Dataset for "Passive Cryogenic Vacuum Metrology from Translational Damping of a Meissner-Levitated Magnetic Sphere"

Pressure metrology in cryogenic ultrahigh vacuum (UHV) is limited by the need for in situ readout that does not perturb the cold environment. We propose a passive gauge based on the vertical translational mode of a ferromagnetic sphere levitated above a superconducting surface by the Meissner effect. In the molecular-flow regime, gas--surface momentum exchange adds a damping rate $\gamma_{\mathrm{gas}}\propto P$, so the pressure can be inferred from mechanical ringdown. Using Fisher-information analysis, we derive Cram\'er--Rao lower bounds for estimating the total damping rate and propagate them to an analytic pressure uncertainty that includes pressure-independent losses from residual dissipation and eddy currents. The resulting scalings with sphere radius $R$ reveal an optimum: larger $R$ improves low-$P$ sensitivity but increases intrinsic damping and narrows the molecular-flow range. For $T_{\mathrm{env}}=4.2~\mathrm{K}$ and intrinsic damping $\gamma_{0}=10^{-6}~\mathrm{s}^{-1}$, we find $R_{\mathrm{opt}}\approx2.4~\mathrm{mm}$ and a resolution floor $\delta P_{\rm mea}\approx4\times10^{-10}~\mathrm{Pa}$ at signal-to-noise ratio 1, with a molecular-flow upper limit of $10^{-2}$--$10^{-1}~\mathrm{Pa}$ set by gas species and the Knudsen criterion. These results provide sizing and integration-time guidelines for levitated-mechanical cryogenic vacuum gauges.