Quantitative many-body theory of unitarity BECs

Perturbative approaches, such as the Gross-Pitaevskii equation, can successfully explain weak interactions in BECs, while they become questionable at unitarity where the scattering length diverges. The first unitary BEC experiment\footnote{P.~Makotyn, {\it et al.}, Nat.~Phys.~{\bf 10},~116--119 (2014).} demonstrated that a surprisingly large BEC fraction survived a quench from weak to unitary interactions. I will show that introducing an excitation picture\footnote{M.~Kira, Ann.~Phys.~{\bf 351}, 200--249 (2014).} identifies how a quench creates noncondensed atoms in a strict sequential order\footnote{M.~Kira, Ann.~Phys.~{\bf 356}, 185--243 (2015).} where large atom clusters only emerge from existing smaller ones. This observation yields an efficient nonperturbative many-body description of unitary BECs, based on a cluster-expansion approach developed originally for semiconductor quantum optics\footnote{M.Kira \& S.W.Koch, {\it Semiconductor Quantum Optics}, (Cambridge Univ.~Press, 2012).}. I will discuss how this method quantitatively explains\footnote{M.Kira, Nat.~Commun.~\textbf{6}, 6624 (2015).} the first unitarity BEC measurement, and how it can be extended to explore, e.g., Efimov physics, universality, and entanglement in one or many strongly interacting BECs.