  We use exact techniques to demonstrate theoretically the pumping of
fractional charges in a single-level non-interacting quantum dot, when the
dot-reservoir coupling is adiabatically driven from weak to strong coupling.
The pumped charge averaged over many cycles is quantized at a fraction of an
electron per cycle, determined by the ratio of Lamb shift to level-broadening;
this ratio is imposed by the reservoir band-structure. For uniform density of
states, half an electron is pumped per cycle. We call this "adiabatic
almost-topological pumping", because the pumping's Berry curvature is sharply
peaked in the parameter space. Hence, so long as the pumping contour does not
touch the peak, the pumped charge depends only on how many times the contour
winds around the peak (up to exponentially small corrections). However, the
topology does not protect against non-adiabatic corrections, which grow
linearly with pump speed. In one limit the peak becomes a delta-function, so
the adiabatic pumping of fractional charges becomes entirely topological. Our
results show that quantization of the adiabatic pumped charge at a fraction of
an electron does not require fractional particles or other exotic physics.
