An Atom Michelson Interferometer on a Chip

An atom Michelson interferometer is implemented on an ``atom chip.'' The chip uses lithographically patterned conductors and external magnetic fields to produce and guide a Bose-Einstein condensate. Splitting, retroreflecting, and recombining of condensate atoms are achieved within the magnetic waveguide by a standing-wave light field having a wave vector aligned along the guide. Splitting and recombining are achieved with a pair of standing light field pulses each 20 $\mu $s in duration and separated by 63 $\mu $s. This pair of pulses is such that an a single BEC cloud initially at rest is converted into a pair of oppositely directed clouds having momentum $p=\pm 2\hbar k$ with essentially no atoms remaining stationary or in higher diffracted orders. Retroreflection of the two clouds is achieved by a longer (150 $\mu $s) pulse of the standing wave. When the atoms have returned to their starting position, the recombining pulse pair leaves the atoms in three clouds representing two different states: one cloud with zero momentum, $\left| {p=0} \right\rangle $ and a pair of clouds representing the state $\left| {p=\pm 2\hbar k} \right\rangle $. The population of these two states corresponds to the intensity of light from the two output ports of the beamsplitter in an optical Michelson interferometer. A differential phase shift between the two arms of the atom interferometer is introduced either with a magnetic-field gradient or with an initial condensate velocity. The populations of the two states is seen to vary sinusoidally and in anti-phase with the path difference as expected. We find that the interference contrast decays with propagation time in the waveguides: 20{\%} contrast is observed with an atom propagation time of 10 ms.