Axion Dark Matter Search with Optical Interferometers

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Axion Dark Matter Search with Optical Interferometers

Ippei Obata (physical cosmology group, MPA)

PRL 123, 111301 (2019) arXiv:1903.02017 PRL 121, 161301 (2018) arXiv:1805.11753 Collaborators ：

Koji Nagano (JAXA), Tomohiro Fujita (ICRR)

Yuta Michimura, Yuka Oshima, Taihei Watanabe, Masaki Ando (University of Tokyo)

2020.10.6 MPA Cosmology seminar

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Overview

Axion

Optical Interferometry

n Important old problem n Candidate for dark matter

n Most recent technological innovation such as gravitational wave detectors n Possible to test a tiny tiny signal of phase modulation

Apply!

KAGRA

→ Pioneering a new phase of axion search!

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What is Axion?

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

n A scalar field with small mass, tiny interactions

(Peccei & Quinn, 1977, …)

A plentitude of axion-like particles provided by the compactifications of extra dimensions

(Witten 1984, …)

→ candidate for cold dark matter

QCD Axion

Axion-like particles (ALPs, string axion)

L ^QCD ✓G G, ˜ | ✓ | . 10 ¹⁰

✓

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! ✓ _e↵ = ✓ + /f ⌧ 1

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Conventional Way for Axion Search

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 : photon

B : magnetic field

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g _a

4 aF _µ⌫ F ˜ ^µ⌫ = g _a aE · B

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Axion-photon Conversion Experiments (1)

ADMX 2014

n A resonant haloscope using a strong magnet.

n It can probe the power signal of QCD axion dark matter with mass around μeV ~ meV.

Axion Haloscope ^l ADMX (Axion Dark Matter eXperiment), HAYSTAC

l MADMAX (MAgnetized Disc and Mirror Axion eXperiment) l …

MADMAX

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Axion-photon Conversion Experiments (2)

CAST 2017

l CAST (CERN Axion Solar Telescope)

l IAXO (International Axion Observatory) : Next generation of CAST Axion Solar Telescope

n A telescope to search for axion particles thermally produced in the Sun.

n The strong magnet converts the solar axion flux into X-rays.

n Possible to probe the axion-photon coupling with broad mass range.

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a

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→

nasa-fermi-mission n Axion-photon conversion will modify the spectrum of cosmic rays.

n The prediction depends on the uncertainty of magnetic field in the cluster background.

B

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B

Astronomical Observation of Axion-Photon

(8)

8 / 22

Overview of Target Spaces

Conlon+ 2017 (prospect)

Huge Discovery Space

(9)

9 / 22

The problem is…

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B

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g _a

4 aF _µ⌫ F ˜ ^µ⌫ = g _a aE ·

n In order to get better sensitivity, the more powerful superconducting magnets would be needed.

n In parallel with these experiments, we might as well suggest another

(perhaps more economical?) experimental approach to axion DM.

(10)

10 / 22

Axion DM Search

without the external magnetic field

g _a

4 aF _µ⌫ F ˜ ^µ⌫ = g _a aE · B

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a(t) = a ₀ cos(mt + _⌧ )

(11)

11 / 22

Modulation of Photon Polarization

<latexit sha1_base64="nxV0dfHyliF+a8gHzakQsFvJ2Wo=">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</latexit>

c _L/R = r

1 ± g _a a ₀ m _a

k sin(m _a t + _⌧ )

n Axion dark matter differentiates the phase velocities of the circular-polarized photons

n This velocity difference provides the rotation of linear-polarized photon

slightly oscillates!

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c _L > c _R

(12)

12 / 22

Axion Search with Resonant Cavity

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

n As a carrier wave, we input the linearly-polarized monochromatic laser light.

n The linear cavity consists of front and end mirrors. The cavity is kept to resonate with a phase measurement.

n The signal is detected in detection port (a) or (b) as polarization modulation.

(13)

13 / 22

Inside Cavity

n Electric vector inside cavity is represented as the superposition of reflected beams:

E _cav (t) = t ₁ E ₀ e ^ikt e ^L e ^R

X 1 n=1

A _n (t) 1 p 2

✓ 1 1

◆ , 8 <

:

A n+1 (t) ⌘ A n (t)R 1 T (t 2L(n 1))

⇥ R ₂ T (t 2L(n 1/2)) (n 1) A 1 = 1

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R i ⌘

✓ 0 r i

r i 0

◆ (i = 1, 2) ,

T (t) ⌘ e ⁱ ^L ^(t) 0 0 e ⁱ ^R ^(t)

! ,

L/R (t) ⌘ kL ⌥ k Z t

t L

c(t ⁰ )dt ⁰

(14)

14 / 22

E _cav (t) = t ₁ E ₀ e ^ikt

1 r ₁ r ₂ e ^L e ^R

✓ 1 + i (t) 0

0 1 i (t)

◆ 1 p 2

✓ 1 1

◆ = t ₁

1 r ₁ r ₂ [E ^p (t) E ^s (t)]

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Inside Cavity

(2kL

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= 2⇡ N )

1 ( * r _i ' 1)

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n When the resonant condition is met, the beam is accumulated inside cavity:

r _i ² + t ² _i = 1

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(15)

15 / 22

(t) =

Z ₁

1 c(m)H _a (m)e ^imt dm 2⇡

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Frequency Response in Signal

L

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= 10 ⁶ m

Longer ^length

&

Higher ^finesse ^{is better}

→ GW detectors!

(t ² ₁ , t ² ₂ ) [ppm] = (3.1 ⇥ 10 ⁵ , 3.1 ⇥ 10 ⁵ ) LIGO

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H _a (m) = i k m

4r ₁ r ₂ sin ² ( ^mL ₂ )

1 r ₁ r ₂ e ^i2mL ( e ^imL )

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mL = ⇡

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Response function of signal

(16)

16 / 22

SN Ratio

(coherent time of axion DM) n We assume the sensitivity is determined by the quantum shot noise

SNR = 8 >

> >

<

> >

> :

p T _obs 2 p

S _shot (m) c ₀ (T _obs . ⌧ ) (T _obs ⌧ ) ^1/4

2 p

S _shot (m) c ₀ (T _obs & ⌧ )

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⌧ = 2⇡

mv ² ⇠ 1yr(10 ¹⁶ eV/m)

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a(t) =

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a ₀ cos(mt + _⌧ )

Kimble+ 2001

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p T ⁱ ⌘ t ₁ t _i 1 r 1 r 2

(i = 1, 2)

n The SNR for axion DM is improved with the measurement time

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p T ⁱ ^shot ⇠ E _vac

E ₀ ! p

S shot (m) =

q k 2P ₀

p T ⁱ | H _a (m) |

(17)

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Potential Sensitivity Curves

T _obs = 1 year

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(18)

18 / 22

The problem is…

n In order to apply our method to the real GW detector, some optics need to be added for detection port.

n As a geometrical demerit of linear cavity, the sensitivity is lost by a parity-flipping effect on the reflection of mirror.

In case

<latexit sha1_base64="lmg9Tm604oXO8tfy6YYS+EmtdGc=">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</latexit>

m ⇠ L ¹

the rotation signal is most accumulated since the oscillatory turning point

matches with the reflection-timing.

,

the rotation signal is not so accumulated…

(19)

19 / 22

Axion DM Tabletop Experiment

@Tokyo University DANCE: Dark matter Axion search with riNg Cavity Experiment

with Y.Oshima, T.Watanabe, Y.Michimra, K.Nagano, IO, T.Fujita, M.Ando

Laser

Photo Detector

n A bowtie-like mirror configuration can sustain the rotational

orientation of photon polarization

(DANCE Act-1: Proto-type experiment)

(20)

20 / 22

First Data of DANCE Act-1 (2020.8)

First Data (assuming 1-year obs. from now) DANCE Act-1 (target sensitivity)

DANCE

Yuka Oshima’s talk @ autumn conference in the Physical Society of Japan

←current CAST limit

(21)

21 / 22

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 We also suggest a tabletop experiment to search for axion DM.

p Achieving the target sensitivity of DANCE is still ongoing…

(22)

22 / 22

Summary & Outlook

p Possible to probe QCD axion DM by interferometers?

p Application of our scheme to other projectable axion experiments? (e.g. LSW experiment)

p Constraining axion DM birefringence from astrophysical or

cosmological measurements? (e.g. CMB)

Axion Dark Matter Search with Optical Interferometers

1 / 22