How did physicists detect Gravitational Waves? Some tools that revealed the GW event. C. Kurtsiefer, Physics enrichment camp NUS

Transcription

1 How did physicists detect Gravitational Waves? Some tools that revealed the GW event C. Kurtsiefer, Physics enrichment camp NUS

2 The Story in the News

3 The Situation small strain σ of space major incident long distance d d 410 Mpc ly m σ = Δl / l 10-21

4 How to test strain σ? Δ Lx Δ Ly σ= = Lx Ly Round trip times of light between fixed points: B Ly A, B, C: masses at rest Lx = Ly in quiet times tx,y = 2 Lx,y / c0 ty tx A Lx C tx - ty = 0: no strain tx - ty 0: strain

5 Michelson and Morley 1887

6 Michelson and Morley Result: Speed of light does not depend on direction of propagation Same speed of light at different times in the year No ether or reference that supports the propagation of light One of the starting points for theory of special relativity v spring Sun v fall Ether wind

7 Michelson Interferometer Mirror Ly Beam Splitter Light source Mirror Lx Output

8 Light as a wave E(x) t>0 t=0 x Light of fixed frequency f: E ( x,t )=E 0 sin(k x ωt ) 2π k=, λ Speed of light c0 is constant: (and independent of direction and reference frame) ω=2 π f ω=c 0 k, c 0 =λ f

9 Symmetric Beam Splitter Ec Ed Ea 1 Ea Ec = 1 1 E d E b ( ) ( )( ) Eb output beams with amplitude reduced by 2

10 Superposition of light waves I 1 Ea Ec = 1 1 E d E b ( ) ( )( ) Ea Eb Ec Ed

11 Superposition of light waves II 1 Ea Ec = 1 1 E d E b ( ) ( )( ) Ea Eb Ec Ed

12 Adding two amplitudes Just before recombination: Ea = Ly Ea E0 Eback Eout Eb = Eb Lx 1 Ea E back = 1 1 E out E b ( ) ( )( ) E0 2 E0 2 cos(2 k L y ω t ) cos(2 k L x ωt ) Output field: 1 E out = ( E a E b ) 2 = = E 0 sin(k (L y L x )) sin(k (L y +L x ) ω t )

13 Light field and optical power Plane wave light field: E ( x,t )= E 0 cos (k x ω t ) Power on detector: ϵ0 2 ϵ0 2 Δ E Δ E Δ V Δ E A Δ l P= = = = 2 E Ac 0 = E 0 Ac 0 Δ t Δ V Δ t ΔV Δ t 2 2 [ Energy per volume ]

14 Power at output of interferometer Output power: P out Ly = P back = Pin Pback Pout Lx 2 P in sin ( k Δ L ) 2 P in cos ( k Δ L ) with Δ L=L y L x

15 Can the demo setup detect GW? Measure Pout near ΔL=λ/8: δ P out d P out = δ (Δ L) d Δ L P in =2 π λ Δ L=λ /8 δ P out λ δ(δ L)= P in 2 π Power resolution Wavelength Position resolution Length Strain resolution GW peak strain δpout / Pin 1% λ δ(δl) 632 nm 1 nm L δσ = δ(δl)/ L σ 0.3 m Missing orders of magnitude...

16 How to increase sensitivity? Reduce strain uncertainty δσ: [ d (P out /P in ) δ(δ L) 1 δσ = = L L d (Δ L) arm length 1 ] 1 δ P out P in power interferometer responsiveness Increase L Increase interferometer responsiveness Increase Pin & decrease δpout (Decrease environmental impact) power uncertainty

17 st Increase Arm Length, 1 try LIGO, Hanford site 4 km 0.3 m 4 km: improve ~4 orders of magnitude in δσ

18 nd Increase Arm Length, 2 try elisa project 106 km 0.3m 109m: improve ~9-10 orders of magnitude in δσ

19 Increase response per length L Michelson & Morley 1887: 4 round trips Reflectivity of metal mirrors Wavelength Silver: R 90% at 500 nm Gold: R 98% at 1064 nm

20 Dielectric Mirrors Interference of reflections from thin transparent films Modern optical mirrors: R > % for round trips doublets

21 Fabry-Perot Resonator Dielectric mirrors For R1 = R2 = R, no losses: P in P out (Δ L)= 2πΔL 1+f sin 2 ( ) λ with f = 4 R 2 (1 R) 1 0 Pout / Pin R= 97% ΔL

22 Fabry-Perot Resonator II 1 Often used: finesse λ /2 F= π FWHM 1 R Pout / Pin F 105 for R = 97% 0 ΔL Fabry-Perot responsiveness: [ 1 FWHM ] d (P out /P in ) 2π 1 λ d (Δ L) 1 R Michelson responsiveness: 0 ΔL [ ] d (P out /P in ) 2π = λ d (Δ L)

23 Fabry-Perot Resonator as Mirror Simple mirror in Michelson interferometer: Pback = Pin Δ ϕm = 4π ΔL λ Asymmetric Fabry-Perot resonator: Pback = Pin Δ ϕc =???

24 Fabry-Perot Mirror reponse Solution: Δ ϕc Δ ϕm 1+ R tan = tan R Δ ϕc R = 99% 90% 4 Near ΔφC = 0: 50% 0% Δ ϕm 1+ R 4 Δ ϕc Δ ϕm Δ ϕm 1 R 1 R

25 Super-Michelson interferometer Keep both Fabry-Perots near resonance Sensitivity enhancement by 4/(1-R) Beam splitter

26 Michelson sensitivity sweet spot Output power: 2 P out (ϕ)=p in sin ϕ φ Phase sensitivity: d P out (ϕ) =P in sin(2 ϕ) dϕ φ Phase sensitivity per output power: d P out (ϕ)/d ϕ ϕ P out 0 = sin(2 ϕ0 ) sin2 ϕ 0 2 ϕ 0 Work near dark fringe (φ0 0), use lots of power! φ

27 Light detection Photodiode Popt Photocurrent I is proportional to Popt Energy absorbed per time Δt : Amp meter Energy = P opt Δ t Number of electrons per Δt : P opt Δ t Energy n = = h f h f Photocurrent: P opt e n e I = = Δt h f

28 Noise in Light detection δn = Uncertainty of electron number: Relative uncertainty in power; n δ P opt 1 = = P opt n More optical power less noise Longer measurement time less noise Shot noise h f P opt Δ t

29 The full setup Phys. Rev. Lett. 116, (2016)

30 Holding the mirrors at rest 4 Aston et al.,class. Quant. Gravity 29, (2012)

31 Pendulum as noise eater Assume harmonic shakes from suspension: x in (t )= x in cos(ωt ) Test mass will shake with same frequency: x out (t )= x out cos(ω t ) x out x in ~ ω -2 ω 0= g l ω / ω0

32 Pendulum chain of 4 Susceptibilities get multiplied x 4 x in f1 = 3.1 Hz f2 = 0.85 Hz f3 = 0.69 Hz f4 = 0.45 Hz ~ ω -8 f /Hz Also: avoid thermal noise in suspension

33 Moving the mirrors quietly... Aston et al.,class. Quant. Gravity 29, (2012)

34 The first result...

35 Where from here? Different gravitational wave telescopes... Souce: elisa consortium