  Matter-wave interference experiments enable us to study matter at its most
basic, quantum level and form the basis of high-precision sensors for
applications such as inertial and gravitational field sensing. Success in both
of these pursuits requires the development of atom-optical elements that can
manipulate matter waves at the same time as preserving their coherence and
phase. Here, we present an integrated interferometer based on a simple,
coherent matter-wave beam splitter constructed on an atom chip. Through the use
of radio-frequency-induced adiabatic double-well potentials, we demonstrate the
splitting of Bose-Einstein condensates into two clouds separated by distances
ranging from 3 to 80 microns, enabling access to both tunnelling and isolated
regimes. Moreover, by analysing the interference patterns formed by combining
two clouds of ultracold atoms originating from a single condensate, we measure
the deterministic phase evolution throughout the splitting process. We show
that we can control the relative phase between the two fully separated samples
and that our beam splitter is phase-preserving.
