Measurements of the low frequency (<2 kHz) noise in the current produced by surface-acoustic-wave-based single-electron pumps are presented. When the current is close to its quantized value I = ef(0) (where e is the electron charge and f(0) is the surface-acoustic-wave frequency), shot noise is seen to be absent at the level of our measurement errors, which are an order of magnitude smaller than the Poissonian value of the shot noise for the same current. By changing the operating conditions so that the current is away from the quantized value, we observe noise that is attributed to switching of impurity states.
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