1. Nergis Mavalvala PAC @ MIT December 2004
Development of Technologies for Sub-Quantum-Noise-Limited Gravitational-wave Interferometers
Nergis Mavalvala MIT December 2004

2. Advanced LIGO

3. A Quantum Limited Interferometer
LIGO I
Ad LIGO
Seismic
Suspension thermal
Test mass thermal
Quantum

4. Limiting Noise Sources: Optical Noise
Shot Noise
Uncertainty in number of photons detected a
Higher circulating power Pbs a low optical losses
Frequency dependence a light (GW signal) storage time in the interferometer
Radiation Pressure Noise
Photons impart momentum to cavity mirrors Fluctuations in number of photons a
Lower power, Pbs
Frequency dependence a response of mass to forces
Shot noise:
Laser light is Poisson distributed  sigma_N = sqrt(N)
dE dt >= hbar  d(N hbar omega) >= hbar  dN dphi >= 1
Radiation Pressure noise:
Pressure fluctuations are anti-correlated between cavities
 Optimal input power depends on frequency

5. Initial LIGO

6. Sub-Quantum Interferometers

7. 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)

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

9. In the presence of correlations
Output = Shot + Radiation pressure + Signal
Heisenberg uncertainty principle in spectral domain
Follows that

10. How to correlate quadratures?
Make noise in each quadrature not independent of each other
(Nonlinear) coupling process needed
Squeezed states of light and vacuum

11. Some quantum states of light
Analogous to the phasor diagram
Stick  dc term
Ball  fluctuations
Common states
Coherent state
Vacuum state
Amplitude squeezed state
Phase squeezed state
McKenzie

12. Squeezed input vacuum state in Michelson Interferometer
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-

13. 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 b1 b2 f
Squeezing produced by back-action force of fluctuating radiation pressure on mirrors a1 a2
“In” mode at omega_0 +/- Omega  |in> = exp(+/- 2*j* beta) S(r, phi) |out>
Heisenberg Picture: state does not evolve, only operators do. So |out> vacuum state is squeezed by factor sinh(r) = kappa/2 and angle phi = 0.5 arcot(kappa/2).
Spectral densities assuming input vacuum state:
S_b1 = exp(-2 r) ~ 1/kappa when kappa >> 1
S_b2 = exp(+2 r) ~ kappa
S_{b1 b2} = 0

14. Frequency-dependent coupling constant
Couples radiation pressure to mirror motion
Newton’s law
Cavity pole a b
Amplitude  b1 = a1
Phase  b2 = -k a1 + a2 + h
Radiation Pressure
Shot Noise

15. “Squeeze angle” describes the quadrature being squeezed
Optimal Squeeze Angle
“Squeeze angle” describes the quadrature being squeezed
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

16. Sub-quantum-limited interferometer
Narrowband
Broadband
Broadband Squeezed X+ X-
Quantum correlations
Input squeezing

17. Frequency-dependent Squeeze Angle
Narrowband
Broadband
Conventional

18. 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

19. Squeezed vacuum Requirements Generation methods Challenges
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
Challenges
Frequency-dependence  filter cavities
Amplitude filters
Squeeze angle rotation filters
Low-loss optical systems

20. Squeezing using nonlinear optical media

21. Non-linear crystals Optical Parametric Amplification (OPA)
Three (or four) wave mixing
Pump (532nm)
Seed (1064nm)

22. Optical Parametric Amplification
Annihilation operator
Amplitude and phase quadrature operators
Amplification
Violates commutation relation
Need to include vacuum state

23. Optical parametric amplification
Need phase sensitive amplification (parametric amplification)
Amplify amplitude quadrature by
Deamplify phase quadrature by
Product of the gains is unity
Commutation relations satisfied

24. Optical Parametric Oscillator

25. What has MIT group done so far?
We are squeezing
At high frequencies
Evidence of modest levels of squeezing at low freqs.
With multiple locking loops
Next-generation crystals acquired
Testing filter cavities
Testing noise couplings
Detailed calculations of noise budget
Photo-thermal noise not a problem
Pump noise coupling being considered

26. Experiment in NW17-069

27. Squeezed Vacuum

28. Low frequency squeezing at ANU
ANU group  quant-ph/
ANU group  quant-ph/

29. PERFORM A SUSPENDED INTERFEROMETER TEST
What’s next
Most important goal
Issues to work out
Coupling into interferometer dark port through output mode cleaner etc
Error signals for optimum quadrature
PERFORM A SUSPENDED INTERFEROMETER TEST

30. Squeezing using back-action effects

31. The principle
A “tabletop” interferometer to generate squeezed light as an alternative to 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

32. The Ponderomotive Interferometer

33. High circulating laser power High-finesse cavities
Key ingredients
High circulating laser power
10 kW
High-finesse cavities
15000
Light, low-noise mechanical oscillator mirror
1 gm with 1 Hz resonant frequency
Optical spring
Detuned arm cavities

34. 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

35. Detuned cavity for optical spring
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

36. Assumed experimental parameters

37. Noise budget

38. Noise budget – Equivalent displacement

39. Work so far Detailed simulation of noise couplings
Uses first fully quantum mechanical simulation code for a GW interferometer (Corbitt)
Used in AdLIGO simulations (Fritschel and Popescu)
“Exported” to Hannover and Glasgow (Schnabel and Strain)
Location and infrastructure
LASTI laser, vacuum envelop and seismic isolation
Cavity geometrical parameters
Mini-mirror suspensions

40. High finesse cavity tests
What’s next
Design completion
Suspension
Control system
High finesse cavity tests
Fixed mini-mirror – optical tests
Suspended mini-mirror – includes mirror dynamics and radiation-pressure coupling
Complete interferometer

41. High finesse cavities with high laser power Mini-mirror dynamics
Risk management
High finesse cavities with high laser power
Power density on optical surfaces
Mini-mirror dynamics
Suspension thermal noise
Static displacement due to radiation pressure
Electrostatic actuation

42. Why is this interesting/important?
First ever demonstration of ponderomotive squeezing
Probes quantum mechanics of optical field-mechanical oscillator coupling at 1 g mass scales
Test of low noise optical spring
Suppression of thermal noise
Simulations and techniques useful for AdLIGO and other GW interferometers
Michelson detuning
Role of feedback control in these quantum systems

43. Resources

44. People Stan Whitcomb (Co-I) sage-at-large
Dave Ottaway (Co-I) optics, suspension
Eugeniy Mikhailov crystal squeezing
Keisuke Goda (G) crystal squeezing
Thomas Corbitt (G) ponderomotive interferometer
Chris Wipf (G) crystal squeezing
Gregg Harry suspensions, thermal noise
Rai Weiss es actuator, electronics
Si-Hui Tan (G) suspension design
Marat Freytsis (UG) CO2 welding for suspension
Caryn Bullard (UG) homodyne detection

45. Time Line Crystal squeezing Ponderomotive ifo
Complete design for an interferometer test, including control system (2Q2005)
Build and test at MIT (4Q2005)
Integrate into (e.g.) 40m prototype (2Q2006)
Sub-QNL (4Q2006)
Go graduates
Ponderomotive ifo
Mini-suspension design (1Q2005)
High finesse cavity optical test (2Q2005)
High finesse cavity dynamics test (4Q2005)
Full interferometer (2Q2006)
Low noise (2Q2007)
Thomas graduates

46. Acknowledgments Space
Optics labs for crystal squeezing experiment
LASTI laser, vacuum envelop and seismic isolation for ponderomotive interferometer
LIGO lab personnel (MechE, ElecE, scientists) and equipment resources
Support
MIT seed money
NSF exploratory grant
Graduate fellowships
ANU crystals
Close collaborations
ANU and Hannover (crystal squeezing)
Integration with 40m program for suspended interferometer test
AEI/Caltech/Maryland (theory)

47. In conclusion...

48. Time is ripe to develop squeezing techniques for GW interferometers
Next generation interferometers likely to be almost entirely quantum noise limited
Time is ripe to develop squeezing techniques for GW interferometers
Nonlinear optical media
Back-action induced correlations
Other Quantum Non-Demolition techniques
Program well-integrated with LIGO Laboratory in mission and execution

49. Budget OPO suspended interferometer test Personnel Travel
3 p-y post-doc
5 p-y grad student
Travel
International $10k/yr
Domestic $10k/yr + $15k for OPO suspended interferometer test
OPO suspended interferometer test
$50k for optical bench
$15k for control electronics
Ponderomotive ifo
$30k for core optics
$40k for auxiliary optics and optoelectronics
$20k for vacuum prep and custom tooling
$80k for digital sensing and controls electronics

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

51. Advance LIGO Sensitivity: Improved and Tunable
broadband
detuned narrowband
SQL  Heisenberg microscope analog
If photon measures TM’s position too well, it’s own angular momentum will become uncertain.
thermal noise

52. 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
Use a low resonant frequency mechanical pendulum to minimize thermal noise
Use an optical spring to produce a flat response out to higher frequencies