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The standard Bloch oscillation normally refers to the oscillatory tunnelingdynamics of quantum particles in a periodic lattice plus a linear gradient. Inthis work we theoretically investigate the generalized form of the Blochoscillation in the presence of additional higher order gradients, anddemonstrate that the higher order gradients can significantly modify thetunneling dynamics, particularly in the spectrum of the density oscillation.The spectrum of the standard Bloch oscillation is composed of a single primefrequency and its higher harmonics, while the higher-order gradients in theexternal potential give rise to fine structures in the spectrum around each ofthese Bloch frequencies, which are composed of serieses of frequency peaks. Ourinvestigation leads to a twofold consequence to the applications of Blochoscillations for measuring external forces: For one thing, under a limitedresolution of the measured spectrum, the fine structures would manifest as ablur to the spectrum, and leads to intrinsic errors to the measurement. Foranother, given that the fine structures could be experimentally resolved, theycan supply more information of the external force than the strength of thelinear gradient, and be used to measure more complicated forces.

Generalized Bloch oscillations of ultracold lattice atoms subject to higher-order gradients