  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.
