The simulation of synthetic dimensions by manipulating internal states of atoms and molecules has provided the opportunity 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.

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• Quantum engineering
• Quantum simulation
• Rydberg atoms & molecules
• Ultracold gases