Casimir Sign Reversal from Finite-Range Bogoliubov Fluctuations

We study the zero-temperature Casimir effect of a three-dimensional Bose fluid with finite-range corrections to its Bogoliubov spectrum. Beyond the universal acoustic contribution scaling as $L^{-3}$, the long-distance expansion contains a nonuniversal $L^{-5}$ correction that can compete with the phononic term. We derive this crossover analytically within a minimal isotropic finite-range model and test the asymptotic result against the full dispersion. A regulator-independent Poisson-resummed calculation confirms that sign reversals of the Casimir energy are possible, while showing that the apparent low-coupling zero inferred by balancing only the $L^{-3}$ and $L^{-5}$ terms is not quantitatively controlled. Robust sign changes instead occur in the stable regime close to roton softening, where the Casimir energy acquires an oscillatory finite-momentum contribution. Strongly dipolar atomic gases provide a natural motivation for microscopic interaction lengths in the nanometric regime. We further discuss how the resulting nonlinear force law could be probed through the frequency response of a driven nanomechanical resonator.