also houses a superconducting
magnet. The IVC is filled with helium exchange gas, which aids in precooling
the DR insert to LHe temperature. Before immersing the DR, the 1 $\mathrm{K}$
pot needs to be pressurized, typically to a pressure of around 1.3
$\mathrm{bar}$. This pressurization is essential to prevent non purified
helium gas, which may include slight nitrogen contamination, from entering
these capillaries connecting the 4 $\mathrm{K}$ pot to the cryostat. If helium
gas mixed with nitrogen were to penetrate these capillaries, it could lead to
the anti-sublimation of nitrogen on the capillary walls. This, in turn, could
block the capillaries, rendering the operation of the 1 $\mathrm{K}$ pot
ineffective or even impossible.

Once the DR insert reaches approximately liquid-helium temperature, we
initiate the process of pumping out the exchange gas from the IVC using dry
rotary and turbo-molecular drag pumps, reducing the pressure below $5\times
10^{-5}$ $\mathrm{mbar}$. This process typically takes about 18 hours to
complete and requires running the sorption pump heater. The primary cooling
process takes place predominantly within the 1 $\mathrm{K}$ pot. LHe is
delivered from the main dewar through two tubes connected to the 4
$\mathrm{K}$ plate. From there, it flows through thin capillaries, filling the
1 $\mathrm{K}$ pot with LHe. To facilitate cooling, the 1 $\mathrm{K}$ pot is
pumped using an external compressor, shown as “1 $\mathrm{K}$ pot comp.” in
Fig. 3. As pumping progresses, the temperature of the 1 $\mathrm{K}$ pot drops
to the range of 1.4–1.8 $\mathrm{K}$, and it also pre-cools the insert part of
the DR.

Once the 1 $\mathrm{K}$ pot is sufficiently cold, the 3He–4He mixture can be
introduced into the fridge by the condensing process. When the mixture is
filled into the MXC, circulation can begin. This circulation causes the still
and mixing chamber to cool to below 1 $\mathrm{K}$. Once the mixing chamber
has reached its base temperature (for fully loaded DR it is currently about 25
m$\mathrm{K}$), the Still heater can be activated, typically requiring a
couple of m$\mathrm{W}$ of power. This way we are able to control the flow
rate of the mixture. Generally, with this level of heating power, the pressure
in the Still line stabilizes at around $8.2\times 10^{-2}$ m$\mathrm{bar}$.

The cooling power and time of each stage in a dilution refrigerator depend on
several factors, including the design of the refrigerator, the heat load
imposed on it, and the heat capacitance of the components integrated into the
custom system. Achieving a good thermal connection between components is a
crucial practical consideration. When two surfaces touch, the actual contact
occurs only at the points where there are protrusions or asperities. To ensure
effective connection, it is necessary to increase the contact area by plastic
deformation by applying pressure during the connection process. Additionally,
to compensate for thermal expansion and contraction in linear dimensions when
using threaded links, spring washers should be employed. To eliminate the
effect of metal oxide on the surface during thermalization, copper parts are
gold-plated.

To increase the surface area of contact between dielectrics or between
dielectrics and metals, we apply Apiezon N grease [59] between them. In
general, we aim to minimize the use of dielectric components or reduce their
size on the $\mathrm{mK}$ stages to expedite the cooling process and limit
their impact.

The RF cables were thermally connected to the bulkheads on the 4 $\mathrm{K}$
stage and the MXC. They were also thermally linked to the heat exchangers of
the DR in between. We used superconducting cables at temperatures below 4
$\mathrm{K}$.

The main evaporation of the He gas comes from the main dewar and the 1
$\mathrm{K}$ pot of the DR. In order to avoid any helium losses during the
maintenance of the main dewar, the insertion of the DR and the data taking
process we use He recovery lines (controlled by V1, V2, V3, see Fig. 3).

The initial He recovery line operates during the insertion of the DR into the
main dewar or while warming up or cleaning the main dewar of contamination
(Mode B in Fig. 3). For this operation, we employ a LHeP60 helium liquefier
plant [60], with the ability to liquefy up to 60 liters helium per day and
equipped with a storage capacity of 60 liters of helium gas in gas tanks.

This line consists of two He recovery bags, a helium compressor, high-pressure
tanks, two purifiers for water absorption, a liquid-nitrogen cold trap, and a
500-liter helium tank (referred to as Liquefier in Fig. 3). Three cold heads,
marked CH1–CH3 in Fig. 3, run the condensing process of the incoming He gas
flow. The PID system, based on the cryogenic level monitor controls the
temperatures of the cold heads and the pressure within the liquefier’s dewar.

After the He liquefaction, the transfer of liquid He to the main dewar is
accomplished by directly connecting the main dewar and the liquefier dewar
using an evacuated siphon. The liquefier dewar is constructed from non-
magnetic metals, allowing its placement in close proximity to the main dewar,
even within the high magnetic field area. The Cryomech He compressor is
complemented by closed-cycle distilled water chillers, positioned outside the
laboratory building for better cooling efficiency.

The second He recovery line, identified in the _Mode A_ in Fig. 3, operates in
a closed He loop and does not require a high-volume He reservoir. The He gas
evaporates from both the He main dewar, through valve 2, and from the 1
$\mathrm{K}$ pot, through valve 3, shown with arrows in Fig. 3 to the
liquefier tank and condenses at the three cold heads.

The liquid helium is returned to the main dewar via a vacuum thermo-isolated
nozzle. The vertical position of the reliquefier (RL) HeRL60 [61], is
adjustable. Varying the height of the RL maintains high operational efficiency
since it keeps the end of the nozzle above the liquid helium level. The
incorporation of an evacuated jacket around the metal nozzle has effectively
reduced internal helium evaporation from the main dewar, resulting in a
substantial decrease in the main dewar pressure from 2.4 psi to nearly 0 psi.
In this way, we are able to set the PID system to support 0.3 psi of the input
pressure using internal heaters inside of the RL. During the data taking, the
liquid He flows continuously, closing the loop between the RL and the main
dewar.

##  III Detection system

###  III.1 Microwave cavity

The axion haloscope employs a tunable cavity with a high quality factor,
placed in a strong magnetic field, to detect signals generated when the axion
frequency falls within the cavity resonance. As seen in Eq. (1), the larger
the magnetic field and cavity volume, the more of the axion dark matter field
is converted into microwave photons. A higher quality factor results in
converted microwave photons surviving inside the cavity for longer periods,
amplifying the signal.

The CAPP-MAX relies on a powerful 12 $\mathrm{T}$ magnetic field generated
within a large 320 $\mathrm{mm}$ bore. This requires the design of a large
cavity that allows high $B^{2}V$. To address this, CAPP designed an ultralight
cavity (ULC) that weighs less than 5 kg including the tuning rod and occupies
a volume of 37 L, while maintaining a Q-factor of approximately $10^{5}$. This
enables axion searches within the range of 1.02$-$1.185 GHz.

The size of the cavity for the CAPP-MAX is influenced by the bore size of the
magnet and the dimensions of its various internal radiation shields. The
innermost 50 $\mathrm{mK}$ shield is positioned within the still radiation
shield, with an inner diameter of 281 $\mathrm{mm}$. Based on this fact, the
outer diameter of the cavity was determined to be 274 $\mathrm{mm}$. In the
described axion experiments, the 50 $\mathrm{mK}$ shield was not utilized.
Without the 50 $\mathrm{mK}$ shield, the additional heat load generated from
the still shield, when calculated according to the Stefan-Boltzmann law, is
negligible, amounting to less than 0.1 $\mathrm{\SIUnitSymbolMicro W}$. This
decision has shortened the system setup time and provided additional space,
enabling the use of larger cavities in subsequent experiments, thereby
enhancing sensitivity.

To minimize space loss due to the thickness of the cavity walls and to reduce
its weight, thin metal sheets were rolled to create the cavity’s side walls.
Oxygen-free high-thermal-conductivity (OFHC) copper, known for its high
thermal and electrical conductivity, was used as the material of choice,
allowing for a high Q-factor while facilitating effective cooling. Figure 4
depicts the structure of the first CAPP-MAX cavity. The top and bottom plates
of the cavity are 6 $\mathrm{mm}$ and 3.5 $\mathrm{mm}$ thick, respectively.
The height of the cavity is 640 $\mathrm{mm}$ with the thickness of its side
walls 0.5 $\mathrm{mm}$. Excluding the tuning rod, the ULC weighs only about 4
kg.

Figure 4:  Photo of the ULC (left), a 3-dimensional cross-sectional view of
the mechanical design (middle), and an enlarged view of the top and bottom
(right). The four cavity fixtures and thermalization rods made of gold-plated
copper thermally anchor the cavity which is affixed to the MXC extension. The
piezo linear positioner adjusts the antenna coupling between the readout chain
and the cavity. The piezo rotator steers the copper tuning rod with the
sapphire axle, which is thermalized via OFHC copper braiding. Indium cold
welding connects the cavity top and bottom to the side walls.

To adjust the resonance frequency of the cavity, we rotated the position of an
empty cylinder with a diameter of 30 $\mathrm{mm}$, a height of 636
$\mathrm{mm}$, a thickness of 0.7 $\mathrm{mm}$ within the cavity, and the
rotation axis located 25 $\mathrm{mm}$ away from the center of the cavity.
This rotation had a 50-$\mathrm{mm}$ diameter that can be used to tune the
TM010-like mode resonance frequency in the range of 1.02$-$1.185 GHz.
Simulations show [62] that the tuning rod’s relatively small size compared to
the cavity diameter and its restricted movement within 50 $\mathrm{mm}$ from
the cavity center help mitigate the mode localization often observed when
using a metal tuning rod in cavities[38]. We attached a sapphire axle to the
center of rotation of the tuning rod, allowing precise tuning with a
resolution of less than 1 millidegree using the piezo rotator from Attocube
Systems AG [63]. This setup allowed for a tuning resolution of less than 1
kHz. Additionally, the alignment of the upper and lower sapphire axles was
adjusted within a 1 $\mathrm{mm}$ margin of error to keep the maximum tilting
angle of the tuning rod below 0.2 degrees, ensuring that the form factor
remains high on average.

Figure 5:  Cavity parameters obtained at 4.2 K. (a) Mode map: resonant
frequency vs. angular position of the tuning rod. The intensity of the lines
correspond to the forward transmission coefficient (S21) in logarithmic scale.
The individual modes are identified from simulation. (b) Unloaded quality
factor as a function of frequency. The two vertical dips correspond to mode
crossings.

Transmission scattering parameters were measured using a vector network
analyzer (VNA) to create a mode map and the Q-factor versus the resonance
frequency of the cavity for the 1$-$1.2 GHz frequency range, as shown in Fig.
5. The mint-colored line at the bottom of the mode map represents the
resonance frequency range of the TM010 mode. Although minor mode crossings
occurred at some frequencies throughout the tuning range, there were no
significant mode mixings, consistent with the initial design. The unloaded
cavity Q-factor was greater than $1.2\times 10^{5}$ when the tuning rod was
farthest from the center (50 mm) and remained at $0.9\times 10^{5}$ when
positioned at the center, maintaining over $10^{5}$ throughout most of the
tunable frequency range.

Effective thermal management is essential to minimize the physical noise from
the cavity and the tuning rod. The key steps involve optimizing thermal
conductivity, reducing the number of thermal interfaces, and enhancing
efficiency at inevitable interfaces [64].

Initially, we secured four OFHC copper rods with gold plating to the upper
part of the cavity using bolts. This approach facilitated efficient
thermalization. Interfaces between the upper and lower cavity sections were
bonded through indium cold welding. Additionally, OFHC copper strips, secured
with bolts, formed a direct connection between the upper and lower cavity
plates, further augmenting thermalization.

The task of cooling the tuning rod posed a multifaceted challenge. Because the
tuning rod must rotate smoothly and cannot be rigidly attached to other
components, conventional cooling methods were rendered impractical.
Furthermore, the substantial heat contribution of the tuning rod relative to
its surface area potentially creates the so-called “hot-rod problem” [36]. To
address this issue, we employed varnish and glue to create robust thermal
interfaces between the upper cap of the tuning rod and the sapphire axle,
resulting in improved thermal conductivity. To further enhance the thermal
connection, copper braiding was employed to link the sapphire axle and the
cavity’s top plate. This braiding was secured with bolts and enveloped with
varnish. To additionally stabilize the resonance frequency and diminish heat
generated by vibrations, the sapphire axle connected to the bottom of the
tuning rod featured a ball-like shape, allowing it to make direct contact with
the OFHC copper floor.

Notwithstanding the considerable size of our experimental cavity, we
successfully crafted an ULC using OFHC copper. Our approach utilized various
techniques, each tailored to address specific thermal interfaces. This ULC
enabled us to attain an low cavity temperature of about 30 mK, marking a
significant milestone in achieving one of the lowest-temperatures and lowest-
noise axion experiments to date.

###  III.2 Readout electronics

One critical element of CAPP-MAX’s readout electronics is the low-noise
amplifier, limited by quantum noise. The noise of these amplifiers is
constrained by the uncertainty principle. Quantum squeezing technology [65]
offers a way to overcome this limitation. However, this approach doesn’t
readily apply to measuring signals with a stochastic phase component, as it
generally necessitates prior knowledge of the anticipated signal’s phase [66].
Although the vacuum squeezing technique has been used in axion experiments to
achieve a two-fold gain in scanning rate [67] for frequencies exceeding 4 GHz,
we have not yet implemented this technique in our work.

We utilize flux-driven Josephson parametric amplifiers (JPAs) [68] as quantum
noise-limited amplifiers for the faint signals from our haloscopes. The
equivalent circuit of our JPAs includes a coplanar-waveguide $\lambda$/4
resonator that is grounded through a nonhysteretic superconducting quantum
interference device (SQUID) (Fig. 6). This resonator is coupled to the
external transmission line through a capacitor $C_{c}$. The signal input and
output share the same port. The JPA operate by modulating the SQUID inductance
through an external pump signal. A SQUID acts as a non-linear inductance whose
value can be modulated by sending a pump signal through a line inductively
coupled to it. The operating frequency can be tuned in a certain range by
adjusting the average inductance of the SQUID by applying DC flux using a
superconducting coil.

Figure 6: Equivalent circuit diagram of a JPA. The magnetic flux bias defines
the average inductance of the SQUID loop (the Josephson junctions are denoted
as $\times$ in the loop), while the pump is modulating this flux at twice the
frequency of the signal to be amplified. Since the signal in and out ports are
the same, a circulator is needed to operate the amplifier (see Fig. 7(a)).

Figure 7:  Simplified diagrams of the JPA connection in the readout chain. (a)
Single-JPA configuration used in Runs 4 and 5. (b) JPA assembly used in Run 6
with two holders connected in series. Each holder has the capacity to
accommodate up to 3 JPAs. To minimize any potential interference between them,
two of them were positioned in Holder 1 and one in Holder 2. The green color
highlights the actual placement of JPAs.

Our JPAs operate in the three-wave mixing mode with the pump ($f_{p}$), signal
($f_{s}$), and idler ($f_{i}$) frequencies satisfying the relation [69]

$\displaystyle f_{p}=f_{s}+f_{i}.$ (4)

The JPA amplifies the signal injected from a source port and reflects it back.
The source can be either noise generated by a wideband 50 $\Omega$ terminator
or the cavity. The signal paths for both cases are shown in Fig. 7(a). A
circulator is employed to separate the incoming and outgoing signals. The
subsequent amplification is achieved by two HEMT amplifiers mounted at the 4 K
stage of the fridge. Further signal processing is performed by a room-
temperature amplifier and Spectrum Analyzer (SA) or a custom DAQ system.

Figure 8:  RF switches with (left) and without (right) a magnetic shield.

In our experimental setup, we encounter the challenge of potential magnetic-
field effects on various components, including circulators, isolators, HEMT
amplifiers, and most importantly, the JPA. The magnet compensation region,
which minimizes the impact of magnetic fields, is predetermined by the magnet
manufacturer and may not accommodate all the components in our setup due to
space limitations.

To overcome this challenge, we employ shielded components, such as circulators
and isolators, and have also developed custom shields (see Fig. 8) dedicated
to safeguarding sensitive components.

To protect the JPAs from strong magnetic fields, we developed a multilayer
nested shield [70]. The shield comprises three components, as shown in Fig. 9.
The outermost layer is crafted from a superconducting NbTi alloy with a high
critical magnetic field. The second layer is made of cryoperm alloy. Its
purpose is to effectively redirect and absorb external magnetic fields,
significantly diminishing the overall magnetic field intensity. Finally, the
innermost layer is composed of a superconducting Al alloy, adding an extra
layer of protection against magnetic field penetration.

Figure 9:  Three-layer magnetic shield for a JPA. (a) Simulated magnetic field
map inside the shield under an external background of 1 T. (b) Drawing of the
cross-sectional view of the shield: Each layer, from the outside to the
inside, is made of NbTi (1), cryoperm (2), and Al (3), respectively. (c)
Photograph of the assembly with the SMA connectors shown.

In the initial conditions at non-cryogenic temperatures, the superconducting
shields exhibit behavior akin to nonmagnetic materials. The reduction of the
initial magnetic field is accomplished by the second shield layer. During the
cooling process, the first layer, constructed from a superconducting material
with a high critical magnetic field, undergoes a transition from its normal
state to the superconducting state. This transformation enables it to
effectively trap the initial magnetic field within the shield. Meanwhile, the
magnetic field within the second shield remains largely unaffected. As the
temperature approaches the critical point for the innermost shield layer, it
freezes the remaining magnetic field from the second shield.

In a detailed simulation using the ANSYS Electronics Desktop [71], it was
found that the magnetic field within the shield dropped to below 100 nT when
exposed to an external field ranging from 0 to 0.1 T, as shown in Fig. 9. The
simulation is confirmed by a measurement at 4 K [70].

The magnet’s residual field at the JPA position, without the shield, measures
approximately 0.01 T. With the implementation of this shield, the field
strength at the JPA is effectively reduced, giving a small shift of the JPA DC
bias as shown in Fig. 10 for ten times as much (0.1 T) external magnetic
field. The corresponding shielding factor is estimated between $10^{5}$ and
$10^{6}$.

Figure 10:  Dependence of resonance frequency ($f_{c}$) in a passive mode of
the JPA on applied DC flux bias, as measured with a separate device with the
resonance frequency at 6 GHz. The two colors correspond to the data taken in
the presence and absence of the residual magnetic field of 0.1 $\mathrm{T}$,
which is ten times higher than expected during axion search experiment.

While the flux-driven JPA offers extremely low noise close to the quantum
noise limit, its original design had a limited tuning range of 45–60 MHz [70].
In Runs 4 and 5 we successfully used one amplifier to scan 20 and 58 MHz,
respectively [32]. This presented a challenge for CAPP-MAX as it required
frequent warm-up and replacement, resulting in significant time loss and the
consumption of large amounts of LHe. Our cavity possesses a tunable range of
200–300 MHz, and the scanning range of each Run was determined by the tuning
capabilities of the JPA. Therefore, our primary goal was to extend the
amplifier’s range without compromising the exceptional noise properties of our
JPAs. To achieve this, we employed two methods, which we recently reported:
serial and parallel connections of the JPAs [72].

During Run 6, we used a combination of parallel and serial connections, using
Holder 1 with two JPAs and Holder 2 with one JPA; see Fig. 7(b). Holder 1
encompasses JPAs designed for frequency ranges of approximately 1.080–1.122
GHz and 1.135–1.183 GHz, while Holder 2 houses a JPA with a tunable range
spanning 1.045–1.060 GHz. To accommodate three JPAs within a single holder, we
designed a specialized printed circuit board (PCB), as illustrated in Fig. 11.
During operation, only a dedicated JPA is activated, with the other two being
disabled by adjusting the resonance frequency. Experimental results
demonstrate that all three JPAs operate effectively without compromising their
noise characteristics. There was an overlap in frequencies between Runs 5 and
6. To enhance sensitivity, we combined the shared data from these runs.

Figure 11:  Top view of the gold-plated PCB with three JPA chips bonded. The
pump and signal lines are connected through SMP connectors.

Our setup has the capacity to incorporate up to 6 JPAs through a combination
of both parallel and serial connections. For our upcoming Run 7, we are using
6 JPAs covering a total range of approximately 300 MHz from 1.2–1.5 GHz [72].

Figure 12:  Experimental setup including the cavity, a cryogenic receiver,
measurement chains and the room temperature DAQ system. The major components
of the receiver chain are JPAs, a three-junction circulator/isolator, and a
series of HEMT amplifiers (HEMT1 and HEMT2). The chain has two JPA
configurations for two data taking runs, Runs 4 and 5, and Run 6. The cavity
properties are measured through several lines: weak cavity coupler (WEAK),
bypass cavity test (BYPASS), and cavity reflection (CAVR). The DAQ system
consists of a radio-frequency signal generator (RF generator), a VNA, a SA, a
radio-frequency local oscillator (LO), an image-rejection mixer (IRM), and a
digitizer. The noise source is used in the equivalent-noise-temperature
calibration of elements in the RF-measurement chain. Transmission coefficients
between points A–B and C–D are defined as $\eta_{u}$, $\eta_{c}$,
respectively, see text.

The readout electronics diagram is depicted in Fig. 12, providing an overview
of the experimental setup used for all characterization measurements and the
running of the experiment. The diagram displays various temperature stages,
beginning from room temperature (300 K), 4 K, 1 K, cold plate, and mixing
chamber (MXC) plate. Each temperature stage includes an attenuator for each RF
line to prevent Johnson noise due to higher temperature stages from affecting
the colder stages.

The setup is not only designed to conduct experiments but is also suitable for
characterizing our JPA. In terms of noise characterization, our setup
incorporates a noise source that enables the measurement of noise temperature
for both the JPA and the HEMT.

Facilitating noise checks, cavity tests, and experiments, a cold RF switch is
integrated within the setup. This RF switch enables seamless switching between
the noise source and the cavity. Additionally, the RF switch features an
intermediate state that allows for the measurement of line losses between the
cavity and the switch, as detailed in reference [32].

The JPA signal is amplified using low-noise cold HEMT amplifiers. Two HEMT
amplifiers LNF-LNC0.6_2A [73] are connected in series and thermally stabilized
at the 4 K stage of the refrigerator. To mitigate the adverse effects of
signal reflections from the amplifier, an isolator is placed between the JPA
assembly and the HEMT. This isolator is thermally anchored to the fridge Cold
plate. Temperature sensors attached to the amplifiers are used to monitor the
enclosure temperature, which typically reads 5 K and 6 K during operation at
optimal voltage and current biases while the fridge is operational.

To measure the noise temperature of the HEMT amplifiers, we employed a
methodology similar to the widely used Y-factor method [74]. We use a single-
channel noise source (NS). The NS consists of a wideband matched 50 $\Omega$
terminator, a heater, a thermometer, and 9-pin Micro-D connectors for the
thermometer and heater. These components are assembled on a gold-plated copper
holder (see Fig. 13) and are specifically designed to be installed on the
mixing-chamber RF assembly. In our test fridge, we utilize a four-channel
version of the NS described in [75].

The NS is connected to the measurement chain using a 0.047-inch-diameter NbTi
microwave coaxial cable, which is superconducting below 11 K and provides
excellent thermal isolation between the NS and other circuits. Superconducting
NbTi twisted pair cables with negligible thermal conductivity are used to
connect the temperature sensor and heater. The temperature sensor is a
calibrated RuO2 sensor produced by Lake Shore Cryotronics, and the heater is a
metal-film 100 $\Omega$ resistance that maintains stability within 1% over a
wide temperature range, from room temperature to the base temperature of the
MXC.

For precise temperature measurement and control, we utilize the 372 AC
resistance bridge and temperature controller provided by Lake Shore
Cryotronics. The NS is securely fixed to the MXC assembly using two 20-mm-long
plastic spacers, and thermal anchoring to the MXC plate is achieved through a
15-cm-long copper wire (see Fig. 13).

Figure 13: RF-noise-source assembly: (1) 50 $\Omega$ terminator connected to
SMA bulkhead, (2) enclosure, (3) thermally isolating plastic stand, (4)
thermometer, (5) DC connector, and 6 - heater. The assembly is weakly
thermally anchored to the MXC by a thin copper wire (not shown).

The Bypass and Output ports (see Fig. 12) were used for direct measurements of
JPA characteristics that effectively bypass the cavity. To assess the noise
level of the HEMT amplifier, we deactivate the JPA pump signal and adjust the
DC flux bias current to shift the passive resonance of the JPA away from the
measurement frequency. In doing so, the JPA behaves as an almost ideal
reflector, minimizing its influence on other circuits within the setup.

Subsequently, we proceed to establish and stabilize the temperature of the
noise source at a specific value. We then measured the power spectral density
(PSD) within the desired frequency range. This process is repeated for 3–4
different temperature settings, allowing us to acquire a range of PSD values
corresponding to various noise temperatures.

The measurement of JPA noise can be accomplished using the modified Y-method,
as described earlier in this paragraph and in articles [52, 31]. However, this
method has some drawbacks, including the lengthy setup and cooling time
required for the noise source and the potential for saturation due to the
limited dynamic range of the JPA. To address these challenges, we employ a
spectrum comparison method. In this approach, we compare the SNR with the JPA
turned off to the SNR with the JPA turned on. This method provides a more
time-efficient measurement technique to assess the noise characteristics of
the JPA [34]. The result of the direct Y-factor method on the JPA for a
limited temperature range is consistent with the SNR-comparison method. Our
flux-driven JPAs demonstrate noise levels that are close to the quantum noise
limit (QNL), as reported in [70].

In our frequency range of 1–8 GHz, the quantum noise limit ranges from 48 to
384 mK, while the minimum added noise due to the amplifier increases from 24
to 192 mK. This highlights the significance of cooling all the readout
components of the initial stages to temperatures below these limits in order
to achieve the lowest possible system noise temperature.

At temperatures below 100 mK, certain effects and phenomena become more
pronounced, which are usually hidden by the thermal motion of the particles at
higher temperatures. Among these effects, acoustic mismatch [76, 77] and
electron–phonon decoupling play a significant role. Also, phonon thermal
conductivity decreases as a result of the reduction in the number and energy
of phonons. Thus, it is advisable to avoid dielectrics during thermalization,
even layers of oxides that form on metals.

By employing metal interfaces and applying a gold coating between the mixing
chamber (MXC) and the various parts and components installed on it, we
successfully achieved notably low temperatures for the cavity, JPA, and cold
RF components in our axion experiment, reaching 22–25 mK. This approach led to
the reduction of the total system noise, bringing it as low as 150 mK.

##  IV Data Acquisition and Monitoring

Figure 14: Instrument connections for data acquisition. Most instruments are
connected to the main DAQ computer via either Ethernet (solid line)
distributed by Ethernet switches or USB/RS-232 (dashed line) directly. Figure
15:  Measurement sequence during data taking. It includes physics data taking,
cavity measurement, and system noise calibration. $\nu_{\textrm{target}}$ is
the target frequency that the resonance frequency of the cavity and the JPA
(with -100 kHz offset) is tuned. $\Delta\nu_{\textrm{target}}$ is the
frequency tuning step, which is kept 10 kHz throughout the data collection.

As shown in Fig. 14, most of the instruments are connected to the main DAQ
computer over Ethernet within a local network. Others are directly connected
to the main DAQ computer via the universal serial bus (USB) and the
recommended standard 232 (RS-232). An additional readout for the magnet
information and measurements of the ambient magnetic field around the system
is also connected over Ethernet. Finally, a dedicated computer for controlling
a fast digitizer is connected over Ethernet as well.

The DAQ is governed by a home-developed data acquisition software, CULDAQ
[78]. The software provides features of controls over devices in the
experiment via various communication protocols, data readout and packaging,
storing monitoring data, and experiment run sequence. In the DAQ software,
there are three layers of classes for the device controls: abstract classes to
support communication protocols such as Ethernet, USB, RS-232, and so on;
wrapper classes that translate the standard commands for programmable
instruments or instructions provided by the manufacturers into user-friendly
functions; classes providing higher level functions that utilize and combine a
set of functions implemented in the wrapper classes to perform practical tasks
conveniently. This hierarchy of classes keeps the software in a modular
structure and provides a good re-usability and readability of the code. The
software also provides utility classes for the convenience that support
database access, logging, and data packaging. The data acquired in the
experiment are packaged in a ROOT format [79]. The data read by a fast
digitizer are also packaged as separate ROOT files, and the former ROOT file
contains a map to match the experiment runs to the fast digitizer data. In
addition, critical information for the experiment operation such as the total
system physical temperatures, pressures, and magnetic fields are recorded in a
database so that an online monitoring is available during the experiment.

When the components implemented in the software are combined, a logical
sequence of the experiment can be formed. An experiment sequence requires a
set of configuration parameters such as a frequency tuning range and step, a
number of spectra to be averaged, parameters of instruments (center and span
frequencies, resolution bandwidth, and so on), and they are given in the
beginning of a measurement. A typical experiment sequence is as follows:

  1. 1.

Initializing the instruments by the given parameters.

  2. 2.

Tuning of the cavity resonant frequency to the initial target frequency.

  3. 3.

Measuring the auxiliary data such as the system physical temperatures,
pressures, magnetic field, and so on.

  4. 4.

Tuning of the JPA at the current resonant frequency and a target gain.

  5. 5.

Characterizing the cavity by measuring the cavity reflection and transmission.

  6. 6.

Characterizing the receiver chain with turning on and off the JPA.

  7. 7.

Taking power spectrum data for about 192 s with a fast digitizer (high
efficiency) and a spectrum analyzer (for consistency checks).

  8. 8.

Characterizing the cavity again.

  9. 9.

Measuring the auxiliary data again.

  10. 10.

Tuning the cavity resonant frequency to the next target frequency, with a step
of about 10 kHz, and repeating the sequence from 3.

The sequence diagram is depicted in Fig. 15. Power spectrum data is taken
using a fast digitizer. In addition, we acquire a small data sample
simultaneously with a spectrum analyzer for consistency checking. We employ an
M4i.4480-x8 manufactured by Spectrum Instrumentation GmbH [80] as the fast
digitizer. For the experiment, we implemented the fast digitizer with a
sampling rate of 45 MSamples/s and a resolution bandwidth of 10 Hz, therefore,
the acquired data is capable of searching not only for virialized axions, but
also for non-virialized axions [53]. The practical DAQ efficiency of the fast
digitizer approaches 100% [81].

The total scanned frequency range within Runs 4, 5, and 6 with different RF
configurations in Fig. 12, is shown in Fig. 16. Runs 4 and 5 were taken with a
single JPA while Run 6 utilizes 2 JPA holders with a total of 3 JPA chips.

Figure 16:  Scanned frequency as a function of calendar time for Runs 4, 5,
and 6. Different colors represent different JPAs, except black, which
corresponds to the scan with no JPA operating in the RF-chain.

##  V Analysis and results

To confirm the integrity of this data, a parallel system using a commercial
spectrum analyzer, is also used in the data stream. In addition, a second
spectrum analyzer is used to collect data using an aerial antenna tuned to the
frequency of interest in order to detect unwanted interference from outside
[82]. Those interference signals are usually narrower than those expected from
standard halo axion dynamics, but perhaps compatible with narrow axion lines
that appear as transients due to the focusing effects of the sun, moon,
planets, and the earth itself [45, 83, 84, 85, 86, 87]. One such signal is
shown in Fig. 17. The signal was intermittent and appeared simultaneously at
the SA connected to the aerial antenna, indicating external interference. It
was most likely due to a radio communication with approaching aircraft into a
nearby airport using the same frequency [88].

Figure 17:  Candidate signal with a large SNR. The signal strength follows the
cavity response, indicating the signal goes through the cavity. The signal was
finally rejected as it was also picked up by the aerial antenna plugged into a
spectrum analyzer placed near the experiment to monitor ambient interferences.
The frequency and width of the interference was at approximately 1149.9905 MHz
and 20 Hz, respectively.

Fig. 17 shows the main analysis strategy for signals with a large SNR ratio.
The criteria for considering those signals as candidates are as follows:

  1. 1.

The signal amplitude needs to follow the cavity response, and

  2. 2.

The signal needs to be absent from the spectrum analyzer connected to the
aerial antenna.

If those conditions are met, we acquire more data for a long time, enough to
establish the stability of the signal as a function of time. If other modes
than the $\rm TM_{010}$ are close to the candidate frequency, the cavity is
tuned to that mode as well [35]. If all is consistent with the signal being an
axion, the final check is testing its magnetic field dependence.

Figure 18:  Overview of the analysis procedures in three different runs (Runs
4, 5, and 6). The group refers to a bundle of the dataset within approximately
the same statistical characteristics. Each group of data is processed
according to the steps outlined in the single-group analysis part.
Subsequently, the resulting grandspectra are optimally combined in order to
construct the global grandspectrum. Re-scan candidates are identified based on
this grandspectrum for additional statistical testing.

The rest of the signals with small SNR require more steps to optimize signal
detection. The overall data-analysis steps are shown in Fig. 18 and are
described in detail below. The flow of the analysis is similar to the
procedures described in [32, 89, 90, 91, 92]. The goal is to construct
grandspectra where the candidates for rescan can be classified or the
exclusion limit can be set. The underlying probability distribution of the
noise fluctuation is Gaussian, as a large number of spectra are averaged
together. Unbiased combination procedures throughout the analysis guarantee
that the final product of the analysis also yields a standard normal
distribution, by properly normalizing the uncertainty and compensating for the
mean offset. The grandspectra from predefined subsets and their rescan
datasets are aligned and combined using the Bayesian power measured (BPM)
analysis framework [93].

The first step of the analysis involves the estimation of the SNR of axions
with an arbitrary coupling strength $g_{\gamma}$ at each data point. This step
plays two important roles: first, the SNR is used for estimating the
experimental sensitivity on the axion–photon coupling $g_{\gamma}$. Next, it
is used as a weighting factor for optimal combination of the data where axions
possibly exist. As defined in Eq. (2), it requires the axion-to-photon
conversion power and the total system noise temperature at each frequency.

The conversion power depends on experimental parameters such as cavity
bandwidth ($\Delta\omega_{c}$), resonance frequency ($\omega_{c}$), loaded
quality factor ($Q=\omega_{c}/\Delta\omega_{c}$) of the cavity, coupling
coefficient of the strong antenna ($\beta$), as well as the root mean square
of the external magnetic flux ($B_{\textrm{rms}}$) inside the cavity volume
($V$) and form factor of the TM010 mode ($C$). The loaded quality factor, the
resonance frequency of the cavity, and the antenna coupling are obtained using
the real and imaginary part of the complex S-parameter through the reflection
line. $B_{\textrm{rms}}$, $V$ and $C$ are obtained from simulation using
COMSOL Multiphysics [62], together with the magnetic field profile, which is a
simulation result provided by the manufacturer.

The system noise temperature when the JPA is off (the pump is off and the
resonant frequency of the JPA is tuned far away from the cavity frequency) is
estimated using the Y-factor method. The noise power spectrum is modeled as

$P_{\textrm{off}}=k_{B}\Delta\nu_{b}G_{\textrm{off}}(T_{\textrm{NS}}^{\textrm{eff}}+T_{\textrm{off}}).$
(5)

$P_{\textrm{off}}$ is the noise power when the JPA is off, $\Delta\nu_{b}$ is
the resolution bandwidth and $T_{\textrm{NS}}^{\textrm{eff}}$ is the thermal
noise from the matched load of the noise source.
$T_{\textrm{off}}=T_{\textrm{down}}/\eta_{u}$ and
$G_{\textrm{off}}=G_{\textrm{down}}\eta_{u}$ are the system noise and gain
correspondingly when the JPA is off. $\eta_{u}$ is defined as the transmission
coefficient between the noise source and the first HEMT amplifier (between C
and D in Fig. 12). $T_{\textrm{down}}$ and $G_{\textrm{down}}$ are the noise
and gain, respectively, contributed from the downstream part of the chain,
corresponding to the first HEMT amplifier and then all the subsequent
components until the signal is digitized. $P_{\textrm{off}}$ is measured at
more than three different temperatures of the noise source, and then the
$P_{\textrm{off}}$ versus $T_{\textrm{NS}}^{\textrm{eff}}$ graph is fitted
using Eq. (5) to estimate $T_{\textrm{off}}$ and $G_{\textrm{off}}$. For a
given noise-source temperature, $P_{\textrm{off}}$ spectra are measured with
sweeping LO frequencies in order to keep an intermediate frequency (IF) of
10.7 MHz for the digitizer. In practice, it is done with 1 MHz frequency step
for a given scanning measurement range. After the data acquisition is finished
and a scanning of $\sim$10 MHz is accomplished, the whole process is repeated
in order to update the $T_{\textrm{off}}$ slowly drifting due to HEMT
amplifiers’ gain stability limitations.

The system noise temperature when the JPA is on (the pump power is on and the
resonant frequency of the JPA is near the cavity frequency) can be estimated
using the SNR improvement method (SNRI) [34]. SNRI is defined as,

$\textrm{SNRI}=\bigg{(}\frac{G_{\textrm{on}}}{P_{\textrm{on}}}\bigg{)}\bigg{(}\frac{G_{\textrm{off}}}{P_{\textrm{off}}}\bigg{)}^{-1}=G_{J}/r.$
(6)

$P_{\textrm{on,off}}$ and $G_{\textrm{on,off}}$ are noise-power and gain when
the JPA is on and off, respectively. After reorganizing the equation,
$r=P_{\textrm{on}}/P_{\textrm{off}}$ is defined as the ratio spectrum, and
$G_{J}=G_{\textrm{on}}/G_{\textrm{off}}$ as the JPA gain, typically around 50.
The JPA gain can be further expressed as
$|S_{\textrm{21,on}}|^{2}/|S_{\textrm{21,off}}|^{2}$ where $S_{21}$ is the
S-parameter measured through the bypass line.

Using the SNRI and the reference noise temperatures, the total system noise
temperature of the JPA can be expressed as,

$\displaystyle T_{\textrm{sys}}$
$\displaystyle=(T_{\textrm{off}}+T_{\textrm{MXC}}^{\textrm{eff}})\cdot\frac{r}{\eta_{c}G_{J}}.$
(7)

$T_{\textrm{MXC}}^{\textrm{eff}}$ is the effective noise temperature of the
attenuator located at the JPA assembly thermally anchored to the mixing
chamber. $\eta_{c}$ is the transmission coefficient of the line between the
cavity and the cryogenic RF switch (between A and B in Fig. 12). It is
estimated to be equal to 0.932 $\pm$ 0.003 using the intermediate state (IS)
of the RF switch shown in Fig. 12, under the assumption that it is frequency-
independent within the frequency range of the data taking [32]. The
measurement results are found to be consistent throughout all the runs,
consistent with the fact that the same RF cables and the strongly coupled
antenna are used. As a result, the total system noise temperature around the
resonance frequency of the cavity is found to be 170 mK and 250 mK on average
in Runs 4 and 5, respectively. In Run 6, it varies from 200 mK to 400 mK with
JPA, and from 1.5 K to 3 K without JPA.

Figure 19: Example of the noise PSD (blue) and frequency responses of the JPA
(black) and the cavity (green) as a function of the offset from the half pump
frequency ($f_{p}/2)$. The total gain is $\sim$110 dB and the frequency
responses are normalized to their maximum value. The probe tone (purple)
injected through the weak port of the cavity is used for cross-checking and
systematic error estimation. The dashed lines represent the idler modes. Since
the axion signal also appears on the idler side, the frequency bands (grey) on
both sides are included in its analysis.

The baselines of the ratio spectra and the JPA gain are estimated to reduce
the statistical uncertainty and define the normalized excess. For the ratio
spectra, 5 neighboring data points are merged together. Of the 1 MHz range, we
utilize 360 kHz of the data; 180 kHz range of the data around the resonance
frequency of the cavity and the same for the range around its idler frequency.
The JPA essentially yields a highly-symmetric output around the half pump
frequency, owing to its three-wave-mixing property as described in Eq. (4)
[52]. Using this fact, both spectra are decomposed into their symmetrical and
asymmetrical parts. Each part in each spectrum is fitted individually, then
combined as the final baseline.

The baseline of $P_{\textrm{off}}$ is modeled and fitted with a fifth-order
polynomial accommodating the frequency response of the circuit components
after the frequency mixer. In doing so, the data close to the resonance
frequency of the cavity are not included in the fit. It is assumed that the
major contributions to the polynomial background are the thermal photons from
the attenuators installed in the measurement lines as shown in Fig. 12, which
are responsible for the terms in the parenthesis of Eq. (7).

The normalized power excess $\delta$ is defined using the ratio spectrum and
its baseline.

$\displaystyle\delta=\frac{r-b_{r}}{\delta
r}=\bigg{(}\frac{r}{b_{r}}-1\bigg{)}\cdot\sqrt{N_{\textrm{avg}}}$ (8)

$\delta{r}=b_{r}/\sqrt{N_{\textrm{avg}}}$ is the expected standard deviation
of $r$ by the central limit theorem, where $N_{\textrm{avg}}$ is the number of
averages, and $b_{r}$ is the baseline of the ratio spectrum. Thus $\delta$ is
expected to follow the standard normal distribution, which leads the reduced
$\chi^{2}$ goodness of the fit to have a mean of 1. Throughout the data, the
normalized excesses fulfill these expectations within the margins of error.

Figure 20:  Statistical distribution of grandspectra excesses for Runs 5 and
6. The total number of entries is approximately 3.7 million. The negative
excesses on the left are due to the distortion of the baseline by minor mode
crossings.

The combination process starts with the signal and idler sides of the data,
shown as gray area in Fig. 19. The SNR in the signal ($R_{S}$) and the idler
($R_{I}$) sides can be defined using the system noise temperature on each side
of the data. Equation (7) is also used for the idler side, but with the JPA
gain for the idler mode $G_{I}=G_{J}-1$. The JPA-induced correlation between
the two analysis bands is considered in optimizing the weights and the error
combination. Then, the spectra are optimally weighted by their expected SNR to
be summed vertically.

After the vertical combination, the SNR of the virialized axion, dispersed in
a bandwidth of around 5 kHz, is combined horizontally according to [22, 91].
Since the axion mass is unknown, the combination is repeated for each axion
rest-mass frequency. The effect of a mismatch between the axion frequency and
the closest frequency point is found to be negligible because the resolution
bandwidth (RBW) used is much smaller than the axion line shape. To account for
the variation at different axion masses, the line shape is evaluated at every
1 MHz.

The combined spectrum is normalized once more by dividing its standard
deviation and subtracting its mean for the purpose of constructing a
grandspectrum. In Run 6 the standard deviation is found to be frequency-
dependent and is mostly larger than expected from simulation. For this reason,
the data taken in Run 6 are divided into 9 different groups, where the
standard deviation is approximately uniform within each group. The group
grandspectra are obtained from their own means and standard deviations, then
they are vertically combined once more to construct a single grandspectrum.
The rescan candidates are defined based on the 3.718$\sigma$ threshold given
by 90% confidence level for a target SNR of 5$\sigma$. For the large narrow
peaks, we follow the procedure outlined at the beginning of this section.
Those peaks confirmed not to be due to axion conversion are removed together
with their left and right single bins in the vertically combined spectra. For
the rest of the candidates, data is taken for at least three times longer than
the initial acquisition.

The grandspectra from all runs and their rescans are combined once more to
report the limit on $g_{\gamma}$. The systematic effect of the baseline
estimation on the final SNR is calibrated using a software-synthesized axion
injected at every 200 kHz in each Run. The overall signal detection efficiency
is found to fluctuate slightly around 90% in Runs 4, 5 and 6. The effect of
the frequency-dependent Gaussian width in Run 6 is considered here during the
normalization procedure. The combined sensitivity is calculated on the basis
of the Bayesian power measurement framework [93]. Figure 20 shows the
statistical distribution of the formed excess from the combined Runs 5 and 6.
About 10% of the candidates above the given threshold are newly found after
further improvement of the analysis after rescan, as well as combining Runs 4,
5, and 6. The effect of such candidates on exclusion of $g_{a\gamma\gamma}$ is
naturally reflected by accomodating the Baysian approach. The 10% prior update
contour with 400 kHz of sub-aggregate window is set for the frequency-
dependent limit corresponding to approximately 90% confidence level. The limit
from the frequentist threshold (FT) approach is reported as a reference, with
the same sub-aggregate window, see Fig. 21. The exclusion plot shown in Fig.
22 includes all major axion dark matter experiments and astrophysical limits
between approximately 0.5 GHz and 8 GHz. The current work is indicated in the
inset. The exclusion plot here corresponds to the blue line of Fig. 21.

Figure 21:  Exclusion limits for axion–photon coupling obtained through the
Bayesian power measured (BPM) analysis (blue). The 10% prior update contour of
the BPM framework is equivalent to the standard 90% exclusion line (green)
achieved with the FT framework. The subaggregated prior update are scaled in
grey.  Figure 22:  Exclusion limits set by this work for axion–photon coupling
at approximately 90% confidence level assuming that axions are 100% of the
local dark matter density with a value of 0.45 GeV/cm3. The yellow band
represents the areas predicted by the theoretical models of KSVZ and DFSZ. The
magnified version is shown in the inset over the mass range between 4.2
$\mu$eV and 5.0 $\mu$eV. The gaps around 1.0881 GHz, 1.0947 GHz, 1.1290–1.1350
GHz, 1.1705 GHz and 1.1762 GHz correspond to mode crossings. The frequency
ranges of 1.0267–1.0443 GHz and 1.1220–1.1229 GHz were scanned with HEMT as
the first-stage amplifier. The remaining gaps correspond to data whose
analysis was not finalized by the publication time for a variety of reasons,
including incomplete stored information. The exclusion limits from other
experiments (Global Cluster [94], Neutron Stars [95, 96, 97, 98], RBF & UF
[99, 100], CAST [101], ADMX [33, 34, 35], HAYSTACK [36, 37, 38], CAPP [28, 31,
29, 30, 32], CAST-CAPP [45], CAPP18T [102, 103], TASEH [104], GrAHal [105])
are taken from Ref. [106].

##  VI Discussion

Over the past few decades, intense experimental effort has been made
internationally to probe the vast parameter space for axions and axion-like
particles. Cavity-based haloscopes have provided the most sensitive searches
in the $\mathcal{O}(10^{0})$ GHz range. However, there are only a few attempts
to go beyond that, and even then, the sensitivities are still far away from
the hadronic axion models. This is mainly due to the loss of cavity detection
volume, the decrease in the cavity quality factor at higher frequencies, and
the linear increase of quantum noise with frequency. Therefore, different
approaches are needed to achieve high sensitivity to frequencies higher than 1
GHz.

It was thought for a long time that superconducting (SC) cavities would
perform worse than copper cavities in a strong magnetic field. Certainly,
there have been previous attempts to manufacture SC cavities but they all
failed to show any improvement until CAPP’s breakthrough achievement using
high-temperature-superconducting (HTS) tapes [107, 108, 109]. CAPP
demonstrated a steady improvement in this field over the years, currently
reaching a quality factor of $13\times 10^{6}$ in 8 T magnetic field. When
data acquisition is optimized, the axion scanning rate can be proportional to
the cavity quality factor even when it exceeds the axion quality factor [110,
111].

CAPP has developed several novel cavity designs that efficiently increase the
search frequency, along with practical tuning mechanisms. They include (i) a
pizza-cavity design consisting of multiple cells divided by equidistant
partitions [112], tuned by a single carousel-like structure and read-out by a
single antenna (ii) a wheel-tuning mechanism suitable for exploiting higher-
order resonant modes such as TM030 [113], and (iii) a tunable photonic crystal
design featuring an array of dielectric rods whose position can be adjusted
using an auxetic structure of rotating squares [114]. In addition, CAPP
recently proposed a new search method based on heterodyne interferometry that
mixes weak axion-induced photons with strong reference photons [115]. The
variance of the interference, whose intensity is proportional to the amplitude
of the reference probe, can be measured using a power detector even at high
dark count rates, enabling sensitive detection nearly quantum-noise limited.

The long-term direction will go towards the development of single-photon
detectors, which are overwhelmingly advantageous, particularly at high
frequencies and low temperatures. Quantum-limited linear amplifiers are
subject to fundamental quantum noise, which is linear in frequency. Single-
photon detectors at low temperatures could improve the scanning speed
dramatically at high frequencies when their dark count is kept low [116, 117,
118, 119] and above 10 GHz [116]. For frequencies below 10 GHz, we are
developing axion detection chains based on single-photon counters. The main
component of one approach is a chip containing a microwave coplanar waveguide
as an input line, terminated by the current-biased Josephson junction (CBJJ)
used as a photon switching detector [118]. The second approach involves
nanobolometers with a resolution of several zeptojoules [120]. Both
approaches, together with the heterodyne interferometry method [115], will
significantly increase the scanning speed of the experiment.

In addition, CAPP plans to develop a microwave photon counter based on Rydberg
atom quantum technologies [121, 122]. The general features of Rydberg atoms,
such as large transition dipole moments, energy transition levels in the GHz
range, tunable transition frequencies via the Stark effect, and long lifetimes
on the order of milliseconds, make them suitable for efficient detection of
microwave photons.

##  VII Summary

We reported on the first high-sensitivity axion haloscope search for
frequencies above 1 GHz and a scanned range of more than 150 MHz. The
achievement described above was made possible by combining a large aperture
12-T magnet with a 37-liter ultralight microwave resonant cavity whose
physical temperature was kept between 40 mK and 22 mK, and JPAs with total
system noise temperature around 200 mK.

The 12 T magnet consists of two coils, an inner coil based on Nb3Sn low
temperature superconducting (LTS) cable and an outer coil based on the more
conventional NbTi LTS cable, made by Oxford Instruments. The total energy
content of the magnet, when fully energized, is 5.562 MJ, comes with a
persistent mode switch, and operates reliably within its specifications. We
have successfully operated for the first time in the world a large volume, 12
T magnet specifically designed to host cavities in the 1-8 GHz frequency
range.

The sensitivity of the experiment relies equally well on the ability to
thermalize and cool the 37-liter microwave cavity and the quantum noise-
limited amplifiers to the lowest possible temperature, preferably below 40 mK.
Our ultra-light-cavity is also implemented for the first time in such large
volume successfully without jeopardizing the reliability of its critical
parameters in axion dark matter research. Combined with the state of the art
thermalization techniques applied in all the important interfaces we managed
to keep the cavity for most of the time well below 40 mK. We gold-plated the
interfaces when good thermalization was needed and partially or totally
isolated the elements when it was appropriate.

The maximum temperature difference between the top and bottom of the cavity
was 15 mk, which was slowly reduced as a function of time. Eventually, since
this run, we have also improved their thermalization and achieved less than 5
mk temperature difference by using annealed copper tapes between the top and
bottom plates of the cavity.

Finally, our JPAs at around 1 GHz are performing near quantum noise limit but
with limited bandwidth between 50 to 100 MHz. In order to reduce the need for
warmup and cooldown in the experiment, we have bundled up several JPAs
together in an optimum manner in order to maintain most of their performance
characteristics without compromising significantly the total system noise.

For all of the above projects we have had a very steep learning curve and by
the time we finished the 150 MHz scan, we have learned how to effectively
combine all of them with high efficiency. The next project is ready to scan
between 1.2 and 1.5 GHz at DFSZ sensitivity at a scan rate of more than 3 MHz
per day, with the added benefit of using a tuning rod covered by high-
temperature superconducting tape. Superconducting cavities combined with the
variance method promise an additional up to two orders of magnitude in real
calendar scanning efficiency, and it is the main current activity at CAPP.

###### Acknowledgements.

This work was supported by the Institute for Basic Science (IBS-R017-D1) and
JSPS KAKENHI (Grant No. JP22H04937). Arjan F. van Loo was supported by a JSPS
postdoctoral fellowship.

##  Appendix A Bayesian power measured analysis

The exclusion limit on $g_{\gamma}$ from the data acquired in all runs and
their rescans is evaluated using a Bayesian power measured framework. The
posterior probability $P_{\textrm{posterior}}$ of axion presented at a certain
frequency bin is updated by number of observation made by the initial scans
and the rescans. For a given observation, the ratio
$P_{\textrm{prior}}/P_{\textrm{posterior}}$ can be approximated by the Bayes
factor of two competing hypotheses (whether or not the signal exists). Then
the total update is given by the product of the Bayes factors from all
observations at the given frequency. Since the coupling strength $g_{\gamma}$
is also unknown, the total update is evaluated until it is meaningful
($10^{-2}-10^{2}$). The color map in Fig. 21 shows the total update in each
frequency bin, aggregated to 300 kHz. The aggregate update can be obtained by
the average of the total update in individual bins, by neglecting the
frequency dependence of the posterior probability in each aggregate window.
The $g_{\gamma}$ which makes the aggregate update to be 0.1 is drawn as blue
line in Fig. 21, corresponding to the 90% confidence level on $g_{\gamma}$ to
be excluded. For comparison, exclusion limit from the threshold based
frequentist approach is also drawn as the green line, aggregated with the same
window size.

##  Appendix B Systematic-error calibration

As previously reported in [32], the systematic error on $g_{a\gamma\gamma}$ in
Run 4 is estimated to be about 3% and is similar in Run 5 as the system
configuration is essentially the same in those Runs. It is estimated to be
about 8% in Run 6, and the main sources of error in comparison to other runs
are the calibration of the SNR for the idler side signal and the drift of
$T_{\textrm{off}}$ due to active devices other than JPAs. The SNR error from
the idler side is estimated using the single-tone calibration as described in
Sec. V of the main text. This error is frequency-dependent and tends to be
higher in the region where the JPA performance is not optimal. The drift of
$T_{\textrm{off}}$ is the dominant source of systematic error for the data
taken without the JPAs in Run 6, and its effect on $g_{a\gamma\gamma}$ is
around 2%. Consequently, the average systematic error on the combined
exclusion limit is approximately 4%, assuming that there is no correlation
between the runs.

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