  Quantum depletion from an atomic quasi one dimensional Bose-Einstein
condensate with a dark soliton is studied in a framework of the Bogoliubov
theory. Depletion is dominated by an anomalous mode localized in a notch of the
condensate wave function. Depletion in the anomalous mode requires different
treatment than depletion without anomalous modes. In particular, quantum
depletion in the Bogoliubov vacuum of the anomalous mode is experimentally
irrelevant. A dark soliton is initially prepared in a state with minimal
depletion which is not a stationary state of the Bogoliubov theory. The notch
fills up with incoherent atoms depleted from the condensate. For realistic
parameters the filling time can be as short as 10 ms.
