Measurement of radiation pressure induced dynamics Thomas Corbitt, David Ottaway, Edith Innerhofer, Jason Pelc, Daniel Sigg, and Nergis Mavalvala Based on LIGO-P050045-00-R or gr-qc/0511022 and some new data

Why radiation pressure? Optical systems that are radiation pressure dominated Study modified mirror oscillator dynamics Manipulate optical field quadratures Phase I – cavity with two 250 g suspended mirrors, finesse of 1000, ~4 W of input power Phase II – cavity with one 250 g and one 1 g suspended mirror, finesse of 8000, ~1 W of input power Ultimate goal – quantum-limited radiation pressure for ponderomotive squeezing interferometer

Unified Feedback Model Mechanical oscillator Optical feedback Optical spring Parametric Instability Electronic servo Force (F) Position (x) F x

A Simulink Model

Properties of optical springs Optical rigidity Modified dynamics Noise suppression

Phase I Experiment X Vacuum 3.6 W PD 2 kW PSL EOM QWP PD 25.2 MHz Frequency control (high freq.) 250 gram Length control (low freq.) PD 25.2 MHz X PDH / T VCO Length

Optical Spring Measured Phase increases by 180˚, so resonance is unstable! But there is lots of gain at this frequency, so it doesn't destabilize the system

Phase II Cavity Use 250 g input and 1 g end mirror in a suspended 1 m long cavity with goal of R < 50 at full power <1 MW/cm2 power density Optical spring resonance at > 1 kHz Final suspension for 1 gm mirror not ready yet, so Double suspension Goals for this stage See noise reduction effects Get optical spring out of the servo bandwidth See instability directly and damp it

Double suspension for mini mirror (the “MOS”)

Noise Suppression

Optical spring at 530 Hz Data (red) vs. model (blue)

And last night... 2 kHz! 2 kW circulating

The End

Feedback model Modified response is identical to a harmonic oscillator with a modified frequency and damping constant, under some (not so good) assumptions

While looking for the optical spring Injected highest available power level into locked cavity Detuned to where the maximum optical rigidity was expected Looked for the optical spring After running for a short time (<1 min), observed large oscillations in the error signal at 28 kHz Already knew this was the drumhead mode frequency Fluctuations disappeared when we went back to the center of the resonance

Parametric Instability!!! Instability depends on power and detuning Is not a feedback effect Must be a parametric instability The drumhead motion of the mirror creates a phase shift on the light The phase shift is converted into intensity fluctuations by the detuned cavity, which in turn push back against the drumhead mode Arises from the same optical rigidity, just applied to a different mode For this mode, the optical rigidity is much weaker than the mechanical restoring force, so how can it destabilize the system?

Parametric Instability Model For drumhead mode, optical restoring force much smaller than mechanical restoring force.

Measuring the Parametric Instability Measure the PI as a function of power and detuning For regions where the mode is unstable, measure the ring-up time (few seconds). For regions where the mode is stable, first go to an unstable region, ring-up, then rapidly go to stable region and measure ring-down time. Do the measurements with 0 gain in the feedback paths at 28 kHz to prevent any interference Frequency feedback path turned off Length control had a 60 dB notch filter at 28 kHz (UGF at ~1 kHz). Measurements show R scales linearly with power. R shows reasonable agreement with predictions for dependence on detuning

Parametric Instability Results

Damping the PI VCO gain turned up

Implications for Advanced LIGO For the parametric instability observed here The mechanical mode frequency (28 kHz) is within the linewidth of the cavity (75 kHz) This is different from the type of instability that people worry about with Advanced LIGO, e.g. Occurs when the mechanical mode frequency is outside the linewidth of the cavity Higher order spatial modes of the cavity must overlap in frequency space with the frequency of the mechanical mode

Optical spring resonance For bulk motion of the mirrors, the dominant mechanical restoring force is gravitational force from the suspensions, with frequency ~1 Hz. Predicted optical rigidity should give optical spring resonance ~ 80 Hz, so the gravitational restoring force is negligible We looked for the resonance, but...

Back to the Optical Spring To have a large optical spring frequency, we wanted to use full power Locked the frequency path with ~50 kHz bandwidth to have sufficient gain at 28 kHz to stabilize the unstable mode at 28 kHz Now that the parametric instability was identified and damped, we returned to the optical spring The resonance was expected at ~80 Hz, well within our servo bandwidth, so Inject signal into feedback paths Measure transfer function from force (either length/frequency path) to error signal (displacement) to measure the modified pendulum response