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July 25, 2019 TianQin Summer School 2019 @ Sun Yat-sen University Laser Interferometry for Gravitational Wave Observations 1. Laser Interferometers Yuta Michimura Department of Physics, University of Tokyo Self Introduction Yuta Michimura

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SLIDE 1

Laser Interferometry for Gravitational Wave Observations

  • 1. Laser Interferometers

Yuta Michimura

Department of Physics, University of Tokyo

TianQin Summer School 2019 @ Sun Yat-sen University July 25, 2019

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SLIDE 2

Self Introduction

  • Yuta Michimura (道村 唯太)

Department of Physics, University of Tokyo

  • Laser interferometric

gravitational wave detectors

  • KAGRA
  • DECIGO
  • Fundamental physics with

laser interferometry

  • Lorentz invariance test
  • Macroscopic quantum

mechanics

  • Axion search

etc…

2

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SLIDE 3

Aim of This Lecture

3

  • Learn how laser interferometric gravitational wave

detector works and learn how to calculate quantum noise of the detector

  • You should be able to

design your own interferometer after the lectures

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SLIDE 4

Contents

4

  • 1. Laser Interferometers (July 25 PM)

Michelson interferometer Fabry-Pérot interferometer

  • 2. Quantum Noise (July 25 PM)

Shot noise and radiation pressure noise Standard quantum limit

  • 3. Sensitivity Design (July 26 AM)

Force noise and displacement noise Inspiral range and time to merger Space interferometer design

  • 4. Status of KAGRA (July 26 AM)

Status of KAGRA detector in Japan Future prospects

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SLIDE 5

Slides Available Online

5

  • 1. Laser Interferometers (July 25 PM)

https://tinyurl.com/YM20190725-1

  • 2. Quantum Noise (July 25 PM)

https://tinyurl.com/YM20190725-2

  • 3. Sensitivity Design (July 26 AM)

https://tinyurl.com/YM20190725-3

  • 4. Status of KAGRA (July 26 AM)

https://tinyurl.com/YM20190725-4

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SLIDE 6

Contents

6

  • 1. Laser Interferometers (July 25 PM)

Michelson interferometer Fabry-Pérot interferometer

  • 2. Quantum Noise (July 25 PM)

Shot noise and radiation pressure noise Standard quantum limit

  • 3. Sensitivity Design (July 26 AM)

Force noise and displacement noise Inspiral range and time to merger Space interferometer design

  • 4. Status of KAGRA (July 26 AM)

Status of KAGRA detector in Japan Future prospects

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SLIDE 7

Gravitational Waves

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  • Ripples in space-time
  • Stretches and squeezes length
  • Amplitude: fraction of length change (strain)
  • Plus (+) and cross (x) polarizations
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SLIDE 8

Detection of GWs

  • Most common detector: laser interferometer
  • Rai Weiss (MIT) proposed in 1960s

8

LIGO-P720002

Internal report (1972)

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SLIDE 9

Constant power when no GW

Laser Interferometric GW Detector

  • measure differential arm length change

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Suspended mirror Laser source Interference Beam splitter Top view Photodiode

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SLIDE 10

Power changes with GW

Laser Interferometric GW Detector

  • measure differential arm length change

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Photodiode Laser source Beam splitter Suspended mirror Interference Top view

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SLIDE 11

Amplitude of GW is Tiny

  • For example, GW150914 had h ~ 10-21

11

1 km

吊るされた鏡 Laser source Photodiode 光の干渉 半透明鏡

10-18 m for 1 km arm Size of hydrogen atom: 10-11 m Size of proton: 10-15 m

1 km

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SLIDE 12

Michelson Interferometer

  • Let’s look into how Michelson interferometer works

12

Suspended mirror Laser source Interference Beam splitter Top view Photodiode

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SLIDE 13
  • Electro-magnetic waves
  • Electric field can be written as

Laser Beam

13

amplitude phase angular frequency

  • f laser

wavelength phase at distance L Electric field: E Magnetic field Speed of light: c

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SLIDE 14

Photodiodes

  • Photodiodes (PDs)

Convert photons into electrons Detects light power (square of amplitude) We can only detect power change Phase change cannot be detected directly

14

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SLIDE 15

Beam Splitter

  • Split beam in two
  • Half in power, 1/√2 in amplitude
  • Sign flip in back reflection

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SLIDE 16

Output of Michelson Interferometer

  • What is the power detected at the photodiode?

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Photodiode Laser Beam splitter phase at distance L

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SLIDE 17

Output of Michelson Interferometer

  • What is the power detected at the photodiode?

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From Y-am From X-arm Differential arm length Input power

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SLIDE 18
  • Power changes with differential arm length change

(interference)

Output of Michelson Interferometer

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Laser Bright fringe in every half wavelength change in differential arm length

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SLIDE 19
  • Ratio between power change and length change

Output of Michelson Interferometer

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Differential arm length change can be detected from power change at the photodiode Laser

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SLIDE 20

How to Further Enhance the Signal

  • Longer arms gives larger length change due to

gravitational waves

  • But making arm length very long is tough

(especially on Earth)

  • Use Fabry-Pérot cavity

laser light go back-and-forth many times to effectively enhance the arm length

20

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SLIDE 21

Fabry-Pérot Cavity

  • Made from two parallel mirrors

21

input mirror end mirror

infinite times with reduced amplitude... partially reflected partially transmitted

amplitude reflectivity, transmittance

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SLIDE 22

Fabry-Pérot Cavity

  • Let’s calculate electric field inside the cavity

22

input mirror end mirror

infinite times with reduced amplitude... partially reflected partially transmitted

amplitude reflectivity, transmittance

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SLIDE 23

infinite geometric series with a common ratio of

Intra-Cavity Field

  • Intra-cavity field can be expressed as

23

input field

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SLIDE 24

Reflected Field

  • Reflected field can be expressed as

24

infinite geometric series with a common ratio of

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SLIDE 25

Intra-Cavity Power

  • Power inside

the cavity

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Intra-cavity power can be much higher than input power

  • n resonance

resonance constructive interference

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SLIDE 26

Intra-Cavity Power

  • Power inside

the cavity

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Almost no intra-cavity power at anti-resonance anti-resonance destructive interference

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SLIDE 27

Finesse

  • Power inside

the cavity

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Resonance Spacing Full width half maximum Sharpness of the resonance can be evaluated with Spacing FWHM Higher finesse for higher reflectivity Finesse

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SLIDE 28

Cavity Build-up

  • Power inside

the cavity

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Cavity build-up with r1~1, r2=1 Intra-cavity power at resonance Resonance

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SLIDE 29

Phase of Reflected light

  • Reflected field

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Phase of the reflected beam changes drastically at the resonance Cavity build-up

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SLIDE 30

Michelson and Fabry-Pérot

  • The phase of the reflected light is different by

→ FP is more sensitive to mirror displacement by (~ finesse) but linear range is smaller

30

Laser Laser

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SLIDE 31

Fabry-Pérot-Michelson Interferometer

  • Displacement sensitivity

higher by

  • Commonly used in

ground-based gravitational wave detectors

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Laser

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SLIDE 32

High-Frequency Response

  • The effect of gravitational waves

cancel at high frequencies

32

Michelson FPMI For a given frequency, there is a limit where longer arm length and higher finesse won’t help increasing the sensitivity Laser

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SLIDE 33

Summary

  • Gravitational waves create differential arm length

change in Michelson interferometer

  • Differential arm length change create power

change at the output of the Michelson interferometer

  • The signal can be enhanced by a factor of

by using Fabry-Pérot cavities

  • The sensitivity at low frequencies can be increased

with longer arm length and higher finesse

33

Finesse

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SLIDE 34

Slides Available Online

34

  • 1. Laser Interferometers (July 25 PM)

https://tinyurl.com/YM20190725-1

  • 2. Quantum Noise (July 25 PM)

https://tinyurl.com/YM20190725-2

  • 3. Sensitivity Design (July 26 AM)

https://tinyurl.com/YM20190725-3

  • 4. Status of KAGRA (July 26 AM)

https://tinyurl.com/YM20190725-4