Controlled theory of quantum fluctuations in dipolar droplets
In plain words
Droplets are held together by quantum fluctuations, described by an approximate correction (Lee-Huang-Yang term). Its predictions miss experimental numbers by sizable amounts.
Precise statement
For Dy-164 and Er-166 with dipolar length $a_{dd}$ and contact length $a_s$, predict the critical atom number $N_c$ for droplet formation and the superfluid-to-supersolid boundary in $a_s/a_{dd}$ within 10% of quantum Monte Carlo and experiment. The local-density extended Gross-Pitaevskii equation fails at this level. Answer: a theory with quantified errors.
What would settle it
A beyond-mean-field theory that matches quantum Monte Carlo and measured $N_c$ with an independently measured $a_s$.
Status in the literature
Agreement with experiment has typically required adjusting $a_{s}$ by several Bohr radii (Bottcher et al., Phys. Rev. Research 2019).