Quantum Noise in Advanced Gravitational Wave Interferometers

1. Quantum Noise in Advanced Gravitational Wave Interferometers NSF Proposal Review Nergis MavalvalaPAC 13, LLODecember 2002

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

3. Strain sensitivity limit due to quantum noise • Shot Noise • Uncertainty in number of photons detected a • (Tunable) interferometer response  Tifo depends on light storage time of GW signal in the interferometer • Radiation Pressure Noise • Photons impart momentum to cavity mirrorsFluctuations in the number of photons a

4. Classical optics Amplitude Phase Power Phasor representation Length  amplitude Angle  phase Quantum optics Annihilation operator Creation operator Photon number and not Hermitian  NOT observables Classical Optics - Quantum Optics

5. Define a Hermitian operator pair is the amplitude quadrature operator is the phase quadrature operator Linearization DC term + fluctuations Fluctuations in amplitude and phase quadratures Defining Observables McKenzie

6. Heisenberg and QND • Heisenberg Uncertainty Principle • Measure position of a particle very precisely • Its momentum very uncertain • Measurement of its position at a later time uncertain since • Quantum non-demolition (QND) • Evade measurement back-action by measuring of an observable that does not effect a later measurement • Good QND variables (observables) • Momentum of a free particle since [p, H] = 0 • Quadrature components of EM field (explained in next few viewgraphs)

7. ‘Ball on stick’ representation • Analogous to the phasor diagram • Stick  dc term • Ball  fluctuations • Common states • Coherent state • Vacuum state • Amplitude squeezed state • Phase squeezed state McKenzie

8. Vacuum State in a Michelson • Michelson on dark fringe  laser contributes only correlated noise • GW signal from anti-correlated effect  phase quadrature • Vacuum noise couples in at the beamsplitter • Phase quadrature fluctuations: Shot Noise • Amplitude quadrature fluctuations: Radiation Pressure Noise McKenzie

9. Squeezed State in a Michelson • Inject squeezed state into the dark port of Michelson to replace vacuum • Amplitude squeezed state oriented to reduce noise in the signal (phase) quadrature McKenzie

10. Squeezed State in a Michelson • GW signal in the phase quadrature • Orient squeezed state to reduce noise in phase quadrature1 McKenzie

11. Standard Quantum Limit • “Traditional” treatment (Caves, PRD 1980) • Shot noise and radiation pressure noise uncorrelated • Vacuum fluctuations entering output port of the beam splitter superpose N1/2 fluctuations on the laser light • Optimal Pbs for a given Tifo • Standard quantum limit in GW detectors • Limit to TM position (strain) sensitivity for that optimal power for a given Tifo and frequency • Minimize total quantum noise (quadrature sum of SN and RPN) for a given frequency and power)

12. RPN(t+t) 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 • t Part of the light leaks out the SRMand contributes to the shot noise BUT the (correlated) part reflectedfrom the SRM returns to the TM and contributes to the RPN at a later time

13. New quantum limits • Quantum correlations  • SQL no longer meaningful • Optomechanical resonance (“optical spring”) • Noise cancellations possible • Quantization of TM position not important(Pace, et. al, 1993 and Braginsky, et. al, 2001) • GW detector measures position changes due to classical forces acting on TM • No information on quantized TM position extracted

14. Quantum Manipulation:AdLIGO as an example • “Control” the quantum noise • Many knobs to turn: Optimize ifo sensitivity with • Choice of homodyne (DC) vs. heterodyne (RF) readout • RSE detuning  reject noise one of the SB frequencies • Non-traditional modulationfunctions • Non-classical light?

15. Quantum manipulation: Avenues for AdLIGO+ • Squeezed light • Increased squeeze efficiency • Non-linear susceptibilities • High pump powers • Internal losses • Low (GW) frequencies • QND readouts • Manipulation of sign of SN-RPN correlation terms • Manipulation of signal vs. noise quadratures (KLMTV, 2000) • Squeezed vacuum into output port ANU, 2002

16. Recent interest in quantum effects and squeezing • AdLIGO is quantum-noise-limited at almost all frequencies • Quantum correlations allow for manipulation of quantum noise • Squeezing is more readily achieved except • More is better (> 6 dB) • Not in GW band (100 Hz)

17. This proposal at a glance Squeezed Source Interferometer Nergis Mavalvala (PI) Stan Whitcomb (co-PI) Post-doc (TBD) Keisuke Goda (Grad) Thomas Corbitt (Grad) 10 dB AdLIGO 100 Hz AdLIGO+ $ 400k/yr

18. 10 dB Internal losses Injection losses c(2) and c(3) non-linearities Pump power Photodetection efficiency 100 Hz Reduce seed noise Correlate multiple squeezed beams Squeezed source

19. Advance LIGO Signal tuned Quantum noise limited SEM  SN and RPN correlated  QND Squeezed input Evaluation in the presence of other noise limits and technical noise AdLIGO + Speedmeters White light interferometers All reflective interferometers Ponderomotive squeezing Squeezed source

20. Experimental Program • Set up a Quantum Measurement (QM) lab within LIGO Laboratory at MIT • Goals • Develop techniques for efficient generation of squeezed light • Explore QND techniques for below QNL readouts of the GW signal (AdLIGO and beyond) • Trajectory • Build OPA squeezer (generation n+) • Build table-top (or suspended optics) experiments to test open questions in below QNL interferometric readouts

21. Programmatics: People • People involved (drafted, conscripted) • PIs • Nergis Mavalvala (PI) • Stan Whitcomb (co-PI) • 1 to 1.5 post-docs • David Ottaway and/or TBD (?) • Yanbei Chen (MIT Fellowship?) • Graduate students (2+) • Keisuke Goda and Thomas Corbitt • Collaborators, advisors, sages • Lam, McClelland (ANU) • Fritschel, Shoemaker, Weiss, Zucker (MIT) • Visitors • McKenzie (ANU). Sept. to Dec. 2002

22. Programmatics: $$ • MIT seed funds supporting presently on-going experimental work • NSF request (average over 3 years) • 350 k$/year • Salaries – 100 k$/yr • 1 post-doc • (2+1) graduate students • 1 month summer salary for NM • Equipment – 100 k$/yr • Lab equipment • Non-linear crystal development • Travel – 20k$/yr

23. Programmatics: Facilities • Space • Optics labs (NW17-069, NW17-034) • Physical environment • Possibly share seismically and acoustically quiet environment of LASTI for QND tests involving suspended optics • Research equipment • Share higher-power, shot-noise-limited, frequency-stabilized laser • In-house low loss optics, low noise photodetection capabilities • Suspended optics interferometer

24. Programmatics: When?Squeezing • Summer, 2002 • Gain experience with OPA squeezer (with Lam, Buchler at ANU) • Fall, 2002 – Summer, 2003 • Building OPA squeezer with “borrowed” crystals (with Goda) • Pathfinder program to learn about remedies for deficiencies in present non-linear crystals • Formation of “10 dB consortium” for next-generation crystal development (with Lam) • 2003 and 2004 • Acquire new crystals • Testing with high-power, low-noise pump • Beyond • Attack open questions in the field subject to personnel, interests, funding and recent developments (and LIGO I status)

25. Programmatics: When?Interferometry • 2002 • AdLIGO quantum noise and optimal readout scheme (with Buonanno and Chen) • Prospects for squeezing (with Corbitt) • Experimental test of simple speedmeter (Whitcomb, Chen, DeVine at ANU) • 2003 • Prospects for squeezing in AdLIGO+ (with Corbitt) • Experimental tests • Beyond • Attack open questions in the field subject to personnel, interests, funding and recent developments (and LIGO I status)

26. If we succeed…