{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"8166a3d0ceb71f0714a25abd5b3e548c367670a1fd6b1e3720df78784016cf6c","created":"2026-10-03T07:17:53Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"ddd28cb8ba5c19ba1d5631d5b80ddbe168bfc0305816c3975a5a40477c421a6d","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"amo.hubbard-simulation.d-wave-pairing","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"In cuprates, electrons form pairs with a four-leaf-clover shape (d-wave) and flow without resistance. The question is whether atoms in an optical lattice, obeying the same model, can be cooled enough to show these pairs.","posed_since":"2002","precise":"Two-dimensional square-lattice Fermi-Hubbard model, $U/t = 6\\ \\text{to}\\ 8$, hole doping $\\delta = 0.1\\ \\text{to}\\ 0.2$, nearest-neighbour hopping $t$ and optional next-nearest hopping t'. Measure the d-wave pair correlation $P_d(r) = \\langle \\Delta_d^{\\mathrm{dag}}(r) \\Delta_d(0)\\rangle$, with $\\Delta_d(r)$ the d-wave singlet pair operator on the four bonds of site r, by quantum gas microscopy or pair-transport protocols at the lowest achievable $T/t$. True long-range order is excluded at $T > 0$ in 2D, so the answer is whether $P_d(r)$ decays algebraically below a Kosterlitz-Thouless temperature $T_{\\mathrm{KT}}$, or at least has a correlation length above 10 lattice sites, together with the temperature and entropy at which this appears.","problem_ref":null,"references":"","settled_by":"A microscope measurement of d-wave pair correlations extending over many sites in a doped, homogeneous Hubbard sample, cross-checked against independent thermometry.","status_note":"2025 experiments reached $T/t = 0.05$ at half filling and resolved a pseudogap in doped samples (arXiv:2502.00095, arXiv:2509.18075), but no d-wave pair correlations have been reported.","title":"Can cold-atom Hubbard simulators observe d-wave pairing 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