Lattice supersolid of magnetic atoms in the dipolar Bose-Hubbard model
In plain words
Magnetic atoms in an optical lattice have formed checkerboard and stripe crystals that do not flow. Theory predicts that adding or removing a few atoms should give a lattice supersolid that is both ordered and superfluid.
Precise statement
Dipolar extended Bose-Hubbard model on a 2D square lattice, H = -t sum_<ij> b_i^dag b_j + (U/2) sum_i n_i(n_i - 1) + sum_i<j V_ij n_i n_j with $V_{ij} \sim (1 - 3 \cos^2 \theta_{ij})/r_{ij}^3$, realized with Er or Dy atoms. Quantum Monte Carlo predicts a supersolid when the checkerboard solid is doped away from half filling (Capogrosso-Sansone et al., PRL 2010). Answer: observation of coexisting checkerboard density order and phase coherence (nonzero superfluid density) at measured filling and $T$, or a bound excluding it at accessible $V/t$.
What would settle it
Quantum gas microscope or time-of-flight measurements showing simultaneous density-wave order and interference peaks from the same doped lattice sample.
Status in the literature
Checkerboard and stripe insulating solids were observed with Er in a lattice (Su et al., Nature 2023, doi:10.1038/s41586-023-06614-3), without reported superfluid coherence in the solid.