Quantum Noise in Advanced Gravitational Wave Interferometers NSF Proposal Review Nergis Mavalvala PAC 13, LLO December 2002

Quantum Noise Measurement process Noise in 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)

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 mirrors Fluctuations in the number of photons a 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

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

Defining Observables 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 McKenzie

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)

‘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

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 So all the light we use in the interferometer has quantum noise on it. This top diagram represents the vacuum state fluctuations. This is a minimum uncertainty state, with equal variances in the phase and amplitude quadratures. This noise is everywhere that there isn’t already a laser beam. But why do we care for the vacuum state in the Michelson? We know the laser beam has quantum noise on it, but it is correlated noise i.e. common to both arms, so it will cancel back at the beam-splitter. The reason is because at the unused port of the beam-splitter the vacuum mode is entering. It interferes with the input beam, and passes on it’s noise statistics, causing anti-correlated noise on each arm’s electric field. When the beams recombine on the beam-splitter noise couples to the the output, which limits the sensitivity of the interferometer. The vacuum mode fluctuations couple into two types of noise – the amplitude quadrature noise of the vacuum couples into phase quadrature noise on the electric fields in the arms, producing anti-correlated phase shifts, which we call. SHOT NOISE. The phase quadrature noise of the vacuum state couples to amplitude quadrature noise on the electric fields in the arms, producing anti-correlated amplitude fluctuations, which gives rise to. RADIATION PRESSURE NOISE. SHOT NOISE scales with 1/sqrt(POWER), at the beam-splitter so it can be reduced by increasing the power of the laser or power recycling factor, where-as RADIATION PRESSURE NOISE scales with sqrt(POWER), so it increases with power at the beam-splitter. As I mentioned earlier, the first generation detectors are be limited by SHOT NOISE but NOT by RADIATION PRESSURE NOISE, and so is the experiment we did. So I will discuss reducing SHOT noise, and not RAD PRESSURE NOISE. So how do we reduce it? McKenzie

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 Squeezing! The HUP says that the product of the variance in the two quadratures must be greater or equal to 1, so if we are limited only by shot noise, and we don’t care about radiation pressure noise, we can use a squeezed state with reduced noise in one quadrature that we care about, at the expense of the other quadrature which we don’t. So we want to reduce shot noise, which means we need to inject a amplitude squeezed state. This is what one looks like 3dB. The noise in the amplitude quadrature is ½ whist the noise in the phase quadrature twice as much as it was. So we inject this into the unused port of the beam-splitter. And since it is there , then vacuum state no longer enters. What does squeezing do in a MIchelson? McKenzie

Squeezed State in a Michelson GW signal in the phase quadrature Orient squeezed state to reduce noise in phase quadrature1 Since a local oscillator ‘selects’ the phase quadrature, where there is a GW signal, we need only worry about this quadrature. This diagram shows the Michelson arm electric fields with the vacuum noise and with squeezed noise at one point in time where the is a GW signal. On the diagram on the left, the vacuum noise has enter the dark port and interfered with the input beam putting noise on each of the electric fields in the arms, which adds up back at the beam-splitter, so that the GW signal has vacuum noise on it. The noise in the plane of the signal is the noise on the signal. You can see that noise is reduced if we inject squeezing in the dark port as in the figure on the right. The squeezing is injected and interferes with the input beam. The noise on the electric fields in each arm is less and when recombined it turns out that the noise in the plane of the signal is much less. So that is the theory behind the experiment, reduced shot noise on the GW signal. McKenzie

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)

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 SN(t) RPN(t+t) Part of the light leaks out the SRM and contributes to the shot noise BUT the (correlated) part reflected from the SRM returns to the TM and contributes to the RPN at a later time

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

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 modulation functions Non-classical light?

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

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)

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

Squeezed source 10 dB 100 Hz 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 Advance LIGO AdLIGO + 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

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

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

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

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

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)

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)

If we succeed…