Quantum Noise in Gravitational-wave Detectors

1. Quantum Noise in Gravitational-wave Detectors Quantum noise and quantum measurement Nergis MavalvalaCaltechAugust 2004

2. “Conventional” InterferometersGeneration 1 (now!)

3. GW interferometer at a glance L ~ 4 km For h ~ 10–21 DL ~ 10-18 m Seismic motion -- ground motion due to natural and anthropogenic sources Thermal noise -- vibrations due to finite temperature Shot noise -- quantum fluctuations in the number of photons detected

4. S2 2nd Science Run Feb - Apr 03 (59 days) S1 1st Science Run Sept 02 (17 days) Strain (1/rtHz) LIGO Target Sensitivity S3 3rd Science Run Nov 03 – Jan 04 (70 days) Frequency (Hz) Science Runs and Sensitivity DL = strain x 4000 m 10-18 m rms

5. Signal-tuned InterferometersThe Next Generation

6. Why a better detector? Astrophysics • Factor 10 to 15 better amplitude sensitivity • (Reach)3 = rate • Factor 4 lower frequency bound • NS Binaries • Initial LIGO: ~20 Mpc • Adv LIGO: ~350 Mpc • BH Binaries • Initial LIGO: 10 Mo, 100 Mpc • Adv LIGO : 50 Mo, z=2 • Stochastic background • Initial LIGO: ~3e-6 • Adv LIGO ~3e-9

7. How will we get there? • Seismic noise • Active isolation system • Mirrors suspended as fourth (!!) stage of quadruple pendulums • Thermal noise • Suspension  fused quartz; ribbons • Test mass  higher mechanical Q material, e.g. sapphire; more massive (40 kg) • Optical noise • Input laser power  increase to ~200 W • Optimize interferometer response signal recycling

8. Limiting Noise Sources: Optical Noise • Shot Noise • Uncertainty in number of photons detected a • Higher circulating power Pbsa low optical losses • Frequency dependence a light (GW signal) storage time in the interferometer • Radiation Pressure Noise • Photons impart momentum to cavity mirrorsFluctuations in number of photons a • Lower power, Pbs • Frequency dependence a response of mass to forces  Optimal input power depends on frequency

9. Initial LIGO

10. The requirement High laser power for good shot noise limited performance Traded off against radiation pressure noise The strategy Increase laser power at input to 180 W  nearly 1 MW of CW power incident on arm cavity optics The challenge High power, low noise laser Power absorption in optics coatings and substrates  absorption and scatter losses for mirror substrates and coatings Mirror substrate mass  40 kg Quantum LIGO Advanced LIGO Test mass thermal Suspension thermal Seismic Higher Laser Power

11. Light bounces back and forth along arms ~100 times 20 kW DL = h L h ~ 10-21 Light is “recycled” ~50 times 300 W input test mass GW Interferometer Configuration end test mass Laser + optical field conditioning signal 6Wsingle mode 4 km All cavities on resonance  interferometer is “locked”

12. Cavity forms compound output coupler with complex reflectivity. Peak response tuned by changing position of SRM ℓ Reflects GW photons back into interferometer to accrue more phase SignalRecycling Signal-recycled Interferometer 800 kW 125 W signal

13. Advance LIGO Sensitivity:Improved and Tunable broadband detunednarrowband thermal noise

14. Part of the light leaks out the SRMand contributes to the shot noise RPN(t+t) BUT the (correlated) part reflectedfrom the SRM returns to the TM and contributes to the RPN at a later time SN(t) Signal recycling mirror  quantum correlations • Shot noise and radiation pressure (back action) noise are correlated(Buonanno and Chen, PRD 2001) • Optical field (which was carrying mirror displacement information) returns to the arm cavity • Radiation pressure (back action) force depends on history of test mass (TM) motion • Dynamical correlations

16. Sub-Quantum InterferometersGeneration 2++

17. Quantum Noise in Optical Measurements • Measurement process • Interaction of light with test mass • Counting signal photons with a PD • Noise in measurement process • Poissonian statistics of force on test mass due to photons  radiation pressure noise (RPN) (amplitude fluctuations) • Poissonian statistics of counting the photons  shot noise (SN) (phase fluctuations)

18. uncorrelated 0.1 MW 1 MW 10 MW Free particle SQL

19. In the presence of correlations • Heisenberg uncertainty principle in spectral domain • Follows that

20. GW signal in the phase quadrature Not true for all interferometer configurations Detuned signal recycled interferometer  GW signal in both quadratures Orient squeezed state to reduce noise in phase quadrature X- X- X- X+ X- X+ X+ X+ Squeezed input vacuum state in Michelson Interferometer

21. Squeezing produced by back-action force of fluctuating radiation pressure on mirrors a2 b2 a1 ba f b1 Back Action Produces Squeezing • Vacuum state enters anti-symmetric port • Amplitude fluctuations of input state drive mirror position • Mirror motion imposes those amplitude fluctuations onto phase of output field

22. Coupling coefficient k converts Da1 to Db2 • k and squeeze angle f depends on I0, fcav, losses, f a b Conventional Interferometer with Arm Cavities Amplitude  b1 = a1 Phase  b2 = -k a1 + a2 + h Radiation Pressure Shot Noise

23. Newton’s law Cavity pole The coupling coefficient • A rather important entity since all QND effects in GW interferometers arise because of this coupling of radiation pressure to mirror motion

24. Optimal Squeeze Angle • If we squeeze a2 • shot noise is reduced at high frequencies BUT • radiation pressure noise at low frequencies is increased • If we could squeeze -k a1+a2 instead • could reduce the noise at all frequencies • “Squeeze angle” describes the quadrature being squeezed

25. Frequency-dependent Squeeze Angle

26. Squeezing – the ubiquitous fix? • All interferometer configurations can benefit from squeezing • Radiation pressure noise can be removed from readout in certain cases • Shot noise limit only improved by more power (yikes!) or squeezing (eek!) • Reduction in shot noise by squeezing can allow for reduction in circulating power (for the same sensitivity) – important for power-handling

27. Squeezed vacuum • Requirements • Squeezing at low frequencies (within GW band) • Frequency-dependent squeeze angle • Increased levels of squeezing • Generation methods • Non-linear optical media (c(2) and c(3) non-linearites)  crystal-based squeezing • Radiation pressure effects in interferometers  ponderomotive squeezing (in design & planning stages) • Challenges • Frequency-dependence  filter cavities • Amplitude filters • Squeeze angle rotation filters • Low-loss optical systems

28. X- X+ Sub-quantum-limited interferometer Quantum correlations(Buonanno and Chen) Input squeezing

29. Squeezing using nonlinear optical media

30. Vacuum seeded OPO ANU group  quant-ph/0405137

31. Squeezing using back-action effects

32. Introduction • A “tabletop” interferometer to generate squeezed light • Use radiation pressure as the squeezing mechanism • Expected noise sources do not prohibit squeezing • Alternative to crystal-based squeezing • Intrinsic quantum physics of optical field --mechanical oscillator correlations

33. Key ingredients • High circulating laser power • 10 kW • High-finesse cavities • 25000 • Light, low-noise mechanical oscillator mirror • 1 gm with 1 Hz resonant frequency • Optical spring • Detuned arm cavities

34. Optical layout

35. Producing Frequency-independent Squeeze Angle • Frequency dependent squeeze angle • Due to the frequency response (f-2) of a free mass to a force • Modify the dynamics of the test mass • Connect to a spring with a high resonant frequency • Below the resonant frequency, the response is frequency-independent

36. Thermal Noise in Springs • Why not use a mechanical spring? • Displacements due to thermal noise introduced by the high frequency (mechanical) spring will wash out the effects of squeezing • An optical spring with a high resonant frequency will not change the thermal force spectrum of the mechanical pendulum • A low resonant frequency mechanical pendulum may be used to minimize thermal noise, while the optical spring produces the flat response up to high frequencies

37. Positive detuning Detuning increases Cavity becomes longer Power in cavity decreases Radiation-pressure force decreases Mirror ‘restored’ to original position Cavity becomes shorter Power in cavity increases Mirror still ‘restored’ to original position Optical springDetuned cavity L

38. Laser Noise

39. All Noise Sources

40. Why is this interesting? • Alternative to crystal squeezing • Test quantum-limited radiation pressure effects • gain confidence that the modeling is correct • Test noise cancellations via Michelson detuning • useful for all interferometers • Squeezing produced even when the sensitivity is far worse than the SQL • due to the optical spring

41. In conclusion...

42. Next generation – quantum noise limited • Squeezing being pursued on two fronts • Nonlinear optical media • Back-action induced correlations • Other Quantum Non-Demolition techniques • Evade measurement back-action by measuring of an observable that does not effect a later measurement • Speed meters (Caltech, Moscow, ANU) • Optical bars (Moscow) • Correlations between the SN and RPN quadratures

43. Gravitational-waves Instruments Tests of General Relativity Quantum Measurement Astrophysics