  The simulation of synthetic dimensions by manipulating internal states of
atoms and molecules has opened the door to investigate regimes outside those of
more traditional quantum many-body platforms. Highly excited Rydberg states of
atoms are a particularly promising platform to engineer Hamiltonians in such
synthetic dimensions due to their large number of addressable states and the
readily available technologies for manipulating their couplings and for
detecting them. In this letter, we demonstrate the realization of topological
quantum pumping in synthetic dimensions by engineering a one-dimensional
Rice-Mele chain from the Rydberg states of cesium atoms, and manipulating their
couplings in a time-dependent fashion through radio-frequency fields. We
implement Thouless protocols for topological pumping and investigate the
efficiency for pumping an effective quantum particle as a function of the
period of pumping and other parameters while allowing for rates of change that
are not necessarily adiabatic. We demonstrate that optimal pumping efficiencies
of up to 90% can be achieved when the pump is operated in the topological
Thouless regime, even when the pumping is accompanied by the wave-packet spread
that arises from the energy dispersion of the particle along the synthetic
dimension.
