A conventional resonant detector is often subject to a trade-off between bandwidth and peak sensitivity. Anomalous dispersion has been shown to improve the bandwidth-sensitivity limit by signal amplification, but its unstable issue in operation needs additional feedback control. Here we propose a stable quantum amplifier enabled by two-mode non-degenerate parametric amplification. As the amplifier operates at threshold, one mode of the amplifier forms a parity-time(PT)-symmetric system with the mode of the original detector, while the other mode of the amplifier collects signal and gets extracted by a readout. Viewed more broadly in the context of coherent quantum control theory, we are attaching a controller that consists of a time reversal of the plant, which, by canceling the inertia of the plant, helps drive up the closed-loop signal gain. Examples of microwave cavity axion detectors and laser-interferometric gravitational-wave detectors will be discussed for this technique.
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