  The standard Bloch oscillation normally refers to the oscillatory tunneling
dynamics of quantum particles in a periodic lattice plus a linear gradient. In
this work we theoretically investigate the generalized form of the Bloch
oscillation in the presence of additional higher order gradients, and
demonstrate that the higher order gradients can significantly modify the
tunneling dynamics, particularly in the spectrum of the density oscillation.
The spectrum of the standard Bloch oscillation is composed of a single prime
frequency and its higher harmonics, while the higher-order gradients in the
external potential give rise to fine structures in the spectrum around each of
these Bloch frequencies, which are composed of serieses of frequency peaks. Our
investigation leads to a twofold consequence to the applications of Bloch
oscillations for measuring external forces: For one thing, under a limited
resolution of the measured spectrum, the fine structures would manifest as a
blur to the spectrum, and leads to intrinsic errors to the measurement. For
another, given that the fine structures could be experimentally resolved, they
can supply more information of the external force than the strength of the
linear gradient, and be used to measure more complicated forces.
