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We study the Mott phase of the Bose-Hubbard model on a tilted lattice. On the(Gutzwiller) mean-field level, the tilt has no effect -- but quantumfluctuations entail particle-hole pair creation via tunneling. For smallpotential gradients (long-wavelength limit), we derive a quantitative analogyto the Sauter-Schwinger effect, i.e., electron-positron pair creation out ofthe vacuum by an electric field. For large tilts, we obtain resonant tunnelingrelated to Bloch oscillations.

Sauter-Schwinger like tunneling in tilted Bose-Hubbard lattices in the Mott phase