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Revisiting the Detection Rate for Axion Haloscope
Dongok Kim1,2, Junu Jeong1,2, Younggeun Kim1,2, Sungwoo Youn1, and Yannis K. Semertzidis1,2
4th TAU Meeting at Jun. 9, 2020
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D{lrq#dqg#SuhflvlrqSk|vlfv#Uhvhdufk
1Center for Axion and Precision Physics Research of Institute for Basic Science (IBS/CAPP)2Korea Advanced Institute of Science and Technology (KAIST)
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Overview• Motivation and Introduction
• Axion Conversion Power
• Noise Powers of the Detection Scheme
• Scanning Rate of the Cavity Experiment for Axion Haloscope Searches
• Summary and Conclusion
2
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
CAPP
Motivation• Axion searches before CAPP
• No path for frequency > 5 GHz
• Now we have a path
• High-frequency cavity design
• Superconducting cavities with large B-field
• Single-photon detector work
• Revisiting detection rate for optimization
3
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Motivation• Axion searches before CAPP
• No path for frequency > 5 GHz
• Now we have a path
• High-frequency cavity design
• Superconducting cavities with large B-field
• Single-photon detector work
• Revisiting detection rate for optimization
4
ftarget ⟶ 3ftarget
[J. Jeong PLB (2018)]
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Motivation• Axion searches before CAPP
• No path for frequency > 5 GHz
• Now we have a path
• High-frequency cavity design
• Superconducting cavities with large B-field
• Single-photon detector work
• Revisiting detection rate for optimization
5
Qcavity ≳ Qaxion
[D. Ahn 2002:08769]
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Motivation• Axion searches before CAPP
• No path for frequency > 5 GHz
• Now we have a path
• High-frequency cavity design
• Superconducting cavities with large B-field
• Single-photon detector work
• Revisiting detection rate for optimization
6
Adapted from O. Morin et al., Phys. Rev. Lett. (2019) by APS/Ashley Mumford
Substantial improvement for high frequency & low temperature
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Motivation• Axion searches before CAPP
• No path for frequency > 5 GHz
• Now we have a path
• High-frequency cavity design
• Superconducting cavities with large B-field
• Single-photon detector work
• Revisiting detection rate for optimization
7
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Introduction• For detecting resonantly converted photon from dark matter axion under a
strong magnetic field based on the scheme: [Sikivie PRL (1983), Sikivie PRD (1985)]
8
a(ωa)
B
E ∝ gaγγa(ωa) B
gaγγ
Antenna
Cavity
Axion signal power:
Noise fluctuation:
Psig =β
1 + βg2
aγγB20VC
ρa
mamin(Ql, Qa)
δPnoise = kBTsysΔνΔt
Scanning rate:dfdt
=1
SNR2g4
aγγρ2
a
m2a
B40V2C2
k2BT2
sys
β2
(1 + β)2Qa min(Ql, Qa)
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Introduction• Development of a high-Q factor SC cavity:
[D. Ahn 1902:04551, 2002:08769]
9
dfdt
=1
SNR2g4
aγγρ2
a
m2a
B40V2C2
k2BT2
sys
β2
(1 + β)2Qa min(Ql, Qa)
Qc = (1 + β)Ql ≃ Qa ≈ 106
QYBCO ≃ 6QCu
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
• Isolator is placed between the cavity and RF chain to match impedance independent of the coupling. Impedance is not matched in general.
• Development of a high-Q factor SC cavity: [D. Ahn 1902:04551, 2002:08769]
10
dfdt
=1
SNR2g4
aγγρ2
a
m2a
B40V2C2
k2BT2
sys
β2
(1 + β)2Qa min(Ql, Qa) Qc = (1 + β)Ql ≃ Qa ≈ 106
Noise source(cavity)
Noise seen by detector
(RF chain)
Introduction
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Axion Conversion Power• Non-smooth part of the traditional formula
• This remedy works only for two extrema:
11
Pconv = g2aγγB2
0VCρa
mamin(Qc, Qa)
Qc ≪ Qa, Qc ≫ Qa
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Axion Conversion Power• Non-smooth part of the traditional formula
• This remedy works only for two extrema:
• Axion electrodynamics for cavity haloscope: [Y. Kim, Phys. Dark Univ. (2019)]
12
∇ × B r =1c2
∂∂t
E r − gAB 01c
∂θ∂t
∇ × E r = −∂∂t
B r
∇ ⋅ E r = 0
∇ ⋅ B r = 0
Pconv = g2aγγB2
0VCρa
mamin(Qc, Qa)
Qc ≪ Qa, Qc ≫ Qa
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Axion Conversion Power• Non-smooth part of the traditional formula
• This remedy works only for two extrema:
• Axion electrodynamics for cavity haloscope: [Y. Kim, Phys. Dark Univ. (2019)]
13
∇ × B r =1c2
∂∂t
E r − gAB 01c
∂θ∂t
∇ × E r = −∂∂t
B r
∇ ⋅ E r = 0
∇ ⋅ B r = 0 Pconv = g2aγγB2
0VCωcQc ∫dω2π
ℱ(ω, ωc)2
𝒜(ω, ωa)2
ℱ(ω, ωc) =1
(ω − ωc) + iωc/2Qc
⟨a2(t)⟩ = ∫dω2π
𝒜(ω, ωa)2
Pconv = g2aγγB2
0VCρa
mamin(Qc, Qa)
Qc ≪ Qa, Qc ≫ Qa
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Cauchy Approximation• Axion velocity distribution is assumed to
follow the Maxwell-Boltzmann in the haloscope.
• Approximation of the axion power distribution as the Cauchy distribution allows for analytical calculation.
14
ℱ(ω, ωc) =1
(ω − ωc) + iωc /2Qc⟨a2(t)⟩ = ∫
dω2π
𝒜(ω, ωa)2
= ∫dω2π
4ρaQa
ωam2a
1
1 + ( ω − ωa
ωa /2Qa )2
Pconv = g2aγγB2
0VCωcQc ∫dω2π
ℱ(ω, ωc)2
𝒜(ω, ωa)2
Cavity response Axion dispersion
Axion dist.Cauchy dist.
-2 0 2 4 60.0
0.1
0.2
0.3
0.4
u [mavrms2/2]
Energydistribution(norm.)
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Axion Conversion Power• Then the corresponding axion conversion power becomes
• The integration becomes straightforward when the cavity frequency ( ) matches the axion frequency ( ) as .
ωcωa ωc = ωa = ω0
15
Pconv = g2aγγB2
0VCωcQc ∫dω2π
ℱ(ω, ωc)2
𝒜(ω, ωa)2
∝ ∫dω2π
1
1 + ( ω − ωc
ωc /2Qc )2
1
1 + ( ω − ωa
ωa/2Qa )2
Pconv = g2aγγB2
0VCρa
ma
QcQa
Qc + Qa
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Axion Signal Power• The axion conversion power is revised to
16
Pconv = g2aγγB2
0VCρa
ma
QcQa
Qc + Qa
1Qμ
≡1
Qc+
1Qa
reduced Q factor is naturally appeard
original formular
Pconv = g2aγγB2
0VCρa
mamin(Qc, Qa)
OriginalRevised
10-2 10-1 100 101 102 1030.0
0.2
0.4
0.6
0.8
1.0
1.2
Qc/Qa
P a�
��(norm.)
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Noise Powers• Two noise sources are major in the cavity haloscope.
• Johnson-Nyquist thermal noise: [Johnson, Phys. Rev. (1928), Nyquist, Phys. Rev. (1928)]
17
Teff = Tphysη(ω) =ℏωkB ( 1
eℏω/kBTphys − 1+
12 )
PJN = kBTeffΔν4β
(1 + β)2
f = 10 GHzf = 5 GHzf = 1 GHz
0.01 0.05 0.10 0.50 1 5 100.01
0.050.10
0.501
510
Tphy [K]T eff[K
]
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Noise Powers• Two noise sources are major in the cavity haloscope.
• Johnson-Nyquist thermal noise: [Johnson, Phys. Rev. (1928), Nyquist, Phys. Rev. (1928)]
• Added noise (equivalent noise temperature) by the RF readout chain:
18
Padd = kBTaddΔν
PJN = kBTeffΔν4β
(1 + β)2
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Noise Powers• Two noise sources are major in the cavity haloscope.
• Johnson-Nyquist thermal noise: [Johnson, Phys. Rev. (1928), Nyquist, Phys. Rev. (1928)]
• Added noise (equivalent noise temperature) by the RF readout chain:
• Total noise:
19
Padd = kBTaddΔν
PJN = kBTeffΔν4β
(1 + β)2
Pnoise = PJN + Padd = kBTeffΔν ( 4β(1 + β)2
+ λ) λ ≡Tadd
Teff
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Experimental Demonstration• We conducted an experiment to demonstrate the acquired noise power
from the cavity through the amplifier at room temperature.
20
Antenna
Cavity ( )ω0/2π ≈ 5.9 GHz
Passive components:
Amp. Network/spectrum analyzers
• Isolator• Directional coupler• Direct connection
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Noise Power• Measured noise powers with respect to the antenna couplings agreed
with expectation.
21
Pnoise = kBTeffΔν ( 4β(1 + β)2
+ λ)IsolatorDirectional couplerNo componentTheoretical estimation
0 5 10 15 200
5
10
15
20
25
30
�
P noise/�� d
[aW/Hz]
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Scanning Rate• Based on the revised forms of axion signal power and noise power, the
scanning rate is newly derived.
22
Psig =β
1 + βg2
aγγB20VC
ρa
ma
QlQa
Ql + Qa
δPnoise = kBTeff ( 4β(1 + β)2
+ λ) ΔνΔt
Psig =β
1 + βg2
aγγB20VC
ρa
mamin(Ql, Qa)
δPnoise = kBTsysΔνΔt
dfdt
=1
SNR2g4
aγγρ2
a
m2a
B40V2C2
k2BT2
sys
β2
(1 + β)2Qa min(Ql, Qa)
dfdt
=1
SNR2g4
aγγρ2
a
m2a
B40V2C2
k2BT2
eff ( β/(1 + β)4β/(1 + β)2 + λ )
2
QaQlQa
Ql + Qa
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Scanning Rate• Based on the revised forms of axion signal power and noise power, the
scanning rate is newly derived.
23
Psig =β
1 + βg2
aγγB20VC
ρa
ma
QlQa
Ql + Qa
δPnoise = kBTeff ( 4β(1 + β)2
+ λ) ΔνΔt
Psig =β
1 + βg2
aγγB20VC
ρa
mamin(Ql, Qa)
δPnoise = kBTsysΔνΔt
dfdt
=1
SNR2g4
aγγρ2
a
m2a
B40V2C2
k2BT2
sys
β2
(1 + β)2Qa min(Ql, Qa)
dfdt
=1
SNR2g4
aγγρ2
a
m2a
B40V2C2
k2BT2
eff ( β/(1 + β)4β/(1 + β)2 + λ )
2
QaQlQa
Ql + Qa
Original relations Revised relations
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Scanning Rate Optimization• Both original and revised forms of the scanning rate can be optimized with
respect to the antenna coupling .β
24
dfdt
=1
SNR2g4
aγγρ2
a
m2a
B40V2C2
k2BT2
sys
β2
(1 + β)2Qa min(Ql, Qa)
βopt = 2
dfdt
=1
SNR2g4
aγγρ2
a
m2a
B40V2C2
k2BT2
eff ( β/(1 + β)4β/(1 + β)2 + λ )
2
QaQlQa
Ql + Qa
and dependenceQc λ
Qc/Qa λ = 10 λ = 1 λ = 0.1
0.01 2.2 4.7 40
0.1 2.3 4.8 40
1 2.9 6.1 42
10 6.9 12.1 55
100 17.2 33.5 112
βopt =
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Optimized Scanning Rate
25
Qc/Qa λ = 10 λ = 1 λ = 0.1
0.01 < 0.1 1 12
0.1 0.3 10 127
1 2.0 87 1245
10 8.2 470 10565
100 15.2 1185 52898
Optimized scanning rate for revised case
(solid line, normalized)
� = 0.1� = 1� = 10
10-2 10-1 100 101 102 10310-210-1100101102103104105106
Qc/Qadf/dt(norm.)
Original formula is compared for each case(dashed line, normalized)
Solid line: revised estimation Dashed line: original estimation
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Summary• The traditional approach to the cavity haloscope for axion search is
revisited to reflect development of technologies in superconducting and quantum science
• Revised axion signal power and scanning rate are
• Further enhancement of the scanning rate is expected with high Q factor cavities and low noise amplifiers.
• This work was published [D. Kim, JCAP (2020)].
26
Psig =β
1 + βg2
aγγB20VC
ρa
ma
QlQa
Ql + Qa
dfdt
=1
SNR2g4
aγγρ2
a
m2a
B40V2C2
k2BT2
eff ( β/(1 + β)4β/(1 + β)2 + λ )
2
QaQlQa
Ql + Qa
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Conclusion• Innovative breakthroughs for high-frequency axion dark matter searches at
IBS/CAPP
• High-frequency detector design
• High-Q SC cavity
• Single-photon detector (initiating)
• Reformulation of the detection rate => non-trivial impacts on axion society
• IBS/CAPP makes significant contributions to axion search business in all experimental aspects!
27
Thank you !CAPP Potential
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Cauchy Approximation• The correction error will be less than 10% in this approximation
29
Axion dist.Cauchy dist.
-2 0 2 4 60.0
0.1
0.2
0.3
0.4
u [mavrms2/2]
Energydistribution(norm.)
10-2 10-1 100 101 1020.8
0.9
1.0
1.1
1.2
Qc/QaP approx./Pexact
Dongok Kim 4th TAU Meeting, IBS Science Culture Center, Daejeon, Jun. 9, 2020
Theoretical Estimation• Based on the noise formula
• We considered the noise parameter effect that may come the amplifier input end.
• The amplifier gain (G) and temperature (λ) are measured and considered as a statistical error.
• The amplifier excess noise ratio (ENR) uncertainty is considered as a systematical error as well.
30
Pnoise/Δν = kBTeffG ( 4β(1 + β)2
+ λ)
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