Concurrent spin squeezing and field tracking with machine learning

Abstract

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.