  An electric analogue of the longitudinal Stern-Gerlach matter-wave
interferometer has been realized for atoms in Rydberg states with high
principal quantum number, $n$. The experiments were performed with He atoms
prepared in coherent superpositions of the $n=55$ and $n=56$ circular Rydberg
states in zero electric field by a $\pi/2$ pulse of resonant microwave
radiation. These atoms were subjected to a pulsed inhomogeneous electric field
to generate a superposition of momentum states before a $\pi$ pulse was applied
to invert the internal states. The same pulsed inhomogeneous electric field was
then reapplied for a second time to transform the motional states to have equal
momenta before a further $\pi/2$ pulse was employed to interrogate the final
Rydberg state populations. This Hahn-echo microwave pulse sequence,
interspersed with a pair of equivalent inhomogeneous electric field pulses,
yielded two spatially separated matter waves. Interferences between these
matter waves were observed as oscillations in the final Rydberg state
populations as the amplitude of the pulsed electric field gradients was
adjusted.
