  Controllability of ultracold atomic gases has reached an unprecedented level,
allowing for experimental realization of the long-sought-after Thouless pump,
which can be interpreted as a dynamical quantum Hall effect. On the other hand,
Weyl semimetals and Weyl nodal line semimetals with touching points and rings
in band structures have sparked tremendous interest in various fields in the
past few years. Here, we show that dynamical Weyl points and dynamical 4D Weyl
nodal rings, which are protected by the first Chern number on a parameter
surface formed by quasi-momentum and time, emerge in a two-dimensional and
three-dimensional system, respectively. We find that the topological pump
occurs in these systems but the amount of pumped particles is not quantized and
can be continuously tuned by controlling experimental parameters over a wide
range. We also propose an experimental scheme to realize the dynamical Weyl
points and 4D Weyl nodal rings and to observe their corresponding topological
pump in cold atomic gases.
