CAREER: Entanglement, Pairing and Superfluidity at the Interface between Atomic and Nuclear Physics.

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Many areas in physics are entering an information age, with computation at the forefront of research. One of the key notions in this new era is the quantum-mechanical property of entanglement, which characterizes how quantum particles are correlated with each other purely as a result of their quantum-mechanical nature. The influence of inter-particle interactions on entanglement is a challenging question, as interactions (in particular strong ones) drive phase transitions and are responsible for intriguing properties of matter. Information-related quantities, such as the entanglement entropy, play an essential role in quantum phase transitions and are central to seemingly disparate areas, such as quantum computation and black holes. The PI will leverage computational progress in atomic, nuclear and condensed matter physics to pursue a deeper understanding of strongly interacting superfluid systems at the interface between those areas, where entanglement properties remain largely unexplored. This project will provide precise predictions of entanglement and its correlation with thermodynamic observables across a wide variety of systems. Graduate and undergraduate students will be engaged at multiple levels, with emphasis on an ongoing curriculum and track-developing collaboration with the University of North Carolina at Pembroke.This project aims for a precise characterization of a wide range of strongly coupled, non-relativistic, few- and many-fermion systems of relevance to atomic, molecular, and nuclear physics. The systems considered here will include multiple spatial dimensions, free space, harmonic traps, and weakly to strongly interacting regimes. Thermodynamic properties (static, dynamic, structural, and pairing correlations) and their connection to entanglement (entanglement entropies, mutual information) will be determined using non-perturbative approaches, including numerical lattice field theory methods as well as semi-analytic expansions (e.g. the virial and operator-product expansions). To this end, advanced computational methods and algorithms will be implemented and new approaches will be explored to calculate entanglement entropies. The methods (codes, scripts, technical notes) and the data (from auxiliary field configurations to the physical results) will be made available online.