Fhqwhu#iru Sk|vlfv#Uhvhdufk Revisiting the Detection Rate for … · 2020-06-09 · Revisiting the...

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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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


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









4

ftarget ⟶ 3ftarget

[J. Jeong PLB (2018)]









5

Qcavity ≳ Qaxion

[D. Ahn 2002:08769]









6

Adapted from O. Morin et al., Phys. Rev. Lett. (2019) by APS/Ashley Mumford

Substantial improvement for high frequency & low temperature









7


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)


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


Qc = (1 + β)Ql ≃ Qa ≈ 106

QYBCO ≃ 6QCu


• 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


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




• 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)





• 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)



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.

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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.)


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


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.)


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

]




• Added noise (equivalent noise temperature) by the RF readout chain:

18

Padd = kBTaddΔν

PJN = kBTeffΔν4β

(1 + β)2




• 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


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


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]


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)


dfdt

=1

SNR2g4

aγγρ2

a

m2a

B40V2C2

k2BT2

sys

β2


dfdt

=1

SNR2g4

aγγρ2

a

m2a

B40V2C2

k2BT2

eff ( β/(1 + β)4β/(1 + β)2 + λ )

2

QaQlQa

Ql + Qa


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)


dfdt

=1

SNR2g4

aγγρ2

a

m2a

B40V2C2

k2BT2

sys

β2


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


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


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 =


Optimized Scanning Rate

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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


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)].

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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


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!

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Thank you !CAPP Potential


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


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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