Broadband sensitivity improvement via coherent quantum feedback with PT symmetry*

A conventional resonant detector is subject to a trade-off between bandwidth and peak sensitivity. This limitation can be traced back to the Quantum Cramer Rao Bound and the coherent state of the conventional resonator. The trade-off can be broken by injecting non-classical states (e.g., squeezed vacuum), but it often has stringent requirements on optical losses. Anomalous dispersion due to an unstable quantum system has been shown to be able to improve the bandwidth-sensitivity product by signal amplification and thus suffer less from losses. But stabilizing the system may cause technical complications and conceptual issues. Here we propose a simple stable quantum amplifier enabled by two-mode non-degenerate parametric amplification. We demonstrate that coherent broadband signal amplification can be achieved without incurring instability. As the amplifier operates at the threshold, one mode of the amplifier forms a PT-symmetric system of the original detector mode, while the other mode collects the signal and transfer it to the readout. We will discuss how to apply this strategy to gravitational-wave detectors.