Phase coherent splitting of Bose-Einstein condensates with an integrated magnetic grating

We report the phase coherent splitting of Bose-Einstein condensates by means of a phase grating produced near the surface of a micro-electronic chip. A lattice potential with a period of $4\mu$m is generated by the superposition of static and oscillating magnetic fields. Precise control of the diffraction is achieved by controlling the currents in the integrated conductors. The interference of overlapping diffraction orders is observed after 8ms of propagation in a harmonic trap and subsequent ballistic expansion of the atomic ensemble. By analyzing the interference pattern we show a reproducible phase relation between the diffraction orders with an uncertainty given by the resolution of the diffraction grating.