Greying of the Dark Soliton: Depletion in the Anomalous Mode of the Bogoliubov Theory

Details Greying of the Dark Soliton: Depletion in the Anomalous Mode of the Bogoliubov Theory Greying of the Dark Soliton: Depletion in the Anomalous Mode of the Bogoliubov Theory

2002-02-08

arxiv.org/abs/cond-mat/0202146v2

Physics

Condensed Matter

5 pages, version to appear in Phys.Rev.A

Scientific paper

10.1103/PhysRevA.66.043620

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.

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