Cooperative Spin Amplification

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.