  Interferometry with trapped atomic Bose-Einstein condensates (BECs) requires
the development of techniques to recombine the two paths of the interferometer
and map the accumulated phase difference to a measurable atom number
difference. We have implemented and compared two recombining procedures in a
double-well based BEC interferometer. The first procedure utilizes the bosonic
Josephson effect and controlled tunneling of atoms through the potential
barrier, similar to laser light in an optical fibre coupler. The second one
relies on the interference of the reflected and transmitted parts of the BEC
wavefunction when impinging on the potential barrier, analogous to light
impinging on a half-silvered mirror. Both schemes were implemented
successfully, yielding an interferometric contrast of about 20% and 42%
respectively. Building efficient matter wave recombiners represents an
important step towards the coherent manipulation of external quantum
superposition states of BECs.
