School of Physics and Astrophysics

Postgraduate research profiles


Michael Page

Start date

Feb 2015

Submission date

Feb 2019

Michael Page


Ultrahigh quality factor enhancement of mechanical resonators


The discovery of gravitational waves in 2015 confirmed the final piece of Einstein's theory of general relativity. The collision of two black holes more than 1 billion light years away produced a signal that required a strain sensitivity of 10^(-23) per Hz^(1/2). However , even with the most sensitive measurement devices ever created, the theoretical detection rate for current gravitational wave detectors is approximately once per month. To test the extremes of general relativity requires not just one gravitational wave event, but a large sample size.

The sensitivity of gravitational wave detector signals can currently be improved in one of two ways. Resonant sideband extraction increases the sensitivity to a particular signal at the cost of bandwidth. Signal recycling increases the detection bandwidth at the cost of peak sensitivity. Breaking this tradeoff requires a novel configuration called the White Light Cavity, which allows many frequencies of light to be resonant, thus increasing sensitivity over a broad band. This works by using optomechanics to create a negative dispersion filter, where the change in refractive index depends on the frequency of light. Since a refractive material changes the wavelength of light for a particular frequency, the correct dispersion relation allows many frequencies to fulfil the resonance condition of having a half-integer multiple of wavelengths fit to the cavity length. However, this optomechanical filter has an extremely strict requirement on the ratio of thermal noise to quality factor.

The ratio of thermal noise to quality factor can be sufficiently reduced by using a technique called optical dilution. When a mechanical resonator is trapped in a powerful laser, the radiation pressure causes the restoring force to be dominated by light rather than mechanics. This allows the quality factor, proportional to the stiffness, to be increased, while keeping the thermal noise the same, since the radiation pressure force is lossless. This effectively dilutes the effect of thermal noise. Q-factor enhancements of 50 have been demonstrated (Ni, et al. PRL 108 214302 (2012)), but current attempts at optical dilution have been limited by suspension losses.

We plan to use a novel resonator called the cat-flap resonator, where a silicon pendulum is suspended by an extremely soft suspension so that the mechanical stiffness is minimised and the tether-to-mass ratio is as low as possible. We aim to increase the frequency of this pendulum from a starting frequency of 0.1-10 Hz to an optical spring frequency of 100 kHz. Combined with known loss mechanisms, we estimate that a maximum Q-factor of 10^(12) should be achievable with current fabrication technologies.

Why my research is important

As mentioned, increasing the sensitivity of gravitational wave detectors increases the detection rate of measurable events. An 10-fold increase in sensitivity allows us to see events of the same magnitude but 10 times further away. This corresponds to a thousand-fold increase in the detection volume and event rate. These events have massive relativistic effects in their neighbourhood. Extremely large mass concentrations moving at a significant fraction of the speed of light produce very strong fluctuating fields. These events allow us to move past weak-field approximations and test general relativity in strong gravitational fields.

Achieving high quality factors in optomechanics has been a goal of many research groups, not just for the purpose of gravitational wave detection. For example, early quantum bits were created using low-temperature microwave-mechanical resonators. Optomechanics is also useful for tests of fundamental quantum theory and possible future prospects of communications. The process of tuning the cat-flap resonator will allow us to investigate loss mechanisms that currently hinder macroscopic resonators.


  • University Postgraduate Award


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