Gravitational-wave detector
using Optical Lattice Clocks in Space
Hisaaki Shinkai（Osaka Inst. Tech），Toru Tamagawa（RIKEN）, Atsushi Noda（JAXA）,Hidetoshi Katori（U Tokyo/RIKEN）, Junʼichiro Makino（Kobe U/RIKEN）,
Toshikazu Ebisuzaki（RIKEN）

SunEarth◆Cassiniʼs Doppler tracking (2001-2002) can be improved 3-order mag.

with current technologies◆“Cassini+++”, “Cassini++++” : sensitivity curve，detectable distance D◆ Event rate by hierarchical formation model of SMBH
2018/7/3 Marcel Grossmann 15@Rome

GW detector using Optical Lattice Clocks in Space2

１. Introduction：Optical Lattice Clock“Optical Lattice Clock”
H. Katori（JPS Journal，2002, p754）
trap atoms at standing laser wave
read frequency of transient phase
Cs atomic clock Δt/t = 5x10-16
Optical Lattice Clock (2015)10-18

magic freq. compensates multi-polarization
OLC targets

Δt/t = 10-19

grav. potential of 15m diﬀerence
relativistically measured
5cmJPS J，2017，p84（１cｍ on the EarthΔt/t＝ 1.1 x10-18 ）GW detector using Optical Lattice Clocks in Space3

１. Introduction

lambda=1pc

2000AU

20AU

0.2AU3000km3km

http://rhcole.com/apps/GWplotter/

GW detector using Optical Lattice Clocks in Space

4

１. Introduction：Existing plans for space GW observatories
LISA (ESA/NASA)

B-DECIGO⇒

DECIGO（Japan）

Laser Interferometer Space Anntena

Deci-hertz Interferometer GW Observatory

mHz range

0.1Hz range

2030 launch

proposed

3 satellites at L4 of Sun-Eartharound earth 2000km ３sattelites ⇒ Sun orbit

2.50 x 106 km

100 kmrobust to acceleration noiselight transponder

Fabry-Perot interferometerrobust to shot-noises

drag-free ﬂight

drag-free ﬂight

Doppler tracking with Laser beamsame as ground interferometer⇒1000 kmGW detector using Optical Lattice Clocks in Space5

2． Doppler tracking of Cassini Saturn Explorer
Cassini 2001-2002 (Armstrong, LRR 2006)
Armstrong et al. ApJ, 599, 806 (2003)

hc(f)G. Cassini (1625-1712)

3x10-15
10-4 Hz
Cassini (1997-2017)atomic clock
troposphereplasmaradiation pressure of Sun
control technology

GW detector using Optical Lattice Clocks in Space6▼

2． Improvement of Doppler sensitivity（１）monitor the time by Opt Lattice Clocks
need to make it portablein 3 satellites

If light transmission,
no eﬀects from plasma.

need R&D

10-5Hzatomic clock
troposphereplasmaOpt. Lattice Clock▼▼ ▼ ▼1 AU baseline▼▼

If radio transmission,
use two frequency ranges（double tracking）
to check phase diﬀerences due to interplanetary plasmain spacelight transmission

rad. pressure
solar panel parasol
control technology

GW detector using Optical Lattice Clocks in Space7

2． Improvement of Doppler sensitivity（２）rad. press. F=P/c
P=1.3 kW/m2
1000 kg, 10 m2
acceleration
a=5x10-8 m/s2
ΔP/P ≒ 1/1000
solar panel parasol

Δg/g ≒ 10-12atomic clock
troposphereplasma

Opt. Lattice Clock▼▼ ▼ ▼10-5Hz▼

1 AU baseline▼Δa/a ≒ 10-11

in spacelight transmission

rad. pressure
solar panel parasol
control technology

<latexit sha1_base64="5pN7MY4zB3DFNlfIFPZCHrTwzcc=">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</latexit>phn (f ) = f Sn (f )GW detector using Optical Lattice Clocks in Space

10-15

��-��

10-17

��-��

10-19

��-��

10-21
��-��

��-��
��-�

10-7

8

2． Improvement of Doppler sensitivity（３）With current technologies, we can obtain 3-order less than Cassini !
�������������� ������ - �����������-��

Cassini
Cassini+

Cassini++
Cassini+++
Cassini+++

Cassini++++bKAGRA

LISA
B-DECIGO

��-����

10-4
10-1

sensitivity f-1
satellite control perturbation
���102

frequency [Hz]sensitivity f2/3+10-18
Opt. Lattice Clock limitation

GW detector using Optical Lattice Clocks in Space

9

3．Previous proposals（Kolkowitz+ 2016）
Kolkowitz +PRD94(2016)124043
3 mHz or 30 mHz‒10 Hz5x107 km or 5x106 km
2 satellites, laser linkcompare freq. w Opt LatticeClockdrag-free ﬂight
Doppler shift with Laser beam

see also
Loeb, Maoz, 1501.00996
Vutha, New J. Phys. 17, 063030

GW detector using Optical Lattice Clocks in Space

10

3. Principle of GW detection
１．Each satellite has Opt Lattice Clock,send out each time to others.
2．Each satellite recognizes
direction・distance・velocityof others，and we know all of them.

Hisaaki Shinkai (Osaka Inst. Tech.)

2018/07/03 Marcel Grossmann 15 @ RomeGW detector using Optical Lattice Clocks in Space

11

3. Principle of GW detection
１．Each satellite has Opt Lattice Clock,send out each time to others.
2．Each satellite recognizes
direction・distance・velocityof others，and we know all of them.

Hisaaki Shinkai (Osaka Inst. Tech.)

2018/07/03 Marcel Grossmann 15 @ RomeGW detector using Optical Lattice Clocks in Space12

3. Principle of GW detection
１．Each satellite has Opt Lattice Clock,send out each time to others.
2．Each satellite recognizes
direction・distance・velocityof others，and we know all of them(including the potentioal of the Sun.)
Note: eﬀects of planets are O(month).

Hisaaki Shinkai (Osaka Inst. Tech.)

2018/07/03 Marcel Grossmann 15 @ RomeGW detector using Optical Lattice Clocks in Space13

3. Principle of GW detection
１．Each satellite has Opt Lattice Clock,send out each time to others.
2．Each satellite recognizes
direction・distance・velocityof others，and we know all of them(including the potentioal of the Sun.)
Note: eﬀects of planets are O(month).
3．When GW passes, we know its
diﬀerences.
If the events are 〜10s (/yr),then we can calibrate them well.

Hisaaki Shinkai (Osaka Inst. Tech.)

2018/07/03 Marcel Grossmann 15 @ Rome<latexit sha1_base64="5pN7MY4zB3DFNlfIFPZCHrTwzcc=">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</latexit>phn (f ) = f Sn (f )GW detector using Optical Lattice Clocks in Space

10-15

��-��

10-17

��-��

10-19

��-��

10-21
��-��

��-��
��-�

10-7

14

2． Improvement of Doppler sensitivity（３）With current technologies, we can obtain 3-order less than Cassini !
�������������� ������ - ���������

��-��

Cassini
Cassini+

Cassini++
Cassini+++
Cassini+++

Cassini++++bKAGRA

LISA
B-DECIGO

��-����

10-4
10-1

sensitivity f-1
satellite control perturbation���102frequency [Hz]sensitivity f2/3+10-18
Opt. Lattice Clock limitation

<latexit sha1_base64="4x+Yd6u1FDtx6lcKhF4FusBNT8s=">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</latexit>hn (f ) =p

f Sn (f ),hc (f )GW detector using Optical Lattice Clocks in Space▽

��-��

10-15

10-17

10-19

10-21
��-��

��-��

��-��

Hisaaki Shinkai (Osaka Inst. Tech.)
��-�

10-7

▽△

◇△△

◇□◇□

15３．GW obs. using Optical Lattice Clocks：target sources
equal-mass Binary BH inspiral at 1Gpc
�������������� ������ - ���������▽
△

◇◇

□

○

��-��

��-��
□

○

▼

□

106+106

○○○

▼

▲

▼
▼

▲

▼104+104

▲
▲

◆

��-�
���

10-4
10-1▲

◆■

LISA

frequency [Hz]2018/07/03 Marcel Grossmann 15 @ Rome◆◆■●■Cassini+++102+102◆■■●●

B-DECIGO���102

<latexit sha1_base64="4x+Yd6u1FDtx6lcKhF4FusBNT8s=">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</latexit>hn (f ) =p

f Sn (f ),hc (f )

GW detector using Optical Lattice Clocks in Space��-�� ▽

10-15

10-17

10-19

10-21
��-��Hisaaki Shinkai (Osaka Inst. Tech.)
▽△

��-��

��-��

��-��

��-�

10-7△◇△◇□◇□

16３．GW obs. using Optical Lattice Clocks：target sources
unequal-mass Binary BH inspiral at 1Gpc
mass ratio q=0.1
�������������� ������ - ���������▽

▽△△
◇◇
□

□

○○

▼

��-��
○106+105

□
○○
▼

▼
▼

▲
▲

◆��-�
���

10-4
10-1

104+103

▲
▲

◆◆

■

LISAB-DECIGO

frequency [Hz]2018/07/03 Marcel Grossmann 15 @ Rome◆◆■●■Cassini+++▼▲

102+101■●

���102

<latexit sha1_base64="4x+Yd6u1FDtx6lcKhF4FusBNT8s=">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</latexit>hn (f ) =p

f Sn (f ),hc (f )

GW detector using Optical Lattice Clocks in Space

��-��

10-15

10-17

10-19

10-21
��-��

Hisaaki Shinkai (Osaka Inst. Tech.)▽▽△��-����-����-��

��-�

10-7
▽

△

◇△△

◇

□

◇□

17３．GW obs. using Optical Lattice Clocks：target sources
unequal-mass Binary BH inspiral at 1Gpc
mass ratio q=0.01
�������������� ������ - ���������▽
△
◇◇□

□

○

��-��
○

▼

○106+104

□○○

▼

▼

▼

▲
▲

◆

LISA

��-�
���

10-4
10-1

104+102▼▲▲◆■

B-DECIGO

frequency [Hz]1 day=8.6x104 s
1 month=2.6x106 s

2018/07/03 Marcel Grossmann 15 @ Rome◆■●Cassini+++▲◆◆

102+1■■●

���102

GW detector using Optical Lattice Clocks in Space18３．GW obs. using Optical Lattice Clocks：detectable distance
S/N=10z

detectable distance [Mpc]�������� ����� [���] - ����� ���� [������] (���=��)
���

9.6

Cassini++++

���

1.4

Cassini+++

����

0.21

Cassini++

0.024

���

Cassini+
0.002

��Cassini
�

���

���

���

���

102
104
106
chirp mass M̲c [Msun]

Hisaaki Shinkai (Osaka Inst. Tech.)

2018/07/03 Marcel Grossmann 15 @ Rome

���

108

GW detector using Optical Lattice Clocks in Space

19３．GW obs. using Optical Lattice Clocks：detectable distance
S/N=100z

detectable distance [Mpc]�������� ����� [���] - ����� ���� [������] (���=���)���9.6���

1.4

Cassini++++

����

0.21

Cassini+++

���

0.024

Cassini++

��

0.002

Cassini+�Cassini���������

���

102
104106chirp mass M̲c [Msun]

Hisaaki Shinkai (Osaka Inst. Tech.)

2018/07/03 Marcel Grossmann 15 @ Rome

���

108

GW detector using Optical Lattice Clocks in Space

20

３．GW obs. using Optical Lattice Clocks：detectable distancedetectable distance [Mpc]

LISA

Cassini+++mass ratio q=0.2

q=0.2
1702.00786

�������� ����� [���] - ����� ���� [������]������

S/N=10�������

S/N=100������������������

chirp mass M̲c [Msun]�������� ����� [���] - ����� ���� [������]������

Cassini+++is better than LISA

����

�����

�

���

Hisaaki Shinkai (Osaka Inst. Tech.)������

������

2018/07/03 Marcel Grossmann 15 @ RomeGW detector using Optical Lattice Clocks in Space

21

３．GW obs. using Optical Lattice Clocks：detectable distancedetectable distance [Mpc]mass ratio q=0.2

LISA

Cassini++++q=0.2
1702.00786

�������� ����� [���] - ����� ���� [������]���

S/N=10�������

S/N=100������������������

���

chirp mass M̲c [Msun]�������� ����� [���] - ����� ���� [������]���Cassini+++is better than LISA�������

������

���

Hisaaki Shinkai (Osaka Inst. Tech.)������

������

2018/07/03 Marcel Grossmann 15 @ RomeGW detector using Optical Lattice Clocks in Space

22GWs from merging IMBHs

4．SMBH formation model：IMBHsʼ hierarchical mergers

HS, Kanda, Ebisuzaki, ApJ, 835 (2017) 276 [arXiv:1610.09505]

How many Galaxies in the Universe?

How many BHs in a Galaxy?
n(M)1012 M

10.000

0.001

10 M

0.01

1M

1.95

1012

within z=110-7100

M
1910z<3within z=5100

105

104

1000

1 × 1011

5 × 1011

1 × 1012

5 × 1012

BH mass

How many BH mergers in the Universe?

Event Rates at bKAGRA(QNM, S/N=10)

zfrequency[Hz]104a = 0.9
a = 0.51000



peak at 60M





100



a = 0.0


10



10

100

1000

104

200 events/yr






MBH /M

range 40M-150M

GW detector using Optical Lattice Clocks in Space

23

4．SMBH formation model：IMBHsʼ hierarchical mergers
How many BHs in a Galaxy?
n(M)How many Galaxies in the Universe?

1012 M

10.000

0.001

0.01

100

1M

1.95

10

12

within z=110-710M
1910 Mz<3within z=5100105

104

1000

1 × 1011

5 × 1011

1 × 1012

5 × 1012

BH mass

How many BH mergers in the Universe?

Event Rates at B-DECIGO(QNM, S/N=30)
1000

peak at 2800M
1440/yr (spin evol.)1010/yr (spin homo.)

100

10range 1600M-3x104M

z1

BH mass

100

1000

104

105

106

BH質量[Msun]

GW detector using Optical Lattice Clocks in Space

24

4．SMBH formation model：IMBHsʼ hierarchical mergers
Event Rate
Cassini+++

0.01

S/N=1010-4event rate [/yr]event rate [/yr]1Cassini++++1

S/N=100.01

S/N=10010-4

S/N=100100102

104

106108104106108

100102

BH mass [Msun]

19.1/yr

0.35/yrfor S/N=10104

106

108

104106108

BH mass [Msun]

19.2/yr29.8/yrfor S/N=10

GW detector using Optical Lattice Clocks in Space

Summary
LISA (ESA/NASA)

B-DECIGO⇒ DECIGO（Japan）

Kolkowitz +Our ProposalmHz range

0.1Hz range

3 mHz or 30 mHz –10 Hz

0.1 mHz ̶1 Hz

2 satellites

Sun-Earth L1-L4-L55x107 km or 5x106 km

１ AUlaser link

light or radio link

3 satellites at L4 of Sun-Earth around earth 2000km ３sattelites ⇒ Sun orbit
2.50 x 106 km

100 km⇒1000 kmlight transponder

Fabry-Perot interferometercompare freq. w Opt
Lattice Clockmonitor time w Opt Lattice
Clocksdrag-free ﬂight

drag-free ﬂight

drag-free ﬂight

no drag-freeDoppler tracking with Laserbeamsame as groundinterferometer

Doppler shift with Laserbeam

Doppler tracking

robust to accel. noise

robust to shot-noise

available at current tech

⭐Cassiniʼs Doppler tracking (2001-2002) can be improved 3-order mag.
with current technologies
Opt Lattice Clocks，３ satellites in space，Solar panel parasol⭐ ”Cassini+++”，some range is better than LISA sensitivity⭐ ”Cassini+++”，stellar-mass BH merger prediction 20 events/yr”Cassini++++”，+ IMBH inspiral 30 events/yr
Hisaaki Shinkai (Osaka Inst. Tech.)

2018/07/03 Marcel Grossmann 15 @ Romebackup原⼦時計を宇宙空間に設置する計画
The Space-Time Explorer and QUantum Equivalence Principle Space Test (STE-QUEST)
ESA, 2024年打ち上げ予定．地球周回軌道にルビジウム同位体原子干渉計．等価原理検証など．
Primary Atomic Reference Clock in Space (PARCS)
NASAが2008年にセシウム原子時計をISSに搭載しようと計画したものだが，Bushの政策Vision for Space
Exploration (VSE) により中止．
Galileo Global Navigation Satellite System
European GNSS Agency とESAが2019年完成目指して，構築しているヨーロッパ発の非軍事GPS. 各衛星は，水素メーザーとルビジウム原子時計を持つ．
Atomic Clock Ensemble in Space (ACES)ESAによる計画． ISSに，セシウム原子時計(PHARAO)と水素メーザー(SHM) の２つの原子時計を設置するもの．
2018年に日本のHTVによって打ち上げ予定．
Deep Space Atomic Clock (DSAC)
NASA JPLが計画する，水銀イオン原子時計を用いて，ナビゲーションの精度を高めようとする計画．
2018年，SpaceX Falcon で地球周回軌道に打ち上げ予定．

光格⼦時計を宇宙空間に設置する計画
space optical clock mission (SOC)
ESA. ISSに光格子時計を搭載して，地球重力赤方偏移，太陽重力，等価原理検証を目指そうとするもの．
2010年からスタート．10年後（もうすぐ？）にISS搭載を目指す．