Axion Dark Matter Search with Interferometric Gravitational Wave - - PowerPoint PPT Presentation

▶

Aug 28, 2023 487 likes •673 views

Axion Dark Matter Search with Interferometric Gravitational Wave Detectors Ippei Obata (theory group, ICRR, University of Tokyo) arXiv:1903.02017 (to be published in PRL) Collaborators Koji Nagano (ICRR, KAGRA member) Tomohiro Fujita (Kyoto

SLIDE 1

1 / 17

Axion Dark Matter Search with Interferometric Gravitational Wave Detectors

Ippei Obata (theory group, ICRR, University of Tokyo)

arXiv:1903.02017 (to be published in PRL) Collaborators： Koji Nagano (ICRR, KAGRA member) Tomohiro Fujita (Kyoto University, Geneva University) Yuta Michimura (University of Tokyo, KAGRA member)

2019.9.10 TAUP

SLIDE 2

2 / 17

Search for Axion (DM) via Photon

n Axion generically couples to photon via the topological term n Axion is converted into photon under the background magnetic field (“axion-photon conversion”)

a : axion γ : photon B : magnetic field

<latexit sha1_base64="OVtWiG3tcWk+WMKFlxB0RnYhvo=">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</latexit>

gaγ 4 aFµν ˜ F µν = gaγaE · B

<latexit sha1_base64="X8TUyTGzEyphurVJHrZ7uBf+enc=">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</latexit>

SLIDE 3

3 / 17

Search for Axion (DM) via Photon

ADMX CAST

SLIDE 4

4 / 17

Axion DM – Photon Interaction

n Decomposing two circular polarized photons, we get

EOM for photon :

gaγ 4 aFµν ˜ F µν = gaγ ˙ aAi✏ijk@jAk + (total derivative)

<latexit sha1_base64="kEGHJ3vnl6TbjOo20LHyC0le4=">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</latexit><latexit sha1_base64="kEGHJ3vnl6TbjOo20LHyC0le4=">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</latexit><latexit sha1_base64="kEGHJ3vnl6TbjOo20LHyC0le4=">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</latexit><latexit sha1_base64="kEGHJ3vnl6TbjOo20LHyC0le4=">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</latexit>

¨ Ai r2Ai + gaγ ˙ a✏ijk@jAk = 0, a(t) = a0 cos(mt + τ)

<latexit sha1_base64="MoEhIH/JTbgMfaILAZVQfHMZuo=">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</latexit><latexit sha1_base64="MoEhIH/JTbgMfaILAZVQfHMZuo=">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</latexit><latexit sha1_base64="MoEhIH/JTbgMfaILAZVQfHMZuo=">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</latexit><latexit sha1_base64="MoEhIH/JTbgMfaILAZVQfHMZuo=">ADAnichVFLaxNRFD4ZX2l8NOpGcHMxNKS2hjOlUBGERjcu+zBNJbcOdya38TZ3HszcBOqQnSD4B1y4UnChrsRtd278Ay7yE8RlBTeCnpkMiBbrGWbOd/9vnPn47iRVolBnJSsEydPnT5TnqmcPXf+wmz14qWtJBzGnmx7oQ7jbVckUqtAto0yWm5HsRS+q2XHdzNzjsjGScqDO6b/Uju+KIfqF3lCUOQU03qvNcLTdoaO4rdYDwQrhYPl1rULbC+kwreF74vxjwjUZJRojQJU7U3GPNIxEYJ7eyxljNgtxmyRcZ5pS4aZp5a4SD3wqThmwXek9oIhxsxnHeqNWxiHuxoYRdFDYpYC6sHwKEHIXgwB8kBGCo1iAgoacLNiBEhO1ASlhMlcrPJYyhQtohsSQxBKED+vap6xZoQH02M8nVHt2i6Y1JyWAOP+MbPMRP+A6/4I9/zkrzGdm/7FN2p1oZObPrmx+/6/Kp2zg0W/VMQqX2DnvwX5tNs51p2BXbiZu1LkMsqRzK83nTB6/Pxw89bGXFrHV/iVnL7ECX4kr8Hom/d6XW68gAqtyv57MUeLraWmjU17fbm2eqdYWhmuwjVo0GZWYBXuwRq06d4J/CyVSzPWE+ut9d76MKVapUJzGf4I6+AXzoC8Uw=</latexit>

Axion DM :

¨ AL/R

+ ω2

L/RAL/R k

= 0, ω2

L/R ≡ k2 ⇣

1 ± gaγa0m k sin(mt + δτ) ⌘

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

Fµν = ∂µAν − ∂νAµ

<latexit sha1_base64="2hxPKcKWVoPw1ObvJzl/fOAVgf4=">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</latexit>

(without using a background magnetic field)

SLIDE 5

5 / 17

Axion DM – Photon Interaction

n The phase velocity of each polarized photon is given by n The difference of phase velocities between two modes:

cL/R ≡ ωL/R k = ⇣ 1 ± gaγa0m k sin(mt + δτ) ⌘1/2

<latexit sha1_base64="6obz3qHPyPTsBYDkMfsi5EMID0Y=">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</latexit>

cL/R(t) ' 1 ± δc(t) ⌘ 1 ± δc0 sin(mt + δτ(t))

<latexit sha1_base64="DTLuPyAZcoCBcUjLJIw3j/z8Ys=">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</latexit>

δc0 c ' 1.3 ⇥ 10−24 ✓ gaγ 10−12 GeV−1 ◆ ✓ λ 1550 nm ◆ ✓ ρa 0.3 GeV/cm3 ◆1/2

<latexit sha1_base64="BIdXd6rgY3w5JBAltPAv7hYgoq0=">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</latexit>

How to measure this phase modulation?

SLIDE 6

6 / 17

Modulation of photon polarization

EL/R = Ep ⌥ iEs

<latexit sha1_base64="lBaAyRxtue4AI3hdVk7G2EijdVw=">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</latexit>

Propagating direction

Axion DM modulates the linear-polarized light!

Photon polarization

n Its magnitude depends on the axion-photon coupling n Its frequency depends on the axion mass

SLIDE 7

7 / 17

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

1903.02017

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

(ri, ti)

<latexit sha1_base64="WUZknGC2jwBbKvTl8c+OjrFEM=">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</latexit>

reflectivity and transmissivity of cavity mirrors

i + t2 i = 1

<latexit sha1_base64="dL743SVwYJ6whnKb1XGW3r5XtI=">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</latexit>

SLIDE 8

8 / 17

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

1903.02017 (superposition of reflected beams)

L : cavity length

<latexit sha1_base64="w2VsJn2EBlAD0Exa0g0INJ040kI=">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</latexit>

Electric vector inside cavity:

SLIDE 9

9 / 17

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

1903.02017 Transfer matrix Reflection matrix

cL/R(t) ' 1 ± δc(t) ⌘ 1 ± δc0 sin(mt + δτ(t))

SLIDE 10

10 / 17

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

1903.02017

Ecav(t) = t1E0eikt 1 − r1r2

eR ✓ 1 + iδφ(t) 1 − iδφ(t) ◆ 1 √ 2 ✓ 1 1 ◆ = t1 1 − r1r2 [Ep(t) − δφEs(t)]

<latexit sha1_base64="XKFVNlCliLMQsB3sx4opTcRD4Bo=">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</latexit>

The signal is enhanced inside the cavity

(2kL = 2πN)

<latexit sha1_base64="91kZCL8pg/LzRQY2ILBW3PcEq3o=">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</latexit>

SLIDE 11

11 / 17

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

1903.02017

EPD(t) = t1t2 1 − r1r2 (α − δφ)Es(t)

<latexit sha1_base64="YrBExiJPpwdzHU4oi47Oik7/SRI=">AC5HichVHPaxNBGH3d+qOmamO9CF6CoZIKDbNRUAShVAWPaWuaSrYus5tJM3R/MTsJtsueBfEm4kEQFDyIf4LevEf8NCjR+2xghcPfvsDRIv1W3bnzZvdnH50SejDVjexPG5LHjJ05OnapMnz5zdqZ6bnYtDkfKFR039EK17vBYeDIQHS21J9YjJbjveKLrbN3OzrtjoWIZBvf1diQ2fL4ZyIF0uSbKrnYsx0/upnZiafFIJ+07adrQ87VbNas/UNxNtG1qu5Um5oKyTUWoYXEvGvIFqy8za1oKOcLi4eFQ5zp7WqdNVletcPALEdZbXD6kdY6COEixF8CATQhD1wxPT0YIhIm4DCXGKkMzPBVJUSDuiLkEdnNgt+m7SrleyAe0zhXu3SLR68iZQ1z7DN7xw7YJ/aefWU/+mV5B7Zv2zT6hRaEdkzTy6s/vivyqdVY/hbdYTCoe6878EV8bjXPTKdxgA38lSUkY5k+V1C4fxzouD1Zsrc8l9obtU9LXbI/tUtZg/N19uyxWXqJCozL/HsxhsNZqmlebreVr9cWlcmhTuIhLaNBkrmMR9BGh+79gC/4hn1jYDw1nhnPi1ZjotScx9lvPoF91q08Q=</latexit>

S-pol.

α ⌧ 1 : mixing angle

<latexit sha1_base64="Ag0qJP+f20dhSHUMLIVlAMj3CbE=">ACr3ichVG7SiRBFD2zx1foybCJo2DshgM1e6CYiSaGPoaR5nRsbotx8LqB901gzqYKvgDBhvtwgbipmtkZuIPGPgJYqhgYuCdngZxRb1Nd506dc6tPlw7UDLSjN0Gc0trW3tHV9SnV3dPb3pv7lyK+Ejsg5vLDFZtHQklP5LTUSqwEoeCurUTe3pmpn+erIoyk7y3pvUCsubzsyS3pcE1UKW0WuQq2uVlUyrQmi1rs6pord6VXNrlXVuKglM6wLIvLfAusBGSQ1JyfvkARm/DhoAIXAh40YQWOiJ4CLDAExK2hRlxISMbnAgdIkbdCKkEKTuwOfcu0KySsR/t6zyh2O3SLojckp4lhds1O2T27Ymfslj2926sW96j/yx6tdsMrglLv8eDi46cul1aN7RfXBw6b1LFudVQcFfIfptPYwkScSlLKIGbqeZ1Gh+r+yf3i5MJwbYT9ZneU9Be7YZeU1as+OH/mxcJPpGhU1v+DeQuWx7LW9+zY/I/M1HQytA58xRC+0WTGMYVZzCFH9x7iL/7h3LCMvLFubDSkRlPiGcCrMuQz0iyfjA=</latexit>

Available for the detector of large t2 (t1=t2)

SLIDE 12

12 / 17

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

1903.02017

EPD(t) = t1t1 1 − r1r2 (α − δφ)Es(t)

<latexit sha1_base64="ghobZC+2mftRLtzh42gOcN8+LA=">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</latexit>

S-pol. Available for the detector of small t2 (t1 > t2)

α ⌧ 1 : mixing angle

SLIDE 13

13 / 17

Response function

Ha(m) ≡ i Ω m 4r1r2 sin2( mL

2 )

1 − r1r2e−i2mL (−e−imL)

<latexit sha1_base64="rEuF7DpaQnb/ghnKswfxz+yoOSg=">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</latexit>

L = 106m

<latexit sha1_base64="2ryuB0MvjL/ZVS41t/yfLoQ7RHw=">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</latexit>

m L ~ 1 is best sensitivity (proportional to 1/m) →longer cavity length is better →GW detectors! LIGO

SLIDE 14

14 / 17

SN ratio

(coherent time of axion DM) The sensitivity is determined by quantum shot noise

p Sshot(m) = q

Ω 2P0

√Ti|Ha(m)|

<latexit sha1_base64="/et1+M3XwEGotjswCqlZF3IZB40=">AC9HichVFLaxRBEK6Mr7g+stGLkMviEokeltpESBCEYC65ZPNZiM7Yejp9O42mVdmehdjp8B/4AHvSgwj+Am9eBM8e8hPEk0Q1IM1DxENxhpmuqr7/t6inIjTyYK8WjEOnP23PkLoxdLly5fuTpWHr+2loSDmIsWD70wXndZIjwZiJaSyhPrUSyY73qi7W4tpP32UMSJDINVtROJDZ/1AtmVnCmCnLKwk+1Y6ajbSUeKZ30Q2XMlH/bVO5XSvZmN2Zc5xb5cWSL3rM6OmGg8aYX02fqT5nl41jS7i05ux1KrXeOUq1jDLConk3qRVKGIRlh+AzZsQgcBuCDgAU5R4wSOjpQB0QIsI2QBMWUyazvgADJdIOiCWIwQjdom+Pqk6BlSnkm5nSLR29MygpM4gd8icf4Dl/hR/zxTy+deaT/skOnm2tF5Iw9udH8+l+VT6eC/m/VKQqX2Bnv4R2x12mfOp2CLsxlU0maMsqQdF6eOwfPz1u3luZ1LfwAD/RpPt4hG9p1mD4hR8ui5VnUKJV1f9ezMlkbpWn6nh8t3q/INiaMwATdhijYzC/OwCA1o0b3v4TN8g+/W0HpuvbAOc6o1Umiuwx9hvf4JP0K+bg=</latexit>

SNR = 8 > > > < > > > : √Tobs 2 p Sshot(m) δc0 (Tobs . τ) (Tobsτ)1/4 2 p Sshot(m) δc0 (Tobs & τ)

<latexit sha1_base64="5pKkKwsFgQ6fxNITnm/hgkE6nkY=">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</latexit>

τ = 2π mv2 ∼ 1yr(10−16eV/m)

<latexit sha1_base64="iM0HP8QqD9Lf4MfCUGMTc8OI0FY=">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</latexit>

EPD(t) = p Ti(↵ − (t)) + ✏0(t) E0

Es(t),

p Ti ≡ t1ti 1 − r1r2 (i = 1, 2)

<latexit sha1_base64="wJ/3nFIo609j1LrpQAElmr+2SxQ=">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</latexit>

PPD(t) ∝ |EPD(t)|2

<latexit sha1_base64="21YRGFHcQvwzf0QtU24ivmg6bmo=">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</latexit>

a(t) = a0 cos(mt + δτ)

<latexit sha1_base64="JtwBL1waeojHPjf9OW6+6InLus=">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</latexit>

SLIDE 15

15 / 17

Sensitivity curves

←current limit (CAST@CERN) aLIGO DECIGO Cosmic Explorer (Note: Axion is DM)

SLIDE 16

16 / 17

Sensitivity curves

←current limit (CAST@CERN) KAGRA DECIGO Cosmic Explorer KAGRA

L = 3 × 103[m], P = 335[W], λ = 1064[nm], (t2

1, t2 2 [ppm]) = (4 × 103, 7)

<latexit sha1_base64="Izn1/8+quL8Q4pYFJyAGFqV0QuI=">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</latexit>

SLIDE 17

17 / 17

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 can coexist with the observation run for gravitational waves. p Which detection port (a) or (b) can be constructed depends on the gravitational wave detectors. p As a first step, we want to apply our scheme to KAGRA detector.