  Adiabatic cyclic modulation of a one-dimensional periodic potential will
result in quantized charge transport, which is termed the Thouless pump. In
contrast to the original Thouless pump restricted by the topology of the energy
band, here we experimentally observe a generalized Thouless pump that can be
extensively and continuously controlled. The extraordinary features of the new
pump originate from interband coherence in nonequilibrium initial states, and
this fact indicates that a quantum superposition of different eigenstates
individually undergoing quantum adiabatic following can also be an important
ingredient unavailable in classical physics. The quantum simulation of this
generalized Thouless pump in a two-band insulator is achieved by applying
delicate control fields to a single spin in diamond. The experimental results
demonstrate all principal characteristics of the generalized Thouless pump.
Because the pumping in our system is most pronounced around a band-touching
point, this work also suggests an alternative means to detect quantum or
topological phase transitions.
