Sensitive Measurement of Forces at the Micron Scale Using Bloch Oscillations of Ultracold Atoms

We show that Bloch oscillations of ultracold fermionic atoms in the periodic potential of an optical lattice can be used for a sensitive measurement of forces at the micrometer length scale, e.g., in the vicinity of a dielectric surface. In particular, the proposed approach allows us to perform a local and direct measurement of the Casimir-Polder force which is, for realistic experimental parameters, as large as ${10}^{-4}$ gravity.