Neural-network quantum states for ultra-cold Fermi gases

Ultra-cold Fermi gases display diverse quantum mechanical properties, including the transition from a fermionic superfluid BCS state to a bosonic superfluid BEC state, which can be probed experimentally with high precision. However, the theoretical description of these properties is challenging due to the onset of strong pairing correlations and the non-perturbative nature of the interaction among the constituent particles. This work introduces a novel Pfaffian-Jastrow neural-network quantum state that includes backflow transformation based on message-passing architecture to efficiently encode pairing correlations. Our approach offers substantial improvements over comparable ansätze constructed within the Slater-Jastrow framework and out-performs state-of-the-art diffusion Monte Carlo methods. We observe the emergence of strong pairing correlations through the opposite-spin pair distribution functions, and we compute the pairing gap. Moreover, we demonstrate that transfer learning stabilizes and accelerates the training of the neural-network wave function, enabling the exploration of the BCS-BEC crossover region near unitarity. Our findings suggest that neural-network quantum states provide a promising strategy for studying ultra-cold Fermi gases.