Fermi-Hubbard quantum simulation with cold atoms

6 problems

• Certified accuracy of a Hubbard simulator where numerics fail

  Open

  Once a simulator goes where computers cannot follow, nobody can check its answers by calculation. The task is to bound its errors using only independent calibrations.

• Can cold-atom Hubbard simulators observe d-wave pairing correlations?

  Open

  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.

• Lowest entropy per site reachable in a doped homogeneous Hubbard sample

  Open

  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.

• Entropy reduction needed to see d-wave correlations in Hubbard simulators

  Open

  Cooling atoms in a lattice is limited by how much disorder (entropy) remains per site. The question is how far below today's best entropy an experiment must go before pairing becomes visible.

• Does cold-atom Hubbard resistivity stay linear in temperature at low T?

  Open

  Many cuprates show electrical resistance growing in proportion to temperature, unlike ordinary metals. Atom experiments saw this down to moderate temperatures, and it is unknown whether it continues when the atoms are colder.

• Do spin-charge stripes appear in an isotropic two-dimensional Hubbard simulator?

  Open

  In some cuprates the holes line up in rows separated by magnetic stripes. Atom experiments saw stripes form in a simplified version of the model where holes move only along one direction; the full two-dimensional case has not shown them.