Concurrent spin squeezing and field tracking with machine learning

Squeezing and entanglement play crucial roles in approaches for quantum metrology. Yet, demonstrating quantum enhancement in continuous signal tracking remains a challenging endeavour because simultaneous entanglement generation and signal perturbations are often incompatible. We demonstrate that concurrent steady-state spin squeezing and sensing are possible using continuous quantum non-demolition measurements under constant optical pumping. We achieve a sustained spin-squeezed state with a large ensemble of hot atoms using metrologically relevant steady-state squeezing. We further employ the system to track different types of continuous time-fluctuating magnetic fields, and we demonstrate the use of deep learning models to infer the time-varying fields from an optical measurement. The quantum enhancement due to spin squeezing was verified by a degraded performance in test experiments where the spin squeezing was deliberately prevented. These results represent an advance in continuous quantum-enhanced metrology with entangled atoms, including the training and application of a deep neural network to infer complex time-dependent perturbations. Simultaneous spin squeezing and the detection of dynamic fields is challenging as entanglement generation and signal interrogation often interfere. An experiment now demonstrates stable spin squeezing and field tracking in a hot atomic ensemble.