  Quantum amplification is recognized as a key resource for precision
measurements. However, most conventional paradigms employ an ensemble of
independent particles that usually limit the performance of quantum
amplification in gain, spectral linewidth, etc. Here we demonstrate a new
signal amplification using cooperative 129Xe nuclear spins embedded within a
feedback circuit, where the noble-gas spin coherence time is enhanced by at
least one order of magnitude. Using such a technique, magnetic field can be
substantially pre-enhanced by more than three orders and is in situ readout
with an embedded 87Rb magnetometer. We realize an ultrahigh magnetic
sensitivity of 4.0 fT/Hz$^{1/2}$ that surpasses the photon-shot noise and even
below the spin-projection noise of the embedded atomic magnetometer, allowing
for exciting applications including searches for dark matter with sensitivity
well beyond supernova constraints. Our findings extend the physics of quantum
amplification to cooperative spin systems and can be generalized to a wide
variety of existing sensors, enabling a new class of cooperative quantum
sensors.
