Imagining the Future

1. Imagining the Future What can we do about the Quantum Noise Limit in Gravitational-wave Detectors? Nergis MavalvalaPenn StateOctober 2004

2. Quantum Noise in Optical Measurements • Measurement process • Interaction of light with test mass • Counting signal photons with a photodetector • 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)

3. 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

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

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

6. Initial LIGO

7. Signal-tuned InterferometersThe Next Generation

8. Quantum LIGO I LIGO II Test mass thermal Suspension thermal Seismic A Quantum Limited Interferometer

9. 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

10. 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

11. Advanced LIGO SensitivityImproved and Tunable broadband detunednarrowband thermal noise

12. Sub-Quantum Interferometers

13. 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

14. 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

15. 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

16. 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

17. Frequency-dependent Squeeze Angle

18. Realizing a frequency-dependent squeeze angle filter cavities • Filter cavities • Difficulties • Low losses • Highly detuned • Multiple cavities • Conventional interferometers  • Kimble, Levin, Matsko, Thorne, and Vyatchanin, Phys. Rev. D 65, 022002 (2001). • Signal tuned interferometers  • Harms, Chen, Chelkowski, Franzen, Vahlbruch, Danzmann, and Schnabel, gr-qc/0303066 (2003).

19. 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

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

21. 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 (recent progress at ANU and MIT) • Radiation pressure effects in interferometers  ponderomotive squeezing (in design & construction phase) • Challenges • Frequency-dependence  filter cavities • Amplitude filters • Squeeze angle rotation filters • Low-loss optical systems

22. Squeezing using nonlinear optical media

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

24. Squeezing using back-action effects

25. The principle • A “tabletop” interferometer to generate squeezed light as an alternative nonlinear optical media • Use radiation pressure as the squeezing mechanism • Relies on intrinsic quantum physics of optical field-mechanical oscillator correlations • Squeezing produced even when the sensitivity is far worse than the SQL • Due to noise suppression a la optical springs

26. Noise budget

27. 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

28. Optical Springs • Modify test mass dynamics • Suppress displacement noise (compared to free mass case) • Why not use a mechanical spring? • Thermal noise • Connect low-frequency mechanical oscillator to (nearly) noiseless optical spring

29. Speed Meters

30. Speed meters • Principle  weakly coupled oscillators • Energy sloshes between the oscillators • p phase shift after one slosh cycle • Driving one oscillator excites the other

31. homodyne detection Implementation of a speed meter • Position signal from arm cavity enters “sloshing” cavity • Exits “sloshing” cavity with p phase shift • Re-enters arm cavity and cancels position signal • Remaining signal  relative velocity of test masses sloshing cavity Purdue and Chen, Phys. Rev. D66, 122004 (2002)

32. Intra-cavity readouts

33. Intra-cavity readouts • Non-classical states of light exist inside cavities (ponderomotive squeezing) • Probe those intra-cavity squeezed fields Braginsky et al., Phys. Lett. A255, (1999)

34. Optical Bars and Optical Levers • Couple a second “probe” mass to the test mass • Probe mass does not interact with the strong light field in the cavity • Analogous to mechanical lever with advantage in the ratio of unequal lever arms Braginsky et al., Phys. Lett. A232, (1997)

35. Interferometer Configurations

36. White Light Interferometers • Broadband antenna response • Make cavity longer for longer wavelengths L0 b a L0 Guido Muller

37. LASER All-reflective Interferometers • Higher power-handling capability • Grating beamsplitters Peter Byersdorf

38. The Ultimate Wishlist

39. Technologies needed • Low-noise high-power lasers • What wavelength? • Low absorption and scatter loss optics • Low loss diffraction gratings • High non-linearity optical materials • High quantum efficiency photodetection • Low mechanical loss oscillators • With optical spring effect, oooh

40. In conclusion...

41. 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 and levers (Moscow) • Correlating SN and RPN quadratures • Variational readout • Power handling • All-reflective • Quadrature squeezing

42. Imagining the Future What can we do about the Quantum Noise Limit in Gravitational-wave Detectors? Plenty!