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The observation of PT symmetry in a coupled optical wave guide system that involves a complex refractive index potential has been demonstrated impressively in the recent experiment by R\"uter el al. (Nature Physics 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 its 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 of the PT symmetric Gross-Pitaevskii equation, describing the condensate, on the PT properties of the condensate. This nonlinearity represents a major difference to the optical analogues. To study these effects we first analyze in detail a simple one-dimensional model system in which the condensate is placed into two PT symmetric delta traps. The analysis serves as a useful guide for understanding the behaviour of Bose-Einstein condensates in realistic PT symmetric double well potentials. |