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Title: Lowest entropy per site reachable in a doped homogeneous Hubbard sample
Plain: Pairing in the Hubbard model needs very cold atoms, and the best experiments reached their coldest temperatures only at half filling, one atom per site. The question is how cold a doped sample with holes can be made, and what stops further cooling.
Precise: Homogeneous (flat-bottom) 2D square-lattice Fermi-Hubbard sample with at least 100 sites, $U/t = 8$, hole doping $\delta = 0.1\ \text{to}\ 0.2$. Determine the minimum entropy per site $s_{\mathrm{min}}$ (units of $k_{B}$) and temperature $T/t$ reachable by entropy redistribution into reservoirs and adiabatic loading, with independent thermometry, and identify the limiting heating processes (lattice-light scattering, technical noise, reservoir capacity). Answer: $s_{\mathrm{min}}$ and $T/t$ in the doped region with an error budget, and whether $T/t < 0.05$ is reachable at $\delta = 0.125$.
Settled by: A doped homogeneous sample with thermometry validated against finite-temperature numerics, plus a measured heating budget.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: A 2025 experiment reached $T/t = 0.05 (+0.06/-0.05)$ at half filling by entropy redistribution (Xu et al., Nature 642, 909, arXiv:2502.00095).
Posed since: (empty)