Deterministic Generation of Correlated Atom Pairs via Hamiltonian Engineering

Correlated atom pairs are fundamental resources for quantum-enhanced sensing, communication and distributed quantum computing. While spontaneous parametric down-conversion (SPDC) and four-wave mixing (SFWM) are established protocols for generating entangled photons, a comparably robust and deterministic source for correlated atoms, in the context of trapped ultracold atoms remains a challenge. In this work, we demonstrate a protocol for generating correlated atom pairs using Hamiltonian engineering for cold atoms trapped in an optical lattice. By tuning the hopping strength, the interaction strength, and the lattice potential via quantum optimal control (QOC), we steer the system toward an SPDC-like state. Unlike the stochastic nature of optical SPDC, our approach provides a deterministic and high-fidelity method for state preparation. Furthermore, we leverage these pairs to realize an atomic analog of the Zou-Wang-Mandel experiment. By establishing path identity for the 'idler' atoms from two spatially separated sources, we demonstrate induced coherence in the companion 'signal' atoms. This allows for the extraction of information about external potentials interacting with the idler atoms without their direct detection, offering a scalable pathway for interaction-free sensing and atomic entanglement in cold-atom platforms. This can be applied for quantum magnetometry, gravimetry and gradiometry using ultracold atoms.