Axion Dark Matter Search with
Interferometric Gravitational
Wave Detectors
Ippei Obata (theory group, ICRR, University of Tokyo)
arXiv:1903.02017,
Collaborators：
Koji Nagano (ICRR)
Tomohiro Fujita (Kyoto University)
Yuta Michimura (University of Tokyo)
2019.5.14 YITPWhat is Axion?
QCD Axion(Peccei & Quinn, 1977)

A pseudo NG boson of PQ mechanism in order tosolve the strong CP problem in QCD physics

LQCD

✓GG̃,

|✓| . 10 10✓ ! ✓e↵ = ✓ + /f ⌧ 1<latexit sha1_base64="bJu1+snspvXOIkIVF6PGD8Z8Ph0=">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</latexit>

Axion-like particles (ALPs, string axion)(Svrcek & Witten 2006)

A plentitude of axion-like particles provided by thecompactifications of extra dimensionsn A scalar field with small mass, tiny interactions→ candidate for dark matterAxion as Dark Matter (misalignment production)V( )¨ + 3H ˙ + m2 = 0
n In early universe (m < H),<latexit sha1_base64="v5sWDxT7TBlpLpPitfKbMRW99bk=">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</latexit>n In late universe (m > H),<latexit sha1_base64="XT/2cH4YHOBIihvVZhkpKXkFuf0=">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</latexit>(background evolution)' const.

(frozen due to the Hubble friction)' a 3/2 0 cos(mt)(start to oscillate)n After oscillation begins, axion behaves as a pressureless matter fluid1 ˙2 1 2 2
⇢0
⇢=
+ m
' 3
2
2
a
P0
1 ˙2 1 2 2m' 3 sin(2mt) ⇠ 0
P =
2
2
a
<latexit sha1_base64="84REa7u8juVNGr/+lpoPPkstdsE=">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</latexit>(Pressure) < (Gravity)→Dark Matter!

Search for Axion (DM) via Photonn Axion generically couples to photon via the topological term

<latexit sha1_base64="X8TUyTGzEyphurVJHrZ7uBf+enc=">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</latexit>ga
aFµ⌫ F̃ µ⌫ = ga aE · B
4a : axion: photon
B : magnetic field<latexit sha1_base64="OVtWiG3tcWk+WMKFlxB00RnYhvo=">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</latexit>

n Axion is converted into photon under the background magnetic field(“axion-photon conversion”)

Search for Axion (DM) via Photon

ADMX

CAST

Axion DM – Photon Interaction(without using a background magnetic field)

Fµ⌫ = @µ A⌫<latexit sha1_base64="2hxPKcKWVoPw1ObvJzl/fOAVgf4=">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</latexit><latexit sha1_base64="kEGHJ33vnl6TbjOo20LHyC00le4=">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</latexit>

@⌫ Aµ

ga
aFµ⌫ F̃ µ⌫ = ga ȧAi ✏ijk @j Ak + (total derivative)4

r2 Ai + ga ȧ✏ijk @j Ak = 0,

EOM for photon :ÄiAxion DM :a(t) = a0 cos(mt + ⌧ )<latexit sha1_base64="MoEhIH/JTbgMfaILLAZVQfHMZuo=">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</latexit>n Decomposing two circular polarized photons, we get the following dispersion relation

L/R<latexit sha1_base64="Gxsfk4VLN0N8oujVRMJEL7fM/XA=">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</latexit>

L/R

2+ !L/RAk = 0,
⇣
⌘
g
a
m
a 0
2
!L/R
⌘ k2 1 ±sin(mt + ⌧ )kÄkAxion DM – Photon Interactionn The phase velocity of each polarized photon is given by

⇣
⌘1/2
!L/R
g a a0 m
cL/R ⌘= 1±
sin(mt + ⌧ )kk<latexit sha1_base64="6obz3qHPyPTsBYDkMfsi5EMID0Y=">AAADGXichVFNa9RQFL2JX3X86FhBBBcGh8pUYfrSCoogFN24cNFOnU5lXg0v6Z30MXlJTF4Ga8ha6B9w0ZWCC/EvuBE3xa246E8QN0IFNy68kwmIVtsbknfeeefcl8N140CmmrFdwzxy9NjxExMna6dOnzk7WT83tZJGWeJhx4uCKFl1RYqBDLGjpQ5wNU5QKDfArju4NzrvDjFJZRQ+1Jsxrinhh7IvPaGJcupbnpNzjU91/qCYHYN2UVgcn2RyaPH1fiK8nEcKffEvYZEPijs8wL5u2jxWld53csF9oZQohMPUSMRTGTaVtq5TTwy0cLgW2QxPpL+hZx7n9uxc4dQbrMXKsvYDuwINqGoxqr8DDusQgQcZKEAIQRMOQEBKTw9sYBATtwY5cQkhWZ4jFFAjb0YqJIUgdkBfn3a9ig1pP+qZlm6PbgnoTchpwTT7zN6wPbbD3rIv7Od/e+Vlj9G/bNLqjr0YO5NbF5d/HOpStGrY+O06wOGSutQ9uobPe90D02now60ylaSUccmM8nrjDsNnL/aWb7en86vsFftKSV+yXfaBsobD797rJWxvQ41GZf89mP1gZa5lz7fY0o3Gwt1qaBNwCa5AkyZzExbgPixCh+79ZlwwLhuWuW2+N3fMj2OpaVSe8/BHmZ9+AQ4MyjY=</latexit>

n Therefore, we get the difference of phase velocities between two modes

cL/R (t) ' 1 ± c(t) ⌘ 1 ± c0 sin(mt + ⌧ (t))<latexit sha1_base64="DTLuuPyAZcoCBcUjLJIw3j/z8Ys=">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</latexit><latexit sha1_base64="BIdXd6rgY3w5JBAltPAv7hYgoq0=">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</latexit>c0' 1.3 ⇥ 10 24c✓ga
10 12 GeV 1◆✓

1550 nm◆✓⇢a
0.3 GeV/cm3

Is it possible to test this tiny phase difference?

◆1/2Modulation of photon polarization
E

L/R<latexit sha1_base64="lBaAyRxtue4AI3hdVk7G2EijdVw=">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</latexit>p= E ⌥ iEs

Propagating direction

Axion DM modulates
the linear-polarized light!

Photonpolarizationn Its magnitude depends on
the axion-photon couplingn Its frequency depends on
the axion mass

T.Fujita, Y.Michimura, IO
Experimental Setup K.Nagano,1903.02017

FI: Faraday isolator
HWP: half wave plate
PBS: polarizing beam splitter
BD: beam dump

(ri , ti )<latexit sha1_base64="WUZknGC2jwBBbKvTl8c+OjjrFEM=">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</latexit>

ri2 + t2i = 1<latexit sha1_base64="dL743SVwYYJ6whnKb1XGW3r5XtI=">AAACoHichVFNLwNRFD3GV9VXy0ZiM9EQIWnelIRIJMLGjqKKopkZDy+mM5OZ1wqNtcQfsBALEkT8BTsbf8DCTxBLEhsLt9NJBMGdvLn3nXfOfe/kGq4lfMnYY41SW1ff0Bhpija3tLa1x+Idi75T9EyeMR3L8ZYM3eeWsHlGCmnxJdfjesGweNbYmaqcZ0vc84VjL8g9l68V9C1bbApTlwTlY3EvL9ZT6qAqgzyuavlYgiVZEOrPQguLBMKYdWK3WMUGHJgoogAOG5JqCzp8+nLQwOAStoYyYR5VIjjnOECUtEVicWLohO7Qf4t2uRC1aV/p6Qdqk26xaHmkVNHLHtg1e2H37IY9sfdfe5WDHpW37FE2qlru5tuPuubf/lUVKEtsf6r+UBjEDnjLA/wwl/3TncQmRgNXgly6AVLxa1Y7lPaPX+bH5nrLfeycPZPTM/bI7sirXXo1L9J87gRRGpX2fTA/i8VUUhtKptLDiYnJcGgRdKMH/TSZEUxgGrPI0L27OMUlrpQeZVqZUdJVqlITajrxJZSVDx2il5g=</latexit>

reflectivity and transmissivity ofcavity mirrors

T.Fujita, Y.Michimura, IO
Experimental Setup K.Nagano,1903.02017

Electric vector inside cavity:(superposition ofreflected beams)

L : cavity length<latexit sha1_base64="w2VsJn2EBlAD0Exa0g0INJ040kI=">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</latexit>

T.Fujita, Y.Michimura, IO
Experimental Setup K.Nagano,1903.02017

Reflection matrix

Transfer matrix

cL/R (t) ' 1 ± c(t) ⌘ 1 ± c0 sin(mt + ⌧ (t))<latexit sha1_base64="DTLuuPyAZcoCBcUjLJIw3j/z8Ys=">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</latexit>

T.Fujita, Y.Michimura, IO
Experimental Setup K.Nagano,1903.02017

ikt✓
1 + i (t)Re0

t 1 E0 eeLEcav (t) =1 r1 r2
t1=[E p (t)1 r1 r2

E s (t)]<latexit sha1_base64="XKFVNlCliLMQsB3sx4opTcRD4Bo=">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</latexit>

The signal is enhanced inside the cavity

1

0
i (t)

◆

(2kL = 2⇡N)<latexit sha1_base64="91kZCL8pg/LzRQY2ILBW3PcEq3o=">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</latexit>

✓ ◆
1 1
p
2 1

T.Fujita, Y.Michimura, IO
Experimental Setup K.Nagano,1903.02017

S-pol.

t1 t2
EPD (t) =(↵1 r1 r2<latexit sha1_base64="YrBExiJPpwdzHU4oi47Oik7/SRI=">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</latexit>)E s (t) ↵ ⌧ 1 : mixing angle

Available for the detector of large t2 (t1=t2)<latexit sha1_base64="Ag0qJP+f20dhSHUMLIVlAMj3CbE=">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</latexit>

T.Fujita, Y.Michimura, IO
Experimental Setup K.Nagano,1903.02017

S-pol.

t1 t1
EPD (t) =(↵1 r1 r2<latexit sha1_base64="ghobZC+2mftRLtzh42gOcNN8+LA=">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</latexit>)E s (t) ↵ ⌧ 1 : mixing angle

Available for the detector of small t2 (t1 > t2)<latexit sha1_base64="Ag0qJP+f20dhSHUMLIVlAMj3CbE=">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</latexit>

Response function⌦ 4r1 r2 sin2 ( mL
imL
2 )Ha (m) ⌘ i
(
e
)
i2mL
m 1 r1 r2 e<latexit sha1_base64="rEuF7DpaQnb/ghnKswfxz+yoOSg=">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</latexit>m L ~ 1 is best sensitivity(proportional to 1/m)
→longer cavity length is better→GW detectors!

L = 106 m<latexit sha1_base64="2ryuB0MvjL/ZVS41t/yfLoQ7RHw=">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</latexit>

LIGO

SN ratio
The sensitivity is determined by quantum shot noise

EPD (t) =<latexit sha1_base64="wJ/3nFIo609j1LrpQAElmr+2SxQ=">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</latexit>

p

Ti (↵

PPD (t) / |EPD (t)|2<latexit sha1_base64="21YRGFHcQvwzf0QtU24ivmg6bmo=">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</latexit>p✏0 (t)t1 tis(t)) +Ti ⌘E (t),(i = 1, 2)
E0
1 r1 r2
p

Sshot (m) = p<latexit sha1_base64="/et1+M3XwEGotjswCqlZF3IZB40=">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</latexit>

8 p
Tobs
>
>
>
p
c0 (Tobs . ⌧ )<2 Sshot (m)SNR =(Tobs ⌧ )1/4>>>
c0 (Tobs & ⌧ ): p
2 Sshot (m)<latexit sha1_base64="5pKkKwsFgQ6fxNITnm/hgkE6nkY=">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</latexit>

q

⌦
2P0

Ti |Ha (m)|a(t) = a0 cos(mt + ⌧ )<latexit sha1_base64="JtwBL1waeojHPjf99OW6+6InLus=">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</latexit>(coherent time of axion DM)⌧=<latexit sha1_base64="iM0HP8QqD9Lf4MfCUGMTc8OI0FY=">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</latexit>2⇡
16⇠
1yr(10eV/m)
mv 2Sensitivity curves

aLIGO
DECIGO

Cosmic Explorer←current limit(CAST@CERN)

Sensitivity curves

KAGRA
L = 3 ⇥ 103 [m], P = 335[W],<latexit sha1_base64="Izn1/8+quL8Q4pYFJyAGFqV0QuI=">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</latexit>

KAGRA
DECIGO
Cosmic Explorer= 1064[nm], (t21 , t22 [ppm]) = (4 ⇥ 103 , 7)

←current limit(CAST@CERN)

Summary & Outlook
p We suggest an experimental scheme to search for axion dark
matter with the linear optical cavity used in gravitational wave
detectors.
p We found that these sensitivities can reach beyond the current
limit with a wide range of axion mass and our new scheme cancoexist with the observation run for gravitational waves.
p Which detection port (a) or (b) can be constructed depends on thegravitational wave detectors.
p We hope that our scheme is applied to KAGRA,DECIGO, ….