  We investigate current-current correlations of adiabatic charge pumping
through interacting quantum dots weakly coupled to reservoirs. To calculate the
zero-frequency noise for a time-dependently driven system, possibly in the
presence of an additional dc bias, we perform within a real-time diagrammatic
approach a perturbative expansion in the tunnel coupling to the reservoirs in
leading and next-to-leading order. We apply this formalism to study the
adiabatic correction to the zero-frequency noise, i.e., the pumping noise, in
the case of a single-level quantum dot charge pump. If no stationary bias is
applied, the adiabatic correction shows Coulomb-interaction-induced deviations
from the fluctuation-dissipation theorem. Furthermore, we show that the
adiabatic correction to the Fano factor carries information about the coupling
asymmetry and is independent of the choice of the pumping parameters. When
including a time-dependent finite bias, we find that there can be pumping noise
even if there is zero adiabatically pumped charge. The pumping noise also
indicates the respective direction of the bias-induced current and the pumping
current.

Mesoscale and Nanoscale Physics