Latched Detection of Zeptojoule Spin Echoes with a Kinetic Inductance Parametric Oscillator

When strongly pumped at twice their resonant frequency, non-linear resonators develop a high-amplitude intracavity field, a phenomenon known as parametric self-oscillations. The boundary over which this instability occurs can be extremely sharp and thereby presents an opportunity for realizing a detector. Here we operate such a device based on a superconducting microwave resonator whose non-linearity is engineered from kinetic inductance. The device indicates the absorption of low-power microwave wavepackets by transitioning to a self-oscillating state. Using calibrated wavepackets we measure the detection efficiency with zeptojoule energy wavepackets. We then apply it to measurements of electron spin resonance, using an ensemble of $^{209}$Bi donors in silicon that are inductively coupled to the resonator. We achieve a latched-readout of the spin signal with an amplitude that is five hundred times greater than the underlying spin echoes.