Probing near-surface potentials with the self-binding threshold of dipolar quantum droplets

Abstract Self-bound quantum droplets formed by strongly magnetic atoms are a platform for quantum metrology experiments. Here, we form a theoretical framework wherein external potentials generated in the interior of a hollow cylinder can be observed via modification of the formation condition of dipolar quantum droplets. Starting from the extended Gross–Pitaevskii energy functional we derive an expression of the wavefunction that enforces the physical boundary condition at the internal cylinder wall and compute all contributions to the energy functional. We identify the self-binding threshold and derive an analytical perturbative shift to the critical atom number that corresponds to a displacement of approximately $$0.2\\,a_0$$ , accessible experimentally via a magnetic field tuned of order 1 mT for $$^{162}$$ Dy. These results provide a road-map for in-situ measurement of Casimir-Polder potentials and upcoming experiments exploiting quantum droplets as precision quantum sensors of short-range and exotic forces.