Finding the optimal detector for linear quantum measurements

Our knowledge of Physics is fundamentally bound by the sensitivity of our detectors to the quantity that we are attempting to measure. For current and future gravitational wave detectors we are now predominantly limited by the Quantum noise, which is due to the fundamental Quantum fluctuations of the vacuum. This hinders our detection of gravitational waves from high-frequency astronomical sources such as neutron star mergers, while also impacting proposed searches for new physics such as axion detection and Quantum gravity experiments. Many techniques have been introduced for reducing the effect of the Quantum noise such as negative dispersion, variational readout, and frequency-dependent squeezing. However, from the outset all of these techniques are inferred via a process of trial and error combined with prior experience, and also often only target specific frequency regimes. Therefore it is not obvious how to systematically engineer a specific desired response for a detector without a large amount of unguided research and development. However, using new techniques for the network synthesis of quantum systems from the quantum control community, I show how it is possible to reproduce a desired quantum filter. This is then used to develop a totally new framework for designing optimal detectors that saturate the Heisenberg limit, culminating in a general and intuitive approach to developing new breakthroughs in detector design. This approach then leads to the proposal of an all-optical PT symmetric amplifier, which is both stable and has infinite DC response