Probing atom-surface interactions from tunneling-time measurements via rotation-transport on an atom chip

We propose a novel method to measure the interaction between an ultracold gas of neutral atoms and a surface. This solution combines an optical dipole trap reflected by the surface, a magnetic trap formed by current carrying wires embedded below the surface, and a rotation of the surface itself. It allows to adiabatically transport a $^{87}$Rb BEC from few $\mu$m to few hundred nm of the surface. At such distances, atom-surface interaction strongly affects the trapping potential, causing an increase of the tunneling rate towards the surface. In this paper, we show that the measurement of the lifetime of the cloud and its comparison to a tunneling model will allow to extract the Casimir-Polder (CP) force coefficient in the retarded regime ($c_4$). Our model includes noise-induced heating, calibration biases of experimentally controlled parameters and accuracy of the atom lifetime measurement. Using typical trapping parameters and experimental uncertainties, we numerically estimate the relative uncertainty of $c_4$ to be 10%. This method can be implemented with any atomic species that can be magnetically and optically trapped.