  The observation of PT symmetry in a coupled optical wave guide system that
involves a complex refractive index has been demonstrated impressively in the
experiment by R\"uter el al. (Nat. Phys. 6, 192, 2010). This is, however, only
an optical analogue of a quantum system, and it would be highly desirable to
observe the manifestation of PT symmetry and the resulting properties also in a
real, experimentally accessible, quantum system. Following a suggestion by
Klaiman et al. (Phys. Rev. Lett. 101, 080402, 2008), we investigate a PT
symmetric arrangement of a Bose-Einstein condensate in a double well potential,
where in one well cold atoms are injected while in the other particles are
extracted from the condensate. We investigate, in particular, the effects of
the nonlinearity in the Gross-Pitaevskii equation on the PT properties of the
condensate. To study these effects we analyze a simple one-dimensional model
system in which the condensate is placed into two PT symmetric delta-function
traps. The analysis will serve as a useful guide for studies of the behaviour
of Bose-Einstein condensates in realistic PT symmetric double wells.
