This thesis demonstrates a full Mach-Zehnder interferometer with
interacting Bose-Einstein condensates confined on an atom chip. It
relies on the coherent manipulation of atoms trapped in a magnetic
double-well potential, for which the author developed a novel type
of beam splitter. Particle-wave duality enables the construction of
interferometers for matter waves, which complement optical
interferometers in precision measurement devices, both for
technological applications and fundamental tests. This requires the
development of atom-optics analogues to beam splitters, phase
shifters and recombiners. Particle interactions in the
Bose-Einstein condensate lead to a nonlinearity, absent in photon
optics. This is exploited to generate a non-classical state with
reduced atom-number fluctuations inside the interferometer. This
state is then used to study the interaction-induced dephasing of
the quantum superposition. The resulting coherence times are found
to be a factor of three longer than expected for coherent states,
highlighting the potential of entanglement as a resource for
quantum-enhanced metrology.
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