Can cold-atom Hubbard simulators observe d-wave pairing correlations? · revision history
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- Title
- Can cold-atom Hubbard simulators observe d-wave pairing correlations?
- 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.
- 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.
- 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.
- Kind
- well-posed
- Answer type
- yes-no
- References
- (empty)
- Literature status
- open
- 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.
- Posed since
- 2002