Quantum Optical Noise in LIGO Interferometers - Week 14, Lectures 25 & 26  [by Alessandra Buonano and Yanbei Chen]

1. Introduction: review of interferometers and their sensitivities; references on quantum optical noise; the experimental challenge: prevent quantum properties of detector and light (the "probe") from affecting the GW information we seek
2. Quantum optical noise in conventional interferometers (LIGO-I, TAMA, VIRGO)

1. vacuum fluctuations from dark port produce shot noise and radiation pressure fluctuations
2. Two-photon formalism for analyzing these noises
3. Application of this formalism to one arm cavity of the interferometer: shot noise; radiation-pressure noise
4. Input-output relations for the full interferometer [input is vacuum fluctuation at dark port and GW force on mirrors; output is GW signal plus noise]
5. Spectral density of quantum optical noise (shot and radiation pressure noise) deduced from input-output relations

Free-mass standard quantum limit [SQL] (for conventional interferometers)

1. Deduced from variation of quantum optical noise with laser power
2. Key issue: absence of shot/radiation-pressure correlations; correlations could invalidate the limit
3. Similarity to Heisenberg microscope

Ways to beat the SQL

1. In conventional interferometer:  measure a different quadrature of output light, one which posseses shot/radiation-pressure correlations
2. Change the test-mass dynamics: via a signal-recycling mirror (LIGO-II) or "optical-bar" configuration

Quantum optical noise in signal-recycled interferometers (LIGO-II)

1. Shot/radiation-pressure correlations
2. "Optical-spring" test-mass dynamics
3. Optical-mechanical instability; control system to overcome it
4. Effects of optical losses

Other noise sources and total noise in LIGO-II; the severity of thermoelastic noise

1. Lowering thermoelastic noise by flattening the light beams

Beyond LIGO-II: How to improve the sensitivity further without radical changes of interferometer's optical topology:

1. At low frequencies: reduce thermal noise via cryogenic cooling of test masses; reduce radiation pressure noise via larger test masses, lower optical power; seismic noise and seismic gravity-gradient noise
2. At high frequencies: reduce coating and substrate absorption so arm-cavity light power can be increased; narrow-band the noise curve

Beyond LIGO-II: New optical topologies

1. Speed-meter interferometers
2. Intracavity readout designs

1. The Nature of Gravitational Waves
2. Gravitational Waves Data Analysis
3. Gravitational Wave Sources in Neutron Stars
4. Introduction to General Relativity: Tidal Gravity
5. Mathematics of General Relativity: Tensor Algebra
6. Mathematics of General Relativity: Tensor Differentiation
7. Introduction to General Relativity (4/5)
8. Introduction to General Relativity (5/5)
9. Weak Gravitational Waves in Flat Spacetime (1/6)
10. Weak Gravitational Waves in Flat Spacetime (2/6)
11. Weak Gravitational Waves in Flat Spacetime (3/6)
12. Weak Gravitational Waves in Flat Spacetime (4/6)
13. Weak Gravitational Waves in Flat Spacetime (5/6)
14. Weak Gravitational Waves in Flat Spacetime (6/6); Propagation of Gravitational Waves Through Curved Spacetime (1/5)
15. Propagation of Gravitational Waves Through Curved Spacetime (2/5)
16. Propagation of Gravitational Waves Through Curved Spacetime (3/5)
17. Propagation of Gravitational Waves Through Curved Spacetime (4/5)
18. Propagation of Gravitational Waves Through Curved Spacetime (5/5)
19. Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (1/2)
20. Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (2/2)
21. Astrophysical Phenomenology of Binary-Star GW Sources (1/5)
22. Astrophysical Phenomenology of Binary-Star GW Sources (2/5)
23. Astrophysical Phenomenology of Binary-Star GW Sources (3/5)
24. Astrophysical Phenomenology of Binary-Star GW Sources (4/5)
25. Astrophysical Phenomenology of Binary-Star GW Sources (5/5); Post-Newtonian G-Waveforms for LIGO & Its Partners (1/2
26. Post-Newtonian Gravitational Waveforms for LIGO & Its Partners (2/2)
27. Supermassive Black Holes and their Gravitational Waves (1/3)
28. Supermassive Black Holes and their Gravitational Waves (2/3)
29. Supermassive Black Holes and their Gravitational Waves (3/3); Gravitational Waves from Inflation (1/2)
30. Gravitational Waves from Inflation (2/2)
31. Gravitational Waves from Neutron-Star Rotation and Pulsation (1/2)
32. Gravitational Waves from Neutron-Star Rotation and Pulsation (2/2)
33. Numerical Relativity as a Tool for Computing GW Generation (1/2)
34. Numerical Relativity as a Tool for Computing GW Generation (2/2)
35. The Physics Underlying Earth-Based Gravitational Wave Interferometers (1/4)
36. The Physics Underlying Earth-Based Gravitational Wave Interferometers (2/4)
37. The Physics Underlying Earth-Based Gravitational Wave Interferometers (3/4)
38. The Physics Underlying Earth-Based Gravitational Wave Interferometers (4/4)
39. Overview of Real LIGO Interferometers (1/2)
40. Overview of Real LIGO Interferometers (2/2)
41. Thermal Noise in LIGO Interferometers and its Control (1/2)
42. Thermal Noise in LIGO Interferometers and its Control (2/2)
43. Control Systems and Laser Frequency Stabilization (1/2)
44. Control Systems and Laser Frequency Stabilization (2/2)
45. Interferometer Simulations and Lock Acquisition in LIGO
46. Seismic Isolation in Earth-Based Interferometers
47. Quantum Optical noise in GW Interferometers (1/2)
48. Quantum Optical noise in GW Interferometers (2/2)
49. LIGO data analysis (1/2)
50. LIGO data analysis (2/2)
51. The Long-Term Future of LIGO: Facility Limits
52. The Long-Term Future of LIGO: Techniques for Improving on LIGO-II
53. Large Experimental Science and LIGO as an Example (1/2)
54. Large Experimental Science and LIGO as an Example (2/2)
55. Resonant-Mass GW Detectors for the HF Band (1/2)
56. Resonant-Mass GW Detectors for the HF Band (2/2)
57. CAJAGWR talk by W.O. Hamilton on Resonant-Mass GW Detectors
58. Doppler tracking of spacecraft for GW detection in the low frequency band
59. Pulsar timing for GW detection in the very low frequency band
60. LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design (1/2)
61. LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design (2/2)
62. LISA's Lasers and Optics (1/2)
63. LISA's Lasers and Optics (2/2)
64. Time-Delay Interferometry [TDI] for LISA (1/2)
65. Time-Delay Interferometry [TDI] for LISA (2/2)
66. LISA's Distrubance Reduction System (DRS) [Drag-Free System] (1/2)
67. LISA's Distrubance Reduction System (DRS) [Drag-Free System] (2/2)
68. The Big-Bang Observatory [BBO]: A Possible Follow-On Mission to LISA
69. GW's from Inflation and GW Detection in ELF Band via Anisotropy of CMB Polarization

Caltech's Physics 237-2002: Gravitational Waves
A Web-Based Course organized and Designed by Kip S. Thorne, Mihai Bondarescu and Yanbei Chen.

This course contains all the materials from a graduate-student-level course on Gravitational Waves taught at the California Institute of Technology, January through May of 2002. The materials include Quicktime videos of the lectures, lists of suggested and supplementary reading, copies of some of the readings, many exercises, and solutions to all exercises. The video files are so large that it may not be possible to stream them from most sites, but they can be downloaded. Alternatively, the course materials on DVD's can be borrowed via Interlibrary Loan from the Caltech Library (click on CLAS, then on Call Number, then enter QC179.T56 2002 ).

Questions and issues about this course and website can be directed to Mihai Bondarescu or Yanbei Chen.

Resources:

• - Part A - Gravitational-Wave Theory and Sources
• - Part B - Gravitational-Wave Detectors - original outline
• - Part B - Gravitational-Wave Detectors - alternative outline with the lectures reordered more logically
• - Course Materials

Credits:
Lectures by Thorne and Guest Lecturers*
Video of lectures by Bondarescu and Chen
Homework problems by Thorne and Guest Lecturers
Homework solutions by Bondarescu and Chen

*John Armstrong (JPL), Barry Barish, Erik Black, Alessandra Buonanno, Yanbei Chen, Riccardo De Salvo, Ronald Drever, Matt Evans, William Folkner (JPL), William Hamilton (LSU), Mark Kamionkowski, Albert Lazzarini, Lee Lindblom, Sterl Phinney, Mark Scheel, Bonny Schumaker (JPL), Robert Spero (JPL), Alan Weinstein, Phil Willems.